FieldBrouwerLyddanePropagator.java

  1. /* Copyright 2002-2022 CS GROUP
  2.  * Licensed to CS GROUP (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.propagation.analytical;

  19. import java.util.Collections;
  20. import java.util.List;

  22. import org.hipparchus.CalculusFieldElement;
  23. import org.hipparchus.Field;
  24. import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
  25. import org.hipparchus.util.CombinatoricsUtils;
  26. import org.hipparchus.util.FastMath;
  27. import org.hipparchus.util.FieldSinCos;
  28. import org.hipparchus.util.MathUtils;
  29. import org.hipparchus.util.Precision;
  30. import org.orekit.attitudes.AttitudeProvider;
  31. import org.orekit.attitudes.InertialProvider;
  32. import org.orekit.errors.OrekitException;
  33. import org.orekit.errors.OrekitMessages;
  34. import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider;
  35. import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics;
  36. import org.orekit.orbits.FieldKeplerianOrbit;
  37. import org.orekit.orbits.FieldOrbit;
  38. import org.orekit.orbits.OrbitType;
  39. import org.orekit.orbits.PositionAngle;
  40. import org.orekit.propagation.FieldSpacecraftState;
  41. import org.orekit.propagation.PropagationType;
  42. import org.orekit.propagation.analytical.tle.FieldTLE;
  43. import org.orekit.time.FieldAbsoluteDate;
  44. import org.orekit.utils.FieldTimeSpanMap;
  45. import org.orekit.utils.ParameterDriver;

  47. /** This class propagates a {@link org.orekit.propagation.FieldSpacecraftState}
  48.  *  using the analytical Brouwer-Lyddane model (from J2 to J5 zonal harmonics).
  49.  * <p>
  50.  * At the opposite of the {@link FieldEcksteinHechlerPropagator}, the Brouwer-Lyddane model is
  51.  * suited for elliptical orbits, there is no problem having a rather small eccentricity or inclination
  52.  * (Lyddane helped to solve this issue with the Brouwer model). Singularity for the critical
  53.  * inclination i = 63.4° is avoided using the method developed in Warren Phipps' 1992 thesis.
  54.  * <p>
  55.  * By default, Brouwer-Lyddane model considers only the perturbations due to zonal harmonics.
  56.  * However, for low Earth orbits, the magnitude of the perturbative acceleration due to
  57.  * atmospheric drag can be significant. Warren Phipps' 1992 thesis considered the atmospheric
  58.  * drag by time derivatives of the <i>mean</i> mean anomaly using the catch-all coefficient
  59.  * {@link #M2Driver}.
  60.  *
  61.  * Usually, M2 is adjusted during an orbit determination process and it represents the
  62.  * combination of all unmodeled secular along-track effects (i.e. not just the atmospheric drag).
  63.  * The behavior of M2 is close to the {@link FieldTLE#getBStar()} parameter for the TLE.
  64.  *
  65.  * If the value of M2 is equal to {@link BrouwerLyddanePropagator#M2 0.0}, the along-track secular
  66.  * effects are not considered in the dynamical model. Typical values for M2 are not known.
  67.  * It depends on the orbit type. However, the value of M2 must be very small (e.g. between 1.0e-14 and 1.0e-15).
  68.  * The unit of M2 is rad/s².
  69.  *
  70.  * The along-track effects, represented by the secular rates of the mean semi-major axis
  71.  * and eccentricity, are computed following Eq. 2.38, 2.41, and 2.45 of Warren Phipps' thesis.
  72.  *
  73.  * @see "Brouwer, Dirk. Solution of the problem of artificial satellite theory without drag.
  74.  *       YALE UNIV NEW HAVEN CT NEW HAVEN United States, 1959."
  75.  *
  76.  * @see "Lyddane, R. H. Small eccentricities or inclinations in the Brouwer theory of the
  77.  *       artificial satellite. The Astronomical Journal 68 (1963): 555."
  78.  *
  79.  * @see "Phipps Jr, Warren E. Parallelization of the Navy Space Surveillance Center
  80.  *       (NAVSPASUR) Satellite Model. NAVAL POSTGRADUATE SCHOOL MONTEREY CA, 1992."
  81.  *
  82.  * @author Melina Vanel
  83.  * @author Bryan Cazabonne
  84.  * @since 11.1
  85.  */
  86. public class FieldBrouwerLyddanePropagator<T extends CalculusFieldElement<T>> extends FieldAbstractAnalyticalPropagator<T>  {

  88.     /** Default convergence threshold for mean parameters conversion. */
  89.     private static final double EPSILON_DEFAULT = 1.0e-13;

  91.     /** Default value for maxIterations. */
  92.     private static final int MAX_ITERATIONS_DEFAULT = 200;

  94.     /** Parameters scaling factor.
  95.      * <p>
  96.      * We use a power of 2 to avoid numeric noise introduction
  97.      * in the multiplications/divisions sequences.
  98.      * </p>
  99.      */
  100.     private static final double SCALE = FastMath.scalb(1.0, -20);

  102.     /** Beta constant used by T2 function. */
  103.     private static final double BETA = FastMath.scalb(100, -11);

  105.     /** Initial Brouwer-Lyddane model. */
  106.     private FieldBLModel<T> initialModel;

  108.     /** All models. */
  109.     private transient FieldTimeSpanMap<FieldBLModel<T>, T> models;

  111.     /** Reference radius of the central body attraction model (m). */
  112.     private double referenceRadius;

  114.     /** Central attraction coefficient (m³/s²). */
  115.     private T mu;

  117.     /** Un-normalized zonal coefficients. */
  118.     private double[] ck0;

  120.     /** Empirical coefficient used in the drag modeling. */
  121.     private final ParameterDriver M2Driver;

  123.     /** Build a propagator from orbit and potential provider.
  124.      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
  125.      *
  126.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  127.      *
  128.      * @param initialOrbit initial orbit
  129.      * @param provider for un-normalized zonal coefficients
  130.      * @param M2 value of empirical drag coefficient in rad/s².
  131.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  132.      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, UnnormalizedSphericalHarmonicsProvider, PropagationType, double)
  133.      */
  134.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  135.                                          final UnnormalizedSphericalHarmonicsProvider provider,
  136.                                          final double M2) {
  137.         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
  138.              initialOrbit.getMu().newInstance(DEFAULT_MASS), provider,
  139.              provider.onDate(initialOrbit.getDate().toAbsoluteDate()), M2);
  140.     }

  142.     /**
  143.      * Private helper constructor.
  144.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  145.      * @param initialOrbit initial orbit
  146.      * @param attitude attitude provider
  147.      * @param mass spacecraft mass
  148.      * @param provider for un-normalized zonal coefficients
  149.      * @param harmonics {@code provider.onDate(initialOrbit.getDate())}
  150.      * @param M2 value of empirical drag coefficient in rad/s².
  151.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  152.      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement,
  153.      * UnnormalizedSphericalHarmonicsProvider, UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics, PropagationType, double)
  154.      */
  155.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  156.                                          final AttitudeProvider attitude,
  157.                                          final T mass,
  158.                                          final UnnormalizedSphericalHarmonicsProvider provider,
  159.                                          final UnnormalizedSphericalHarmonics harmonics,
  160.                                          final double M2) {
  161.         this(initialOrbit, attitude,  mass, provider.getAe(), initialOrbit.getMu().newInstance(provider.getMu()),
  162.              harmonics.getUnnormalizedCnm(2, 0),
  163.              harmonics.getUnnormalizedCnm(3, 0),
  164.              harmonics.getUnnormalizedCnm(4, 0),
  165.              harmonics.getUnnormalizedCnm(5, 0),
  166.              M2);
  167.     }

  169.     /** Build a propagator from orbit and potential.
  170.      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
  171.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  172.      * are related to both the normalized coefficients
  173.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  174.      *  and the J<sub>n</sub> one as follows:</p>
  175.      *
  176.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  177.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  178.      *
  179.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  180.      *
  181.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  182.      *
  183.      * @param initialOrbit initial orbit
  184.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  185.      * @param mu central attraction coefficient (m³/s²)
  186.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  187.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  188.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  189.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  190.      * @param M2 value of empirical drag coefficient in rad/s².
  191.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  192.      * @see org.orekit.utils.Constants
  193.      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, double, CalculusFieldElement, double, double, double, double, double)
  194.      */
  195.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  196.                                          final double referenceRadius, final T mu,
  197.                                          final double c20, final double c30, final double c40,
  198.                                          final double c50, final double M2) {
  199.         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
  200.              initialOrbit.getMu().newInstance(DEFAULT_MASS),
  201.              referenceRadius, mu, c20, c30, c40, c50, M2);
  202.     }

  204.     /** Build a propagator from orbit, mass and potential provider.
  205.      * <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
  206.      *
  207.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  208.      *
  209.      * @param initialOrbit initial orbit
  210.      * @param mass spacecraft mass
  211.      * @param provider for un-normalized zonal coefficients
  212.      * @param M2 value of empirical drag coefficient in rad/s².
  213.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  214.      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, UnnormalizedSphericalHarmonicsProvider, double)
  215.      */
  216.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit, final T mass,
  217.                                          final UnnormalizedSphericalHarmonicsProvider provider,
  218.                                          final double M2) {
  219.         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
  220.              mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()), M2);
  221.     }

  223.     /** Build a propagator from orbit, mass and potential.
  224.      * <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
  225.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  226.      * are related to both the normalized coefficients
  227.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  228.      *  and the J<sub>n</sub> one as follows:</p>
  229.      *
  230.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  231.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  232.      *
  233.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  234.      *
  235.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  236.      *
  237.      * @param initialOrbit initial orbit
  238.      * @param mass spacecraft mass
  239.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  240.      * @param mu central attraction coefficient (m³/s²)
  241.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  242.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  243.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  244.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  245.      * @param M2 value of empirical drag coefficient in rad/s².
  246.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  247.      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, double, CalculusFieldElement, double, double, double, double, double)
  248.      */
  249.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit, final T mass,
  250.                                          final double referenceRadius, final T mu,
  251.                                          final double c20, final double c30, final double c40,
  252.                                          final double c50, final double M2) {
  253.         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
  254.              mass, referenceRadius, mu, c20, c30, c40, c50, M2);
  255.     }

  257.     /** Build a propagator from orbit, attitude provider and potential provider.
  258.      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
  259.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  260.      * @param initialOrbit initial orbit
  261.      * @param attitudeProv attitude provider
  262.      * @param provider for un-normalized zonal coefficients
  263.      * @param M2 value of empirical drag coefficient in rad/s².
  264.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  265.      */
  266.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  267.                                          final AttitudeProvider attitudeProv,
  268.                                          final UnnormalizedSphericalHarmonicsProvider provider,
  269.                                          final double M2) {
  270.         this(initialOrbit, attitudeProv, initialOrbit.getMu().newInstance(DEFAULT_MASS), provider,
  271.              provider.onDate(initialOrbit.getDate().toAbsoluteDate()), M2);
  272.     }

  274.     /** Build a propagator from orbit, attitude provider and potential.
  275.      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
  276.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  277.      * are related to both the normalized coefficients
  278.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  279.      *  and the J<sub>n</sub> one as follows:</p>
  280.      *
  281.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  282.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  283.      *
  284.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  285.      *
  286.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  287.      *
  288.      * @param initialOrbit initial orbit
  289.      * @param attitudeProv attitude provider
  290.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  291.      * @param mu central attraction coefficient (m³/s²)
  292.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  293.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  294.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  295.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  296.      * @param M2 value of empirical drag coefficient in rad/s².
  297.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  298.      */
  299.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  300.                                          final AttitudeProvider attitudeProv,
  301.                                          final double referenceRadius, final T mu,
  302.                                          final double c20, final double c30, final double c40,
  303.                                          final double c50, final double M2) {
  304.         this(initialOrbit, attitudeProv, initialOrbit.getMu().newInstance(DEFAULT_MASS),
  305.              referenceRadius, mu, c20, c30, c40, c50, M2);
  306.     }

  308.     /** Build a propagator from orbit, attitude provider, mass and potential provider.
  309.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  310.      * @param initialOrbit initial orbit
  311.      * @param attitudeProv attitude provider
  312.      * @param mass spacecraft mass
  313.      * @param provider for un-normalized zonal coefficients
  314.      * @param M2 value of empirical drag coefficient in rad/s².
  315.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  316.      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, UnnormalizedSphericalHarmonicsProvider, PropagationType, double)
  317.      */
  318.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  319.                                          final AttitudeProvider attitudeProv,
  320.                                          final T mass,
  321.                                          final UnnormalizedSphericalHarmonicsProvider provider,
  322.                                          final double M2) {
  323.         this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()), M2);
  324.     }

  326.     /** Build a propagator from orbit, attitude provider, mass and potential.
  327.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  328.      * are related to both the normalized coefficients
  329.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  330.      *  and the J<sub>n</sub> one as follows:</p>
  331.      *
  332.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  333.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  334.      *
  335.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  336.      *
  337.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  338.      *
  339.      * @param initialOrbit initial orbit
  340.      * @param attitudeProv attitude provider
  341.      * @param mass spacecraft mass
  342.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  343.      * @param mu central attraction coefficient (m³/s²)
  344.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  345.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  346.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  347.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  348.      * @param M2 value of empirical drag coefficient in rad/s².
  349.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  350.      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, double, CalculusFieldElement, double, double, double, double, PropagationType, double)
  351.      */
  352.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  353.                                          final AttitudeProvider attitudeProv,
  354.                                          final T mass,
  355.                                          final double referenceRadius, final T mu,
  356.                                          final double c20, final double c30, final double c40,
  357.                                          final double c50, final double M2) {
  358.         this(initialOrbit, attitudeProv, mass, referenceRadius, mu, c20, c30, c40, c50, PropagationType.OSCULATING, M2);
  359.     }


  362.     /** Build a propagator from orbit and potential provider.
  363.      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
  364.      *
  365.      * <p>Using this constructor, it is possible to define the initial orbit as
  366.      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
  367.      *
  368.      * @param initialOrbit initial orbit
  369.      * @param provider for un-normalized zonal coefficients
  370.      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
  371.      * @param M2 value of empirical drag coefficient in rad/s².
  372.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  373.      */
  374.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  375.                                          final UnnormalizedSphericalHarmonicsProvider provider,
  376.                                          final PropagationType initialType,
  377.                                          final double M2) {
  378.         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
  379.              initialOrbit.getMu().newInstance(DEFAULT_MASS), provider,
  380.              provider.onDate(initialOrbit.getDate().toAbsoluteDate()), initialType, M2);
  381.     }

  383.     /** Build a propagator from orbit, attitude provider, mass and potential provider.
  384.      * <p>Using this constructor, it is possible to define the initial orbit as
  385.      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
  386.      * @param initialOrbit initial orbit
  387.      * @param attitudeProv attitude provider
  388.      * @param mass spacecraft mass
  389.      * @param provider for un-normalized zonal coefficients
  390.      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
  391.      * @param M2 value of empirical drag coefficient in rad/s².
  392.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  393.      */
  394.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  395.                                          final AttitudeProvider attitudeProv,
  396.                                          final T mass,
  397.                                          final UnnormalizedSphericalHarmonicsProvider provider,
  398.                                          final PropagationType initialType,
  399.                                          final double M2) {
  400.         this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()), initialType, M2);
  401.     }

  403.     /**
  404.      * Private helper constructor.
  405.      * <p>Using this constructor, it is possible to define the initial orbit as
  406.      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
  407.      * @param initialOrbit initial orbit
  408.      * @param attitude attitude provider
  409.      * @param mass spacecraft mass
  410.      * @param provider for un-normalized zonal coefficients
  411.      * @param harmonics {@code provider.onDate(initialOrbit.getDate())}
  412.      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
  413.      * @param M2 value of empirical drag coefficient in rad/s².
  414.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  415.      */
  416.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  417.                                          final AttitudeProvider attitude,
  418.                                          final T mass,
  419.                                          final UnnormalizedSphericalHarmonicsProvider provider,
  420.                                          final UnnormalizedSphericalHarmonics harmonics,
  421.                                          final PropagationType initialType,
  422.                                          final double M2) {
  423.         this(initialOrbit, attitude, mass, provider.getAe(), initialOrbit.getMu().newInstance(provider.getMu()),
  424.              harmonics.getUnnormalizedCnm(2, 0),
  425.              harmonics.getUnnormalizedCnm(3, 0),
  426.              harmonics.getUnnormalizedCnm(4, 0),
  427.              harmonics.getUnnormalizedCnm(5, 0),
  428.              initialType, M2);
  429.     }

  431.     /** Build a propagator from orbit, attitude provider, mass and potential.
  432.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  433.      * are related to both the normalized coefficients
  434.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  435.      *  and the J<sub>n</sub> one as follows:</p>
  436.      *
  437.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  438.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  439.      *
  440.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  441.      *
  442.      * <p>Using this constructor, it is possible to define the initial orbit as
  443.      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
  444.      *
  445.      * @param initialOrbit initial orbit
  446.      * @param attitudeProv attitude provider
  447.      * @param mass spacecraft mass
  448.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  449.      * @param mu central attraction coefficient (m³/s²)
  450.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  451.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  452.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  453.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  454.      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
  455.      * @param M2 value of empirical drag coefficient in rad/s².
  456.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  457.      */
  458.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  459.                                          final AttitudeProvider attitudeProv,
  460.                                          final T mass,
  461.                                          final double referenceRadius, final T mu,
  462.                                          final double c20, final double c30, final double c40,
  463.                                          final double c50,
  464.                                          final PropagationType initialType,
  465.                                          final double M2) {
  466.         this(initialOrbit, attitudeProv, mass, referenceRadius, mu,
  467.              c20, c30, c40, c50, initialType, M2, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
  468.     }

  470.     /** Build a propagator from orbit, attitude provider, mass and potential.
  471.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  472.      * are related to both the normalized coefficients
  473.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  474.      *  and the J<sub>n</sub> one as follows:</p>
  475.      *
  476.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  477.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  478.      *
  479.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  480.      *
  481.      * <p>Using this constructor, it is possible to define the initial orbit as
  482.      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
  483.      *
  484.      * @param initialOrbit initial orbit
  485.      * @param attitudeProv attitude provider
  486.      * @param mass spacecraft mass
  487.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  488.      * @param mu central attraction coefficient (m³/s²)
  489.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  490.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  491.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  492.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  493.      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
  494.      * @param M2 value of empirical drag coefficient in rad/s².
  495.      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
  496.      * @param epsilon convergence threshold for mean parameters conversion
  497.      * @param maxIterations maximum iterations for mean parameters conversion
  498.      * @since 11.2
  499.      */
  500.     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
  501.                                          final AttitudeProvider attitudeProv,
  502.                                          final T mass,
  503.                                          final double referenceRadius, final T mu,
  504.                                          final double c20, final double c30, final double c40,
  505.                                          final double c50,
  506.                                          final PropagationType initialType,
  507.                                          final double M2, final double epsilon, final int maxIterations) {

  509.         super(mass.getField(), attitudeProv);

  511.         // store model coefficients
  512.         this.referenceRadius = referenceRadius;
  513.         this.mu  = mu;
  514.         this.ck0 = new double[] {0.0, 0.0, c20, c30, c40, c50};

  516.         // initialize M2 driver
  517.         this.M2Driver = new ParameterDriver(BrouwerLyddanePropagator.M2_NAME, M2, SCALE,
  518.                                             Double.NEGATIVE_INFINITY,
  519.                                             Double.POSITIVE_INFINITY);

  521.         // compute mean parameters if needed
  522.         resetInitialState(new FieldSpacecraftState<>(initialOrbit,
  523.                                                  attitudeProv.getAttitude(initialOrbit,
  524.                                                                           initialOrbit.getDate(),
  525.                                                                           initialOrbit.getFrame()),
  526.                                                  mass),
  527.                                                  initialType, epsilon, maxIterations);

  529.     }

  531.     /** Conversion from osculating to mean orbit.
  532.      * <p>
  533.      * Compute mean orbit <b>in a Brouwer-Lyddane sense</b>, corresponding to the
  534.      * osculating SpacecraftState in input.
  535.      * </p>
  536.      * <p>
  537.      * Since the osculating orbit is obtained with the computation of
  538.      * short-periodic variation, the resulting output will depend on
  539.      * both the gravity field parameterized in input and the
  540.      * atmospheric drag represented by the {@code m2} parameter.
  541.      * </p>
  542.      * <p>
  543.      * The computation is done through a fixed-point iteration process.
  544.      * </p>
  545.      * @param <T> type of the filed elements
  546.      * @param osculating osculating orbit to convert
  547.      * @param provider for un-normalized zonal coefficients
  548.      * @param harmonics {@code provider.onDate(osculating.getDate())}
  549.      * @param M2Value value of empirical drag coefficient in rad/s².
  550.      *        If equal to {@code BrouwerLyddanePropagator.M2} drag is not considered
  551.      * @return mean orbit in a Brouwer-Lyddane sense
  552.      * @since 11.2
  553.      */
  554.     public static <T extends CalculusFieldElement<T>> FieldKeplerianOrbit<T> computeMeanOrbit(final FieldOrbit<T> osculating,
  555.                                                                                               final UnnormalizedSphericalHarmonicsProvider provider,
  556.                                                                                               final UnnormalizedSphericalHarmonics harmonics,
  557.                                                                                               final double M2Value) {
  558.         return computeMeanOrbit(osculating, provider, harmonics, M2Value, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
  559.     }

  561.     /** Conversion from osculating to mean orbit.
  562.      * <p>
  563.      * Compute mean orbit <b>in a Brouwer-Lyddane sense</b>, corresponding to the
  564.      * osculating SpacecraftState in input.
  565.      * </p>
  566.      * <p>
  567.      * Since the osculating orbit is obtained with the computation of
  568.      * short-periodic variation, the resulting output will depend on
  569.      * both the gravity field parameterized in input and the
  570.      * atmospheric drag represented by the {@code m2} parameter.
  571.      * </p>
  572.      * <p>
  573.      * The computation is done through a fixed-point iteration process.
  574.      * </p>
  575.      * @param <T> type of the filed elements
  576.      * @param osculating osculating orbit to convert
  577.      * @param provider for un-normalized zonal coefficients
  578.      * @param harmonics {@code provider.onDate(osculating.getDate())}
  579.      * @param M2Value value of empirical drag coefficient in rad/s².
  580.      *        If equal to {@code BrouwerLyddanePropagator.M2} drag is not considered
  581.      * @param epsilon convergence threshold for mean parameters conversion
  582.      * @param maxIterations maximum iterations for mean parameters conversion
  583.      * @return mean orbit in a Brouwer-Lyddane sense
  584.      * @since 11.2
  585.      */
  586.     public static <T extends CalculusFieldElement<T>> FieldKeplerianOrbit<T> computeMeanOrbit(final FieldOrbit<T> osculating,
  587.                                                                                               final UnnormalizedSphericalHarmonicsProvider provider,
  588.                                                                                               final UnnormalizedSphericalHarmonics harmonics,
  589.                                                                                               final double M2Value,
  590.                                                                                               final double epsilon, final int maxIterations) {
  591.         return computeMeanOrbit(osculating,
  592.                                 provider.getAe(), provider.getMu(),
  593.                                 harmonics.getUnnormalizedCnm(2, 0),
  594.                                 harmonics.getUnnormalizedCnm(3, 0),
  595.                                 harmonics.getUnnormalizedCnm(4, 0),
  596.                                 harmonics.getUnnormalizedCnm(5, 0),
  597.                                 M2Value, epsilon, maxIterations);
  598.     }

  600.     /** Conversion from osculating to mean orbit.
  601.      * <p>
  602.      * Compute mean orbit <b>in a Brouwer-Lyddane sense</b>, corresponding to the
  603.      * osculating SpacecraftState in input.
  604.      * </p>
  605.      * <p>
  606.      * Since the osculating orbit is obtained with the computation of
  607.      * short-periodic variation, the resulting output will depend on
  608.      * both the gravity field parameterized in input and the
  609.      * atmospheric drag represented by the {@code m2} parameter.
  610.      * </p>
  611.      * <p>
  612.      * The computation is done through a fixed-point iteration process.
  613.      * </p>
  614.      * @param <T> type of the filed elements
  615.      * @param osculating osculating orbit to convert
  616.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  617.      * @param mu central attraction coefficient (m³/s²)
  618.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  619.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  620.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  621.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  622.      * @param M2Value value of empirical drag coefficient in rad/s².
  623.      *        If equal to {@code BrouwerLyddanePropagator.M2} drag is not considered
  624.      * @param epsilon convergence threshold for mean parameters conversion
  625.      * @param maxIterations maximum iterations for mean parameters conversion
  626.      * @return mean orbit in a Brouwer-Lyddane sense
  627.      * @since 11.2
  628.      */
  629.     public static <T extends CalculusFieldElement<T>> FieldKeplerianOrbit<T> computeMeanOrbit(final FieldOrbit<T> osculating,
  630.                                                                                              final double referenceRadius, final double mu,
  631.                                                                                              final double c20, final double c30, final double c40,
  632.                                                                                              final double c50, final double M2Value,
  633.                                                                                              final double epsilon, final int maxIterations) {
  634.         final FieldBrouwerLyddanePropagator<T> propagator =
  635.                         new FieldBrouwerLyddanePropagator<>(osculating,
  636.                                                             InertialProvider.of(osculating.getFrame()),
  637.                                                             osculating.getMu().newInstance(DEFAULT_MASS),
  638.                                                             referenceRadius, osculating.getMu().newInstance(mu),
  639.                                                             c20, c30, c40, c50,
  640.                                                             PropagationType.OSCULATING, M2Value,
  641.                                                             epsilon, maxIterations);
  642.         return propagator.initialModel.mean;
  643.     }

  645.     /** {@inheritDoc}
  646.      * <p>The new initial state to consider
  647.      * must be defined with an osculating orbit.</p>
  648.      * @see #resetInitialState(FieldSpacecraftState, PropagationType)
  649.      */
  650.     @Override
  651.     public void resetInitialState(final FieldSpacecraftState<T> state) {
  652.         resetInitialState(state, PropagationType.OSCULATING);
  653.     }

  655.     /** Reset the propagator initial state.
  656.      * @param state new initial state to consider
  657.      * @param stateType mean Brouwer-Lyddane orbit or osculating orbit
  658.      */
  659.     public void resetInitialState(final FieldSpacecraftState<T> state, final PropagationType stateType) {
  660.         resetInitialState(state, stateType, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
  661.     }

  663.     /** Reset the propagator initial state.
  664.      * @param state new initial state to consider
  665.      * @param stateType mean Brouwer-Lyddane orbit or osculating orbit
  666.      * @param epsilon convergence threshold for mean parameters conversion
  667.      * @param maxIterations maximum iterations for mean parameters conversion
  668.      * @since 11.2
  669.      */
  670.     public void resetInitialState(final FieldSpacecraftState<T> state, final PropagationType stateType,
  671.                                   final double epsilon, final int maxIterations) {
  672.         super.resetInitialState(state);
  673.         final FieldKeplerianOrbit<T> keplerian = (FieldKeplerianOrbit<T>) OrbitType.KEPLERIAN.convertType(state.getOrbit());
  674.         this.initialModel = (stateType == PropagationType.MEAN) ?
  675.                              new FieldBLModel<>(keplerian, state.getMass(), referenceRadius, mu, ck0) :
  676.                              computeMeanParameters(keplerian, state.getMass(), epsilon, maxIterations);
  677.         this.models = new FieldTimeSpanMap<FieldBLModel<T>, T>(initialModel, state.getA().getField());
  678.     }

  680.     /** {@inheritDoc} */
  681.     @Override
  682.     protected void resetIntermediateState(final FieldSpacecraftState<T> state, final boolean forward) {
  683.         resetIntermediateState(state, forward, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
  684.     }

  686.     /** Reset an intermediate state.
  687.      * @param state new intermediate state to consider
  688.      * @param forward if true, the intermediate state is valid for
  689.      * propagations after itself
  690.      * @param epsilon convergence threshold for mean parameters conversion
  691.      * @param maxIterations maximum iterations for mean parameters conversion
  692.      * @since 11.2
  693.      */
  694.     protected void resetIntermediateState(final FieldSpacecraftState<T> state, final boolean forward,
  695.                                           final double epsilon, final int maxIterations) {
  696.         final FieldBLModel<T> newModel = computeMeanParameters((FieldKeplerianOrbit<T>) OrbitType.KEPLERIAN.convertType(state.getOrbit()),
  697.                                                                state.getMass(), epsilon, maxIterations);
  698.         if (forward) {
  699.             models.addValidAfter(newModel, state.getDate());
  700.         } else {
  701.             models.addValidBefore(newModel, state.getDate());
  702.         }
  703.         stateChanged(state);
  704.     }

  706.     /** Compute mean parameters according to the Brouwer-Lyddane analytical model computation
  707.      * in order to do the propagation.
  708.      * @param osculating osculating orbit
  709.      * @param mass constant mass
  710.      * @param epsilon convergence threshold for mean parameters conversion
  711.      * @param maxIterations maximum iterations for mean parameters conversion
  712.      * @return Brouwer-Lyddane mean model
  713.      */
  714.     private FieldBLModel<T> computeMeanParameters(final FieldKeplerianOrbit<T> osculating, final T mass,
  715.                                                   final double epsilon, final int maxIterations) {

  717.         // sanity check
  718.         if (osculating.getA().getReal() < referenceRadius) {
  719.             throw new OrekitException(OrekitMessages.TRAJECTORY_INSIDE_BRILLOUIN_SPHERE,
  720.                                            osculating.getA());
  721.         }

  723.         final Field<T> field = mass.getField();
  724.         final T one = field.getOne();
  725.         final T zero = field.getZero();
  726.         // rough initialization of the mean parameters
  727.         FieldBLModel<T> current = new FieldBLModel<T>(osculating, mass, referenceRadius, mu, ck0);

  729.         // threshold for each parameter
  730.         final T thresholdA      = current.mean.getA().abs().add(1.0).multiply(epsilon);
  731.         final T thresholdE      = current.mean.getE().add(1.0).multiply(epsilon);
  732.         final T thresholdAngles = one.getPi().multiply(epsilon);

  734.         int i = 0;
  735.         while (i++ < maxIterations) {

  737.             // recompute the osculating parameters from the current mean parameters
  738.             final FieldKeplerianOrbit<T> parameters = current.propagateParameters(current.mean.getDate(), getParameters(mass.getField()));

  740.             // adapted parameters residuals
  741.             final T deltaA     = osculating.getA()  .subtract(parameters.getA());
  742.             final T deltaE     = osculating.getE()  .subtract(parameters.getE());
  743.             final T deltaI     = osculating.getI()  .subtract(parameters.getI());
  744.             final T deltaOmega = MathUtils.normalizeAngle(osculating.getPerigeeArgument().subtract(parameters.getPerigeeArgument()), zero);
  745.             final T deltaRAAN  = MathUtils.normalizeAngle(osculating.getRightAscensionOfAscendingNode().subtract(parameters.getRightAscensionOfAscendingNode()), zero);
  746.             final T deltaAnom  = MathUtils.normalizeAngle(osculating.getMeanAnomaly().subtract(parameters.getMeanAnomaly()), zero);


  749.             // update mean parameters
  750.             current = new FieldBLModel<T>(new FieldKeplerianOrbit<T>(current.mean.getA()            .add(deltaA),
  751.                                                      FastMath.max(current.mean.getE().add(deltaE), zero),
  752.                                                      current.mean.getI()                            .add(deltaI),
  753.                                                      current.mean.getPerigeeArgument()              .add(deltaOmega),
  754.                                                      current.mean.getRightAscensionOfAscendingNode().add(deltaRAAN),
  755.                                                      current.mean.getMeanAnomaly()                  .add(deltaAnom),
  756.                                                      PositionAngle.MEAN,
  757.                                                      current.mean.getFrame(),
  758.                                                      current.mean.getDate(), mu),
  759.                                   mass, referenceRadius, mu, ck0);
  760.             // check convergence
  761.             if (FastMath.abs(deltaA.getReal())     < thresholdA.getReal() &&
  762.                 FastMath.abs(deltaE.getReal())     < thresholdE.getReal() &&
  763.                 FastMath.abs(deltaI.getReal())     < thresholdAngles.getReal() &&
  764.                 FastMath.abs(deltaOmega.getReal()) < thresholdAngles.getReal() &&
  765.                 FastMath.abs(deltaRAAN.getReal())  < thresholdAngles.getReal() &&
  766.                 FastMath.abs(deltaAnom.getReal())  < thresholdAngles.getReal()) {
  767.                 return current;
  768.             }
  769.         }
  770.         throw new OrekitException(OrekitMessages.UNABLE_TO_COMPUTE_BROUWER_LYDDANE_MEAN_PARAMETERS, i);
  771.     }


  774.     /** {@inheritDoc} */
  775.     public FieldKeplerianOrbit<T> propagateOrbit(final FieldAbsoluteDate<T> date, final T[] parameters) {
  776.         // compute Cartesian parameters, taking derivatives into account
  777.         final FieldBLModel<T> current = models.get(date);
  778.         return current.propagateParameters(date, parameters);
  779.     }

  781.     /**
  782.      * Get the value of the M2 drag parameter.
  783.      * @return the value of the M2 drag parameter
  784.      */
  785.     public double getM2() {
  786.         return M2Driver.getValue();
  787.     }

  789.     /** Local class for Brouwer-Lyddane model. */
  790.     private static class FieldBLModel<T extends CalculusFieldElement<T>> {

  792.         /** Mean orbit. */
  793.         private final FieldKeplerianOrbit<T> mean;

  795.         /** Constant mass. */
  796.         private final T mass;

  798.         /** Central attraction coefficient. */
  799.         private final T mu;

  801.         // CHECKSTYLE: stop JavadocVariable check

  803.         // preprocessed values

  805.         // Constant for secular terms l'', g'', h''
  806.         // l standing for true anomaly, g for perigee argument and h for raan
  807.         private final T xnotDot;
  808.         private final T n;
  809.         private final T lt;
  810.         private final T gt;
  811.         private final T ht;


  814.         // Long periodT
  815.         private final T dei3sg;
  816.         private final T de2sg;
  817.         private final T deisg;
  818.         private final T de;


  821.         private final T dlgs2g;
  822.         private final T dlgc3g;
  823.         private final T dlgcg;


  826.         private final T dh2sgcg;
  827.         private final T dhsgcg;
  828.         private final T dhcg;


  831.         // Short perioTs
  832.         private final T aC;
  833.         private final T aCbis;
  834.         private final T ac2g2f;


  837.         private final T eC;
  838.         private final T ecf;
  839.         private final T e2cf;
  840.         private final T e3cf;
  841.         private final T ec2f2g;
  842.         private final T ecfc2f2g;
  843.         private final T e2cfc2f2g;
  844.         private final T e3cfc2f2g;
  845.         private final T ec2gf;
  846.         private final T ec2g3f;


  849.         private final T ide;
  850.         private final T isfs2f2g;
  851.         private final T icfc2f2g;
  852.         private final T ic2f2g;


  855.         private final T glf;
  856.         private final T gll;
  857.         private final T glsf;
  858.         private final T glosf;
  859.         private final T gls2f2g;
  860.         private final T gls2gf;
  861.         private final T glos2gf;
  862.         private final T gls2g3f;
  863.         private final T glos2g3f;


  866.         private final T hf;
  867.         private final T hl;
  868.         private final T hsf;
  869.         private final T hcfs2g2f;
  870.         private final T hs2g2f;
  871.         private final T hsfc2g2f;


  874.         private final T edls2g;
  875.         private final T edlcg;
  876.         private final T edlc3g;
  877.         private final T edlsf;
  878.         private final T edls2gf;
  879.         private final T edls2g3f;

  881.         // Drag terms
  882.         private final T aRate;
  883.         private final T eRate;

  885.         // CHECKSTYLE: resume JavadocVariable check

  887.         /** Create a model for specified mean orbit.
  888.          * @param mean mean Fieldorbit
  889.          * @param mass constant mass
  890.          * @param referenceRadius reference radius of the central body attraction model (m)
  891.          * @param mu central attraction coefficient (m³/s²)
  892.          * @param ck0 un-normalized zonal coefficients
  893.          */
  894.         FieldBLModel(final FieldKeplerianOrbit<T> mean, final T mass,
  895.                 final double referenceRadius, final T mu, final double[] ck0) {

  897.             this.mean = mean;
  898.             this.mass = mass;
  899.             this.mu   = mu;
  900.             final T one  = mass.getField().getOne();

  902.             final T app = mean.getA();
  903.             xnotDot = mu.divide(app).sqrt().divide(app);

  905.             // preliminary processing
  906.             final T q = app.divide(referenceRadius).reciprocal();
  907.             T ql = q.multiply(q);
  908.             final T y2 = ql.multiply(-0.5 * ck0[2]);

  910.             n = ((mean.getE().multiply(mean.getE()).negate()).add(1.0)).sqrt();
  911.             final T n2 = n.multiply(n);
  912.             final T n3 = n2.multiply(n);
  913.             final T n4 = n2.multiply(n2);
  914.             final T n6 = n4.multiply(n2);
  915.             final T n8 = n4.multiply(n4);
  916.             final T n10 = n8.multiply(n2);

  918.             final T yp2 = y2.divide(n4);
  919.             ql = ql.multiply(q);
  920.             final T yp3 = ql.multiply(ck0[3]).divide(n6);
  921.             ql = ql.multiply(q);
  922.             final T yp4 = ql.multiply(0.375 * ck0[4]).divide(n8);
  923.             ql = ql.multiply(q);
  924.             final T yp5 = ql.multiply(ck0[5]).divide(n10);


  927.             final FieldSinCos<T> sc = FastMath.sinCos(mean.getI());
  928.             final T sinI1 = sc.sin();
  929.             final T sinI2 = sinI1.multiply(sinI1);
  930.             final T cosI1 = sc.cos();
  931.             final T cosI2 = cosI1.multiply(cosI1);
  932.             final T cosI3 = cosI2.multiply(cosI1);
  933.             final T cosI4 = cosI2.multiply(cosI2);
  934.             final T cosI6 = cosI4.multiply(cosI2);
  935.             final T C5c2 = T2(cosI1).reciprocal();
  936.             final T C3c2 = cosI2.multiply(3.0).subtract(1.0);

  938.             final T epp = mean.getE();
  939.             final T epp2 = epp.multiply(epp);
  940.             final T epp3 = epp2.multiply(epp);
  941.             final T epp4 = epp2.multiply(epp2);

  943.             if (epp.getReal() >= 1) {
  944.                 // Only for elliptical (e < 1) orbits
  945.                 throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL,
  946.                                           mean.getE().getReal());
  947.             }

  949.             // secular multiplicative
  950.             lt = one.add(yp2.multiply(n).multiply(C3c2).multiply(1.5)).
  951.                      add(yp2.multiply(0.09375).multiply(yp2).multiply(n).multiply(n2.multiply(25.0).add(n.multiply(16.0)).add(-15.0).
  952.                              add(cosI2.multiply(n2.multiply(-90.0).add(n.multiply(-96.0)).add(30.0))).
  953.                              add(cosI4.multiply(n2.multiply(25.0).add(n.multiply(144.0)).add(105.0))))).
  954.                      add(yp4.multiply(0.9375).multiply(n).multiply(epp2).multiply(cosI4.multiply(35.0).add(cosI2.multiply(-30.0)).add(3.0)));

  956.             gt = yp2.multiply(-1.5).multiply(C5c2).
  957.                      add(yp2.multiply(0.09375).multiply(yp2).multiply(n2.multiply(25.0).add(n.multiply(24.0)).add(-35.0).
  958.                             add(cosI2.multiply(n2.multiply(-126.0).add(n.multiply(-192.0)).add(90.0))).
  959.                             add(cosI4.multiply(n2.multiply(45.0).add(n.multiply(360.0)).add(385.0))))).
  960.                      add(yp4.multiply(0.3125).multiply(n2.multiply(-9.0).add(21.0).
  961.                             add(cosI2.multiply(n2.multiply(126.0).add(-270.0))).
  962.                             add(cosI4.multiply(n2.multiply(-189.0).add(385.0)))));

  964.             ht = yp2.multiply(-3.0).multiply(cosI1).
  965.                      add(yp2.multiply(0.375).multiply(yp2).multiply(cosI1.multiply(n2.multiply(9.0).add(n.multiply(12.0)).add(-5.0)).
  966.                                                                     add(cosI3.multiply(n2.multiply(-5.0).add(n.multiply(-36.0)).add(-35.0))))).
  967.                      add(yp4.multiply(1.25).multiply(cosI1).multiply(n2.multiply(-3.0).add(5.0)).multiply(cosI2.multiply(-7.0).add(3.0)));

  969.             final T cA = one.subtract(cosI2.multiply(11.0)).subtract(cosI4.multiply(40.0).divide(C5c2));
  970.             final T cB = one.subtract(cosI2.multiply(3.0)).subtract(cosI4.multiply(8.0).divide(C5c2));
  971.             final T cC = one.subtract(cosI2.multiply(9.0)).subtract(cosI4.multiply(24.0).divide(C5c2));
  972.             final T cD = one.subtract(cosI2.multiply(5.0)).subtract(cosI4.multiply(16.0).divide(C5c2));

  974.             final T qyp2_4 = yp2.multiply(3.0).multiply(yp2).multiply(cA).
  975.                              subtract(yp4.multiply(10.0).multiply(cB));
  976.             final T qyp52 = cosI1.multiply(epp3).multiply(cD.multiply(0.5).divide(sinI1).
  977.                                                           add(sinI1.multiply(cosI4.divide(C5c2).divide(C5c2).multiply(80.0).
  978.                                                                              add(cosI2.divide(C5c2).multiply(32.0).
  979.                                                                              add(5.0)))));
  980.             final T qyp22 = epp2.add(2.0).subtract(epp2.multiply(3.0).add(2.0).multiply(11.0).multiply(cosI2)).
  981.                             subtract(epp2.multiply(5.0).add(2.0).multiply(40.0).multiply(cosI4.divide(C5c2))).
  982.                             subtract(epp2.multiply(400.0).multiply(cosI6).divide(C5c2).divide(C5c2));
  983.             final T qyp42 = one.divide(5.0).multiply(qyp22.
  984.                                                      add(one.multiply(4.0).multiply(epp2.
  985.                                                                                     add(2.0).
  986.                                                                                     subtract(cosI2.multiply(epp2.multiply(3.0).add(2.0))))));
  987.             final T qyp52bis = cosI1.multiply(sinI1).multiply(epp).multiply(epp2.multiply(3.0).add(4.0)).
  988.                                                                    multiply(cosI4.divide(C5c2).divide(C5c2).multiply(40.0).
  989.                                                                             add(cosI2.divide(C5c2).multiply(16.0)).
  990.                                                                             add(3.0));
  991.            // long periodic multiplicative
  992.             dei3sg =  yp5.divide(yp2).multiply(35.0 / 96.0).multiply(epp2).multiply(n2).multiply(cD).multiply(sinI1);
  993.             de2sg = qyp2_4.divide(yp2).multiply(epp).multiply(n2).multiply(-1.0 / 12.0);
  994.             deisg = sinI1.multiply(yp5.multiply(-35.0 / 128.0).divide(yp2).multiply(epp2).multiply(n2).multiply(cD).
  995.                             add(n2.multiply(0.25).divide(yp2).multiply(yp3.add(yp5.multiply(5.0 / 16.0).multiply(epp2.multiply(3.0).add(4.0)).multiply(cC)))));
  996.             de = epp2.multiply(n2).multiply(qyp2_4).divide(24.0).divide(yp2);

  998.             final T qyp52quotient = epp.multiply(epp4.multiply(81.0).add(-32.0)).divide(n.multiply(epp2.multiply(9.0).add(4.0)).add(epp2.multiply(3.0)).add(4.0));
  999.             dlgs2g = yp2.multiply(48.0).reciprocal().multiply(yp2.multiply(-3.0).multiply(yp2).multiply(qyp22).
  1000.                             add(yp4.multiply(10.0).multiply(qyp42))).
  1001.                             add(n3.divide(yp2).multiply(qyp2_4).divide(24.0));
  1002.             dlgc3g =  yp5.multiply(35.0 / 384.0).divide(yp2).multiply(n3).multiply(epp).multiply(cD).multiply(sinI1).
  1003.                             add(yp5.multiply(35.0 / 1152.0).divide(yp2).multiply(qyp52.multiply(2.0).multiply(cosI1).subtract(epp.multiply(cD).multiply(sinI1).multiply(epp2.multiply(2.0).add(3.0)))));
  1004.             dlgcg = yp3.negate().multiply(cosI2).multiply(epp).divide(yp2.multiply(sinI1).multiply(4.0)).
  1005.                     add(yp5.divide(yp2).multiply(0.078125).multiply(cC).multiply(cosI2.divide(sinI1).multiply(epp.negate()).multiply(epp2.multiply(3.0).add(4.0)).
  1006.                                                                     add(sinI1.multiply(epp2).multiply(epp2.multiply(9.0).add(26.0)))).
  1007.                     subtract(yp5.divide(yp2).multiply(0.46875).multiply(qyp52bis).multiply(cosI1)).
  1008.                     add(yp3.divide(yp2).multiply(0.25).multiply(sinI1).multiply(epp).divide(n3.add(1.0)).multiply(epp2.multiply(epp2.subtract(3.0)).add(3.0))).
  1009.                     add(yp5.divide(yp2).multiply(0.078125).multiply(n2).multiply(cC).multiply(qyp52quotient).multiply(sinI1)));
  1010.             final T qyp24 = yp2.multiply(yp2).multiply(3.0).multiply(cosI4.divide(sinI2).multiply(200.0).add(cosI2.divide(sinI1).multiply(80.0)).add(11.0)).
  1011.                             subtract(yp4.multiply(10.0).multiply(cosI4.divide(sinI2).multiply(40.0).add(cosI2.divide(sinI1).multiply(16.0)).add(3.0)));
  1012.             dh2sgcg = yp5.divide(yp2).multiply(qyp52).multiply(35.0 / 144.0);
  1013.             dhsgcg = qyp24.multiply(cosI1).multiply(epp2.negate()).divide(yp2.multiply(12.0));
  1014.             dhcg = yp5.divide(yp2).multiply(qyp52).multiply(-35.0 / 576.0).
  1015.                    add(cosI1.multiply(epp).divide(yp2.multiply(sinI1).multiply(4.0)).multiply(yp3.add(yp5.multiply(0.3125).multiply(cC).multiply(epp2.multiply(3.0).add(4.0))))).
  1016.                    add(yp5.multiply(qyp52bis).multiply(1.875).divide(yp2.multiply(4.0)));

  1018.             // short periodic multiplicative
  1019.             aC = yp2.negate().multiply(C3c2).multiply(app).divide(n3);
  1020.             aCbis = y2.multiply(app).multiply(C3c2);
  1021.             ac2g2f = y2.multiply(app).multiply(sinI2).multiply(3.0);

  1023.             T qe = y2.multiply(C3c2).multiply(0.5).multiply(n2).divide(n6);
  1024.             eC = qe.multiply(epp).divide(n3.add(1.0)).multiply(epp2.multiply(epp2.subtract(3.0)).add(3.0));
  1025.             ecf = qe.multiply(3.0);
  1026.             e2cf = qe.multiply(3.0).multiply(epp);
  1027.             e3cf = qe.multiply(epp2);
  1028.             qe = y2.multiply(0.5).multiply(n2).multiply(3.0).multiply(cosI2.negate().add(1.0)).divide(n6);
  1029.             ec2f2g = qe.multiply(epp);
  1030.             ecfc2f2g = qe.multiply(3.0);
  1031.             e2cfc2f2g = qe.multiply(3.0).multiply(epp);
  1032.             e3cfc2f2g = qe.multiply(epp2);
  1033.             qe = yp2.multiply(-0.5).multiply(n2).multiply(cosI2.negate().add(1.0));
  1034.             ec2gf = qe.multiply(3.0);
  1035.             ec2g3f = qe;

  1037.             T qi = yp2.multiply(epp).multiply(cosI1).multiply(sinI1);
  1038.             ide = cosI1.multiply(epp.negate()).divide(sinI1.multiply(n2));
  1039.             isfs2f2g = qi;
  1040.             icfc2f2g = qi.multiply(2.0);
  1041.             qi = yp2.multiply(cosI1).multiply(sinI1);
  1042.             ic2f2g = qi.multiply(1.5);

  1044.             T qgl1 = yp2.multiply(0.25);
  1045.             T qgl2 =  yp2.multiply(epp).multiply(n2).multiply(0.25).divide(n.add(1.0));
  1046.             glf = qgl1.multiply(C5c2).multiply(-6.0);
  1047.             gll = qgl1.multiply(C5c2).multiply(6.0);
  1048.             glsf = qgl1.multiply(C5c2).multiply(-6.0).multiply(epp).
  1049.                    add(qgl2.multiply(C3c2).multiply(2.0));
  1050.             glosf = qgl2.multiply(C3c2).multiply(2.0);
  1051.             qgl1 = qgl1.multiply(cosI2.multiply(-5.0).add(3.0));
  1052.             qgl2 = qgl2.multiply(3.0).multiply(cosI2.negate().add(1.0));
  1053.             gls2f2g = qgl1.multiply(3.0);
  1054.             gls2gf = qgl1.multiply(3.0).multiply(epp).
  1055.                      add(qgl2);
  1056.             glos2gf = qgl2.negate();
  1057.             gls2g3f = qgl1.multiply(epp).
  1058.                       add(qgl2.multiply(1.0 / 3.0));
  1059.             glos2g3f = qgl2;

  1061.             final T qh = yp2.multiply(cosI1).multiply(3.0);
  1062.             hf = qh.negate();
  1063.             hl = qh;
  1064.             hsf = qh.multiply(epp).negate();
  1065.             hcfs2g2f = yp2.multiply(cosI1).multiply(epp).multiply(2.0);
  1066.             hs2g2f = yp2.multiply(cosI1).multiply(1.5);
  1067.             hsfc2g2f = yp2.multiply(cosI1).multiply(epp).negate();

  1069.             final T qedl = yp2.multiply(n3).multiply(-0.25);
  1070.             edls2g = qyp2_4.multiply(1.0 / 24.0).multiply(epp).multiply(n3).divide(yp2);
  1071.             edlcg = yp3.divide(yp2).multiply(-0.25).multiply(n3).multiply(sinI1).
  1072.                     subtract(yp5.divide(yp2).multiply(0.078125).multiply(n3).multiply(sinI1).multiply(cC).multiply(epp2.multiply(9.0).add(4.0)));
  1073.             edlc3g = yp5.divide(yp2).multiply(n3).multiply(epp2).multiply(cD).multiply(sinI1).multiply(35.0 / 384.0);
  1074.             edlsf = qedl.multiply(C3c2).multiply(2.0);
  1075.             edls2gf = qedl.multiply(3.0).multiply(cosI2.negate().add(1.0));
  1076.             edls2g3f = qedl.multiply(1.0 / 3.0);

  1078.             // secular rates of the mean semi-major axis and eccentricity
  1079.             // Eq. 2.41 and Eq. 2.45 of Phipps' 1992 thesis
  1080.             aRate = app.multiply(-4.0).divide(xnotDot.multiply(3.0));
  1081.             eRate = epp.multiply(n).multiply(n).multiply(-4.0).divide(xnotDot.multiply(3.0));

  1083.         }

  1085.         /**
  1086.          * Accurate computation of E - e sin(E).
  1087.          *
  1088.          * @param E eccentric anomaly
  1089.          * @return E - e sin(E)
  1090.          */
  1091.         private FieldUnivariateDerivative2<T> eMeSinE(final FieldUnivariateDerivative2<T> E) {
  1092.             FieldUnivariateDerivative2<T> x = E.sin().multiply(mean.getE().negate().add(1.0));
  1093.             final FieldUnivariateDerivative2<T> mE2 = E.negate().multiply(E);
  1094.             FieldUnivariateDerivative2<T> term = E;
  1095.             FieldUnivariateDerivative2<T> d    = E.getField().getZero();
  1096.             // the inequality test below IS intentional and should NOT be replaced by a check with a small tolerance
  1097.             for (FieldUnivariateDerivative2<T> x0 = d.add(Double.NaN); !Double.valueOf(x.getValue().getReal()).equals(Double.valueOf(x0.getValue().getReal()));) {
  1098.                 d = d.add(2);
  1099.                 term = term.multiply(mE2.divide(d.multiply(d.add(1))));
  1100.                 x0 = x;
  1101.                 x = x.subtract(term);
  1102.             }
  1103.             return x;
  1104.         }

  1106.         /**
  1107.          * Gets eccentric anomaly from mean anomaly.
  1108.          * <p>The algorithm used to solve the Kepler equation has been published in:
  1109.          * "Procedures for  solving Kepler's Equation", A. W. Odell and R. H. Gooding,
  1110.          * Celestial Mechanics 38 (1986) 307-334</p>
  1111.          * <p>It has been copied from the OREKIT library (KeplerianOrbit class).</p>
  1112.          *
  1113.          * @param mk the mean anomaly (rad)
  1114.          * @return the eccentric anomaly (rad)
  1115.          */
  1116.         private FieldUnivariateDerivative2<T> getEccentricAnomaly(final FieldUnivariateDerivative2<T> mk) {
  1117.             final double k1 = 3 * FastMath.PI + 2;
  1118.             final double k2 = FastMath.PI - 1;
  1119.             final double k3 = 6 * FastMath.PI - 1;
  1120.             final double A  = 3.0 * k2 * k2 / k1;
  1121.             final double B  = k3 * k3 / (6.0 * k1);

  1123.             final T zero = mean.getE().getField().getZero();

  1125.             // reduce M to [-PI PI] interval
  1126.             final FieldUnivariateDerivative2<T> reducedM = new FieldUnivariateDerivative2<T>(MathUtils.normalizeAngle(mk.getValue(), zero ),
  1127.                                                                              mk.getFirstDerivative(),
  1128.                                                                              mk.getSecondDerivative());

  1130.             // compute start value according to A. W. Odell and R. H. Gooding S12 starter
  1131.             FieldUnivariateDerivative2<T> ek;
  1132.             if (reducedM.getValue().abs().getReal() < 1.0 / 6.0) {
  1133.                 if (reducedM.getValue().abs().getReal() < Precision.SAFE_MIN) {
  1134.                     // this is an Orekit change to the S12 starter.
  1135.                     // If reducedM is 0.0, the derivative of cbrt is infinite which induces NaN appearing later in
  1136.                     // the computation. As in this case E and M are almost equal, we initialize ek with reducedM
  1137.                     ek = reducedM;
  1138.                 } else {
  1139.                     // this is the standard S12 starter
  1140.                     ek = reducedM.add(reducedM.multiply(6).cbrt().subtract(reducedM).multiply(mean.getE()));
  1141.                 }
  1142.             } else {
  1143.                 if (reducedM.getValue().getReal() < 0) {
  1144.                     final FieldUnivariateDerivative2<T> w = reducedM.add(FastMath.PI);
  1145.                     ek = reducedM.add(w.multiply(-A).divide(w.subtract(B)).subtract(FastMath.PI).subtract(reducedM).multiply(mean.getE()));
  1146.                 } else {
  1147.                     final FieldUnivariateDerivative2<T> minusW = reducedM.subtract(FastMath.PI);
  1148.                     ek = reducedM.add(minusW.multiply(A).divide(minusW.add(B)).add(FastMath.PI).subtract(reducedM).multiply(mean.getE()));
  1149.                 }
  1150.             }

  1152.             final T e1 = mean.getE().negate().add(1.0);
  1153.             final boolean noCancellationRisk = (e1.add(ek.getValue().multiply(ek.getValue())).getReal() / 6) >= 0.1;

  1155.             // perform two iterations, each consisting of one Halley step and one Newton-Raphson step
  1156.             for (int j = 0; j < 2; ++j) {
  1157.                 final FieldUnivariateDerivative2<T> f;
  1158.                 FieldUnivariateDerivative2<T> fd;
  1159.                 final FieldUnivariateDerivative2<T> fdd  = ek.sin().multiply(mean.getE());
  1160.                 final FieldUnivariateDerivative2<T> fddd = ek.cos().multiply(mean.getE());
  1161.                 if (noCancellationRisk) {
  1162.                     f  = ek.subtract(fdd).subtract(reducedM);
  1163.                     fd = fddd.subtract(1).negate();
  1164.                 } else {
  1165.                     f  = eMeSinE(ek).subtract(reducedM);
  1166.                     final FieldUnivariateDerivative2<T> s = ek.multiply(0.5).sin();
  1167.                     fd = s.multiply(s).multiply(mean.getE().multiply(2.0)).add(e1);
  1168.                 }
  1169.                 final FieldUnivariateDerivative2<T> dee = f.multiply(fd).divide(f.multiply(0.5).multiply(fdd).subtract(fd.multiply(fd)));

  1171.                 // update eccentric anomaly, using expressions that limit underflow problems
  1172.                 final FieldUnivariateDerivative2<T> w = fd.add(dee.multiply(0.5).multiply(fdd.add(dee.multiply(fdd).divide(3))));
  1173.                 fd = fd.add(dee.multiply(fdd.add(dee.multiply(0.5).multiply(fdd))));
  1174.                 ek = ek.subtract(f.subtract(dee.multiply(fd.subtract(w))).divide(fd));
  1175.             }

  1177.             // expand the result back to original range
  1178.             ek = ek.add(mk.getValue().subtract(reducedM.getValue()));

  1180.             // Returns the eccentric anomaly
  1181.             return ek;
  1182.         }

  1184.         /**
  1185.          * This method is used in Brouwer-Lyddane model to avoid singularity at the
  1186.          * critical inclination (i = 63.4°).
  1187.          * <p>
  1188.          * This method, based on Warren Phipps's 1992 thesis (Eq. 2.47 and 2.48),
  1189.          * approximate the factor (1.0 - 5.0 * cos²(inc))^-1 (causing the singularity)
  1190.          * by a function, named T2 in the thesis.
  1191.          * </p>
  1192.          * @param cosInc cosine of the mean inclination
  1193.          * @return an approximation of (1.0 - 5.0 * cos²(inc))^-1 term
  1194.          */
  1195.         private T T2(final T cosInc) {

  1197.             // X = (1.0 - 5.0 * cos²(inc))
  1198.             final T x  = cosInc.multiply(cosInc).multiply(-5.0).add(1.0);
  1199.             final T x2 = x.multiply(x);

  1201.             // Eq. 2.48
  1202.             T sum = x.getField().getZero();
  1203.             for (int i = 0; i <= 12; i++) {
  1204.                 final double sign = i % 2 == 0 ? +1.0 : -1.0;
  1205.                 sum = sum.add(FastMath.pow(x2, i).multiply(FastMath.pow(BETA, i)).multiply(sign).divide(CombinatoricsUtils.factorialDouble(i + 1)));
  1206.             }

  1208.             // Right term of equation 2.47
  1209.             T product = x.getField().getOne();
  1210.             for (int i = 0; i <= 10; i++) {
  1211.                 product = product.multiply(FastMath.exp(x2.multiply(BETA).multiply(FastMath.scalb(-1.0, i))).add(1.0));
  1212.             }

  1214.             // Return (Eq. 2.47)
  1215.             return x.multiply(BETA).multiply(sum).multiply(product);

  1217.         }

  1219.         /** Extrapolate an orbit up to a specific target date.
  1220.          * @param date target date for the orbit
  1221.          * @param parameters model parameters
  1222.          * @return propagated parameters
  1223.          */
  1224.         public FieldKeplerianOrbit<T> propagateParameters(final FieldAbsoluteDate<T> date, final T[] parameters) {

  1226.             // Field
  1227.             final Field<T> field = date.getField();
  1228.             final T one  = field.getOne();
  1229.             final T zero = field.getZero();

  1231.             // Empirical drag coefficient M2
  1232.             final T m2 = parameters[0];

  1234.             // Keplerian evolution
  1235.             final FieldUnivariateDerivative2<T> dt = new FieldUnivariateDerivative2<>(date.durationFrom(mean.getDate()), one, zero);
  1236.             final FieldUnivariateDerivative2<T> xnot = dt.multiply(xnotDot);

  1238.             //____________________________________
  1239.             // secular effects

  1241.             // mean mean anomaly
  1242.             final FieldUnivariateDerivative2<T> dtM2  = dt.multiply(m2);
  1243.             final FieldUnivariateDerivative2<T> dt2M2 = dt.multiply(dtM2);
  1244.             final FieldUnivariateDerivative2<T> lpp = new FieldUnivariateDerivative2<T>(MathUtils.normalizeAngle(mean.getMeanAnomaly().add(lt.multiply(xnot.getValue())).add(dt2M2.getValue()), zero),
  1245.                                                                                         lt.multiply(xnotDot).add(dtM2.multiply(2.0).getValue()),
  1246.                                                                                         m2.multiply(2.0));
  1247.             // mean argument of perigee
  1248.             final FieldUnivariateDerivative2<T> gpp = new FieldUnivariateDerivative2<T>(MathUtils.normalizeAngle(mean.getPerigeeArgument().add(gt.multiply(xnot.getValue())), zero),
  1249.                                                                                         gt.multiply(xnotDot),
  1250.                                                                                         zero);
  1251.             // mean longitude of ascending node
  1252.             final FieldUnivariateDerivative2<T> hpp = new FieldUnivariateDerivative2<T>(MathUtils.normalizeAngle(mean.getRightAscensionOfAscendingNode().add(ht.multiply(xnot.getValue())), zero),
  1253.                                                                                         ht.multiply(xnotDot),
  1254.                                                                                         zero);

  1256.             // ________________________________________________
  1257.             // secular rates of the mean semi-major axis and eccentricity

  1259.             // semi-major axis
  1260.             final FieldUnivariateDerivative2<T> appDrag = dt.multiply(aRate.multiply(m2));

  1262.             // eccentricity
  1263.             final FieldUnivariateDerivative2<T> eppDrag = dt.multiply(eRate.multiply(m2));

  1265.             //____________________________________
  1266.             // Long periodical terms
  1267.             final FieldUnivariateDerivative2<T> cg1 = gpp.cos();
  1268.             final FieldUnivariateDerivative2<T> sg1 = gpp.sin();
  1269.             final FieldUnivariateDerivative2<T> c2g = cg1.multiply(cg1).subtract(sg1.multiply(sg1));
  1270.             final FieldUnivariateDerivative2<T> s2g = cg1.multiply(sg1).add(sg1.multiply(cg1));
  1271.             final FieldUnivariateDerivative2<T> c3g = c2g.multiply(cg1).subtract(s2g.multiply(sg1));
  1272.             final FieldUnivariateDerivative2<T> sg2 = sg1.multiply(sg1);
  1273.             final FieldUnivariateDerivative2<T> sg3 = sg1.multiply(sg2);


  1276.             // de eccentricity
  1277.             final FieldUnivariateDerivative2<T> d1e = sg3.multiply(dei3sg).
  1278.                                                add(sg1.multiply(deisg)).
  1279.                                                add(sg2.multiply(de2sg)).
  1280.                                                add(de);

  1282.             // l' + g'
  1283.             final FieldUnivariateDerivative2<T> lp_p_gp = s2g.multiply(dlgs2g).
  1284.                                                add(c3g.multiply(dlgc3g)).
  1285.                                                add(cg1.multiply(dlgcg)).
  1286.                                                add(lpp).
  1287.                                                add(gpp);

  1289.             // h'
  1290.             final FieldUnivariateDerivative2<T> hp = sg2.multiply(cg1).multiply(dh2sgcg).
  1291.                                                add(sg1.multiply(cg1).multiply(dhsgcg)).
  1292.                                                add(cg1.multiply(dhcg)).
  1293.                                                add(hpp);

  1295.             // Short periodical terms
  1296.             // eccentric anomaly
  1297.             final FieldUnivariateDerivative2<T> Ep = getEccentricAnomaly(lpp);
  1298.             final FieldUnivariateDerivative2<T> cf1 = (Ep.cos().subtract(mean.getE())).divide(Ep.cos().multiply(mean.getE().negate()).add(1.0));
  1299.             final FieldUnivariateDerivative2<T> sf1 = (Ep.sin().multiply(n)).divide(Ep.cos().multiply(mean.getE().negate()).add(1.0));
  1300.             final FieldUnivariateDerivative2<T> f = FastMath.atan2(sf1, cf1);

  1302.             final FieldUnivariateDerivative2<T> c2f = cf1.multiply(cf1).subtract(sf1.multiply(sf1));
  1303.             final FieldUnivariateDerivative2<T> s2f = cf1.multiply(sf1).add(sf1.multiply(cf1));
  1304.             final FieldUnivariateDerivative2<T> c3f = c2f.multiply(cf1).subtract(s2f.multiply(sf1));
  1305.             final FieldUnivariateDerivative2<T> s3f = c2f.multiply(sf1).add(s2f.multiply(cf1));
  1306.             final FieldUnivariateDerivative2<T> cf2 = cf1.multiply(cf1);
  1307.             final FieldUnivariateDerivative2<T> cf3 = cf1.multiply(cf2);

  1309.             final FieldUnivariateDerivative2<T> c2g1f = cf1.multiply(c2g).subtract(sf1.multiply(s2g));
  1310.             final FieldUnivariateDerivative2<T> c2g2f = c2f.multiply(c2g).subtract(s2f.multiply(s2g));
  1311.             final FieldUnivariateDerivative2<T> c2g3f = c3f.multiply(c2g).subtract(s3f.multiply(s2g));
  1312.             final FieldUnivariateDerivative2<T> s2g1f = cf1.multiply(s2g).add(c2g.multiply(sf1));
  1313.             final FieldUnivariateDerivative2<T> s2g2f = c2f.multiply(s2g).add(c2g.multiply(s2f));
  1314.             final FieldUnivariateDerivative2<T> s2g3f = c3f.multiply(s2g).add(c2g.multiply(s3f));

  1316.             final FieldUnivariateDerivative2<T> eE = (Ep.cos().multiply(mean.getE().negate()).add(1.0)).reciprocal();
  1317.             final FieldUnivariateDerivative2<T> eE3 = eE.multiply(eE).multiply(eE);
  1318.             final FieldUnivariateDerivative2<T> sigma = eE.multiply(n.multiply(n)).multiply(eE).add(eE);

  1320.             // Semi-major axis
  1321.             final FieldUnivariateDerivative2<T> a = eE3.multiply(aCbis).add(appDrag.add(mean.getA())).
  1322.                                             add(aC).
  1323.                                             add(eE3.multiply(c2g2f).multiply(ac2g2f));

  1325.             // Eccentricity
  1326.             final FieldUnivariateDerivative2<T> e = d1e.add(eppDrag.add(mean.getE())).
  1327.                                             add(eC).
  1328.                                             add(cf1.multiply(ecf)).
  1329.                                             add(cf2.multiply(e2cf)).
  1330.                                             add(cf3.multiply(e3cf)).
  1331.                                             add(c2g2f.multiply(ec2f2g)).
  1332.                                             add(c2g2f.multiply(cf1).multiply(ecfc2f2g)).
  1333.                                             add(c2g2f.multiply(cf2).multiply(e2cfc2f2g)).
  1334.                                             add(c2g2f.multiply(cf3).multiply(e3cfc2f2g)).
  1335.                                             add(c2g1f.multiply(ec2gf)).
  1336.                                             add(c2g3f.multiply(ec2g3f));

  1338.             // Inclination
  1339.             final FieldUnivariateDerivative2<T> i = d1e.multiply(ide).
  1340.                                             add(mean.getI()).
  1341.                                             add(sf1.multiply(s2g2f.multiply(isfs2f2g))).
  1342.                                             add(cf1.multiply(c2g2f.multiply(icfc2f2g))).
  1343.                                             add(c2g2f.multiply(ic2f2g));

  1345.             // Argument of perigee + True anomaly
  1346.             final FieldUnivariateDerivative2<T> g_p_l = lp_p_gp.add(f.multiply(glf)).
  1347.                                              add(lpp.multiply(gll)).
  1348.                                              add(sf1.multiply(glsf)).
  1349.                                              add(sigma.multiply(sf1).multiply(glosf)).
  1350.                                              add(s2g2f.multiply(gls2f2g)).
  1351.                                              add(s2g1f.multiply(gls2gf)).
  1352.                                              add(sigma.multiply(s2g1f).multiply(glos2gf)).
  1353.                                              add(s2g3f.multiply(gls2g3f)).
  1354.                                              add(sigma.multiply(s2g3f).multiply(glos2g3f));


  1357.             // Longitude of ascending node
  1358.             final FieldUnivariateDerivative2<T> h = hp.add(f.multiply(hf)).
  1359.                                             add(lpp.multiply(hl)).
  1360.                                             add(sf1.multiply(hsf)).
  1361.                                             add(cf1.multiply(s2g2f).multiply(hcfs2g2f)).
  1362.                                             add(s2g2f.multiply(hs2g2f)).
  1363.                                             add(c2g2f.multiply(sf1).multiply(hsfc2g2f));

  1365.             final FieldUnivariateDerivative2<T> edl = s2g.multiply(edls2g).
  1366.                                             add(cg1.multiply(edlcg)).
  1367.                                             add(c3g.multiply(edlc3g)).
  1368.                                             add(sf1.multiply(edlsf)).
  1369.                                             add(s2g1f.multiply(edls2gf)).
  1370.                                             add(s2g3f.multiply(edls2g3f)).
  1371.                                             add(sf1.multiply(sigma).multiply(edlsf)).
  1372.                                             add(s2g1f.multiply(sigma).multiply(edls2gf.negate())).
  1373.                                             add(s2g3f.multiply(sigma).multiply(edls2g3f.multiply(3.0)));

  1375.             final FieldUnivariateDerivative2<T> A = e.multiply(lpp.cos()).subtract(edl.multiply(lpp.sin()));
  1376.             final FieldUnivariateDerivative2<T> B = e.multiply(lpp.sin()).add(edl.multiply(lpp.cos()));

  1378.             // True anomaly
  1379.             final FieldUnivariateDerivative2<T> l = FastMath.atan2(B, A);

  1381.             // Argument of perigee
  1382.             final FieldUnivariateDerivative2<T> g = g_p_l.subtract(l);

  1384.             // Return a keplerian orbit
  1385.             return new FieldKeplerianOrbit<>(a.getValue(), e.getValue(), i.getValue(),
  1386.                                              g.getValue(), h.getValue(), l.getValue(),
  1387.                                              a.getFirstDerivative(), e.getFirstDerivative(), i.getFirstDerivative(),
  1388.                                              g.getFirstDerivative(), h.getFirstDerivative(), l.getFirstDerivative(),
  1389.                                              PositionAngle.MEAN, mean.getFrame(), date, this.mu);

  1391.         }
  1392.     }

  1394.     /** {@inheritDoc} */
  1395.     @Override
  1396.     protected T getMass(final FieldAbsoluteDate<T> date) {
  1397.         return models.get(date).mass;
  1398.     }

  1400.     /** {@inheritDoc} */
  1401.     @Override
  1402.     protected List<ParameterDriver> getParametersDrivers() {
  1403.         return Collections.singletonList(M2Driver);
  1404.     }

  1406. }
Created with JaCoCo 0.8.8.202204050719