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    * Licensed to CS GROUP (CS) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *   http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
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  package org.orekit.propagation.analytical;
  
  import java.util.Collections;
  import java.util.List;
  
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.Field;
  import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
  import org.hipparchus.util.CombinatoricsUtils;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.FieldSinCos;
  import org.hipparchus.util.MathArrays;
  import org.hipparchus.util.MathUtils;
  import org.hipparchus.util.Precision;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.attitudes.InertialProvider;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider;
  import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics;
  import org.orekit.orbits.FieldKeplerianOrbit;
  import org.orekit.orbits.FieldOrbit;
  import org.orekit.orbits.OrbitType;
  import org.orekit.orbits.PositionAngle;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.PropagationType;
  import org.orekit.propagation.analytical.tle.FieldTLE;
  import org.orekit.time.FieldAbsoluteDate;
  import org.orekit.utils.FieldTimeSpanMap;
  import org.orekit.utils.ParameterDriver;
  
  /** This class propagates a {@link org.orekit.propagation.FieldSpacecraftState}
   *  using the analytical Brouwer-Lyddane model (from J2 to J5 zonal harmonics).
   * <p>
   * At the opposite of the {@link FieldEcksteinHechlerPropagator}, the Brouwer-Lyddane model is
   * suited for elliptical orbits, there is no problem having a rather small eccentricity or inclination
   * (Lyddane helped to solve this issue with the Brouwer model). Singularity for the critical
   * inclination i = 63.4° is avoided using the method developed in Warren Phipps' 1992 thesis.
   * <p>
   * By default, Brouwer-Lyddane model considers only the perturbations due to zonal harmonics.
   * However, for low Earth orbits, the magnitude of the perturbative acceleration due to
   * atmospheric drag can be significant. Warren Phipps' 1992 thesis considered the atmospheric
   * drag by time derivatives of the <i>mean</i> mean anomaly using the catch-all coefficient
   * {@link #M2Driver}.
   *
   * Usually, M2 is adjusted during an orbit determination process and it represents the
   * combination of all unmodeled secular along-track effects (i.e. not just the atmospheric drag).
   * The behavior of M2 is close to the {@link FieldTLE#getBStar()} parameter for the TLE.
   *
   * If the value of M2 is equal to {@link BrouwerLyddanePropagator#M2 0.0}, the along-track secular
   * effects are not considered in the dynamical model. Typical values for M2 are not known.
   * 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).
   * The unit of M2 is rad/s².
   *
   * The along-track effects, represented by the secular rates of the mean semi-major axis
   * and eccentricity, are computed following Eq. 2.38, 2.41, and 2.45 of Warren Phipps' thesis.
   *
   * @see "Brouwer, Dirk. Solution of the problem of artificial satellite theory without drag.
   *       YALE UNIV NEW HAVEN CT NEW HAVEN United States, 1959."
   *
   * @see "Lyddane, R. H. Small eccentricities or inclinations in the Brouwer theory of the
   *       artificial satellite. The Astronomical Journal 68 (1963): 555."
   *
   * @see "Phipps Jr, Warren E. Parallelization of the Navy Space Surveillance Center
   *       (NAVSPASUR) Satellite Model. NAVAL POSTGRADUATE SCHOOL MONTEREY CA, 1992."
   *
   * @author Melina Vanel
   * @author Bryan Cazabonne
   * @since 11.1
   */
  public class FieldBrouwerLyddanePropagator<T extends CalculusFieldElement<T>> extends FieldAbstractAnalyticalPropagator<T>  {
  
      /** Parameters scaling factor.
       * <p>
       * We use a power of 2 to avoid numeric noise introduction
       * in the multiplications/divisions sequences.
       * </p>
       */
      private static final double SCALE = FastMath.scalb(1.0, -20);
  
      /** Beta constant used by T2 function. */
      private static final double BETA = FastMath.scalb(100, -11);
  
     /** Initial Brouwer-Lyddane model. */
     private FieldBLModel<T> initialModel;
 
     /** All models. */
     private transient FieldTimeSpanMap<FieldBLModel<T>, T> models;
 
     /** Reference radius of the central body attraction model (m). */
     private double referenceRadius;
 
     /** Central attraction coefficient (m³/s²). */
     private T mu;
 
     /** Un-normalized zonal coefficients. */
     private double[] ck0;
 
     /** Empirical coefficient used in the drag modeling. */
     private final ParameterDriver M2Driver;
 
     /** Build a propagator from orbit and potential provider.
      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial orbit
      * @param provider for un-normalized zonal coefficients
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, UnnormalizedSphericalHarmonicsProvider, PropagationType, double)
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final UnnormalizedSphericalHarmonicsProvider provider,
                                          final double M2) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
              initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider,
              provider.onDate(initialOrbit.getDate().toAbsoluteDate()), M2);
     }
 
     /**
      * Private helper constructor.
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      * @param initialOrbit initial orbit
      * @param attitude attitude provider
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @param harmonics {@code provider.onDate(initialOrbit.getDate())}
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement,
      * UnnormalizedSphericalHarmonicsProvider, UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics, PropagationType, double)
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final AttitudeProvider attitude,
                                          final T mass,
                                          final UnnormalizedSphericalHarmonicsProvider provider,
                                          final UnnormalizedSphericalHarmonics harmonics,
                                          final double M2) {
         this(initialOrbit, attitude,  mass, provider.getAe(), initialOrbit.getA().getField().getZero().add(provider.getMu()),
              harmonics.getUnnormalizedCnm(2, 0),
              harmonics.getUnnormalizedCnm(3, 0),
              harmonics.getUnnormalizedCnm(4, 0),
              harmonics.getUnnormalizedCnm(5, 0),
              M2);
     }
 
     /** Build a propagator from orbit and potential.
      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      *
      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *
      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial orbit
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      * @see org.orekit.utils.Constants
      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, double, CalculusFieldElement, double, double, double, double, double)
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final double referenceRadius, final T mu,
                                          final double c20, final double c30, final double c40,
                                          final double c50, final double M2) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
              initialOrbit.getDate().getField().getZero().add(DEFAULT_MASS),
              referenceRadius, mu, c20, c30, c40, c50, M2);
     }
 
     /** Build a propagator from orbit, mass and potential provider.
      * <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial orbit
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, UnnormalizedSphericalHarmonicsProvider, double)
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit, final T mass,
                                          final UnnormalizedSphericalHarmonicsProvider provider,
                                          final double M2) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
              mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()), M2);
     }
 
     /** Build a propagator from orbit, mass and potential.
      * <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      *
      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *
      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial orbit
      * @param mass spacecraft mass
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, double, CalculusFieldElement, double, double, double, double, double)
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit, final T mass,
                                          final double referenceRadius, final T mu,
                                          final double c20, final double c30, final double c40,
                                          final double c50, final double M2) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
              mass, referenceRadius, mu, c20, c30, c40, c50, M2);
     }
 
     /** Build a propagator from orbit, attitude provider and potential provider.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      * @param initialOrbit initial orbit
      * @param attitudeProv attitude provider
      * @param provider for un-normalized zonal coefficients
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final AttitudeProvider attitudeProv,
                                          final UnnormalizedSphericalHarmonicsProvider provider,
                                          final double M2) {
         this(initialOrbit, attitudeProv, initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider,
              provider.onDate(initialOrbit.getDate().toAbsoluteDate()), M2);
     }
 
     /** Build a propagator from orbit, attitude provider and potential.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      *
      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *
      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial orbit
      * @param attitudeProv attitude provider
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final AttitudeProvider attitudeProv,
                                          final double referenceRadius, final T mu,
                                          final double c20, final double c30, final double c40,
                                          final double c50, final double M2) {
         this(initialOrbit, attitudeProv, initialOrbit.getDate().getField().getZero().add(DEFAULT_MASS),
              referenceRadius, mu, c20, c30, c40, c50, M2);
     }
 
     /** Build a propagator from orbit, attitude provider, mass and potential provider.
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      * @param initialOrbit initial orbit
      * @param attitudeProv attitude provider
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, UnnormalizedSphericalHarmonicsProvider, PropagationType, double)
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final AttitudeProvider attitudeProv,
                                          final T mass,
                                          final UnnormalizedSphericalHarmonicsProvider provider,
                                          final double M2) {
         this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()), M2);
     }
 
     /** Build a propagator from orbit, attitude provider, mass and potential.
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      *
      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *
      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial orbit
      * @param attitudeProv attitude provider
      * @param mass spacecraft mass
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      * @see #FieldBrouwerLyddanePropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, double, CalculusFieldElement, double, double, double, double, PropagationType, double)
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final AttitudeProvider attitudeProv,
                                          final T mass,
                                          final double referenceRadius, final T mu,
                                          final double c20, final double c30, final double c40,
                                          final double c50, final double M2) {
         this(initialOrbit, attitudeProv, mass, referenceRadius, mu, c20, c30, c40, c50, PropagationType.OSCULATING, M2);
     }
 
 
     /** Build a propagator from orbit and potential provider.
      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
      *
      * <p>Using this constructor, it is possible to define the initial orbit as
      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
      *
      * @param initialOrbit initial orbit
      * @param provider for un-normalized zonal coefficients
      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final UnnormalizedSphericalHarmonicsProvider provider,
                                          final PropagationType initialType,
                                          final double M2) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
              initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider,
              provider.onDate(initialOrbit.getDate().toAbsoluteDate()), initialType, M2);
     }
 
     /** Build a propagator from orbit, attitude provider, mass and potential provider.
      * <p>Using this constructor, it is possible to define the initial orbit as
      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
      * @param initialOrbit initial orbit
      * @param attitudeProv attitude provider
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final AttitudeProvider attitudeProv,
                                          final T mass,
                                          final UnnormalizedSphericalHarmonicsProvider provider,
                                          final PropagationType initialType,
                                          final double M2) {
         this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()), initialType, M2);
     }
 
     /**
      * Private helper constructor.
      * <p>Using this constructor, it is possible to define the initial orbit as
      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
      * @param initialOrbit initial orbit
      * @param attitude attitude provider
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @param harmonics {@code provider.onDate(initialOrbit.getDate())}
      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final AttitudeProvider attitude,
                                          final T mass,
                                          final UnnormalizedSphericalHarmonicsProvider provider,
                                          final UnnormalizedSphericalHarmonics harmonics,
                                          final PropagationType initialType,
                                          final double M2) {
         this(initialOrbit, attitude, mass, provider.getAe(), initialOrbit.getA().getField().getZero().add(provider.getMu()),
              harmonics.getUnnormalizedCnm(2, 0),
              harmonics.getUnnormalizedCnm(3, 0),
              harmonics.getUnnormalizedCnm(4, 0),
              harmonics.getUnnormalizedCnm(5, 0),
              initialType, M2);
     }
 
     /** Build a propagator from orbit, attitude provider, mass and potential.
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      *
      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *
      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, it is possible to define the initial orbit as
      * a mean Brouwer-Lyddane orbit or an osculating one.</p>
      *
      * @param initialOrbit initial orbit
      * @param attitudeProv attitude provider
      * @param mass spacecraft mass
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param initialType initial orbit type (mean Brouwer-Lyddane orbit or osculating orbit)
      * @param M2 value of empirical drag coefficient in rad/s².
      *        If equal to {@link BrouwerLyddanePropagator#M2} drag is not computed
      */
     public FieldBrouwerLyddanePropagator(final FieldOrbit<T> initialOrbit,
                                          final AttitudeProvider attitudeProv,
                                          final T mass,
                                          final double referenceRadius, final T mu,
                                          final double c20, final double c30, final double c40,
                                          final double c50,
                                          final PropagationType initialType,
                                          final double M2) {
 
         super(mass.getField(), attitudeProv);
 
         // store model coefficients
         this.referenceRadius = referenceRadius;
         this.mu  = mu;
         this.ck0 = new double[] {0.0, 0.0, c20, c30, c40, c50};
 
         // initialize M2 driver
         this.M2Driver = new ParameterDriver(BrouwerLyddanePropagator.M2_NAME, M2, SCALE,
                                             Double.NEGATIVE_INFINITY,
                                             Double.POSITIVE_INFINITY);
 
         // compute mean parameters if needed
         resetInitialState(new FieldSpacecraftState<>(initialOrbit,
                                                  attitudeProv.getAttitude(initialOrbit,
                                                                           initialOrbit.getDate(),
                                                                           initialOrbit.getFrame()),
                                                  mass),
                                                  initialType);
 
     }
 
 
     /** {@inheritDoc}
      * <p>The new initial state to consider
      * must be defined with an osculating orbit.</p>
      * @see #resetInitialState(FieldSpacecraftState, PropagationType)
      */
     @Override
     public void resetInitialState(final FieldSpacecraftState<T> state) {
         resetInitialState(state, PropagationType.OSCULATING);
     }
 
     /** Reset the propagator initial state.
      * @param state new initial state to consider
      * @param stateType mean Brouwer-Lyddane orbit or osculating orbit
      * @since 10.2
      */
     public void resetInitialState(final FieldSpacecraftState<T> state, final PropagationType stateType) {
         super.resetInitialState(state);
         final FieldKeplerianOrbit<T> keplerian = (FieldKeplerianOrbit<T>) OrbitType.KEPLERIAN.convertType(state.getOrbit());
         this.initialModel = (stateType == PropagationType.MEAN) ?
                              new FieldBLModel<>(keplerian, state.getMass(), referenceRadius, mu, ck0) :
                              computeMeanParameters(keplerian, state.getMass());
         this.models = new FieldTimeSpanMap<FieldBLModel<T>, T>(initialModel, state.getA().getField());
     }
 
     /** {@inheritDoc} */
     @Override
     protected void resetIntermediateState(final FieldSpacecraftState<T> state, final boolean forward) {
         final FieldBLModel<T> newModel = computeMeanParameters((FieldKeplerianOrbit<T>) OrbitType.KEPLERIAN.convertType(state.getOrbit()),
                                                        state.getMass());
         if (forward) {
             models.addValidAfter(newModel, state.getDate());
         } else {
             models.addValidBefore(newModel, state.getDate());
         }
         stateChanged(state);
     }
 
     /** Compute mean parameters according to the Brouwer-Lyddane analytical model computation
      * in order to do the propagation.
      * @param osculating osculating orbit
      * @param mass constant mass
      * @return Brouwer-Lyddane mean model
      */
     private FieldBLModel<T> computeMeanParameters(final FieldKeplerianOrbit<T> osculating, final T mass) {
 
         // sanity check
         if (osculating.getA().getReal() < referenceRadius) {
             throw new OrekitException(OrekitMessages.TRAJECTORY_INSIDE_BRILLOUIN_SPHERE,
                                            osculating.getA());
         }
 
         final Field<T> field = mass.getField();
         final T one = field.getOne();
         final T zero = field.getZero();
         // rough initialization of the mean parameters
         FieldBLModel<T> current = new FieldBLModel<T>(osculating, mass, referenceRadius, mu, ck0);
 
         // threshold for each parameter
         final T epsilon         = one.multiply(1.0e-13);
         final T thresholdA      = epsilon.multiply(current.mean.getA().abs().add(1.0));
         final T thresholdE      = epsilon.multiply(current.mean.getE().add(1.0));
         final T thresholdAngles = epsilon.multiply(one.getPi());
 
         int i = 0;
         while (i++ < 200) {
 
             // recompute the osculating parameters from the current mean parameters
             final FieldUnivariateDerivative2<T>[] parameters = current.propagateParameters(current.mean.getDate(), getParameters(mass.getField()));
 
             // adapted parameters residuals
             final T deltaA     = osculating.getA()  .subtract(parameters[0].getValue());
             final T deltaE     = osculating.getE()  .subtract(parameters[1].getValue());
             final T deltaI     = osculating.getI()  .subtract(parameters[2].getValue());
             final T deltaOmega = MathUtils.normalizeAngle(osculating.getPerigeeArgument().subtract(parameters[3].getValue()), zero);
             final T deltaRAAN  = MathUtils.normalizeAngle(osculating.getRightAscensionOfAscendingNode().subtract(parameters[4].getValue()), zero);
             final T deltaAnom  = MathUtils.normalizeAngle(osculating.getMeanAnomaly().subtract(parameters[5].getValue()), zero);
 
 
             // update mean parameters
             current = new FieldBLModel<T>(new FieldKeplerianOrbit<T>(current.mean.getA()            .add(deltaA),
                                                      current.mean.getE()                            .add(deltaE),
                                                      current.mean.getI()                            .add(deltaI),
                                                      current.mean.getPerigeeArgument()              .add(deltaOmega),
                                                      current.mean.getRightAscensionOfAscendingNode().add(deltaRAAN),
                                                      current.mean.getMeanAnomaly()                  .add(deltaAnom),
                                                      PositionAngle.MEAN,
                                                      current.mean.getFrame(),
                                                      current.mean.getDate(), mu),
                                   mass, referenceRadius, mu, ck0);
             // check convergence
             if (FastMath.abs(deltaA.getReal())     < thresholdA.getReal() &&
                 FastMath.abs(deltaE.getReal())     < thresholdE.getReal() &&
                 FastMath.abs(deltaI.getReal())     < thresholdAngles.getReal() &&
                 FastMath.abs(deltaOmega.getReal()) < thresholdAngles.getReal() &&
                 FastMath.abs(deltaRAAN.getReal())  < thresholdAngles.getReal() &&
                 FastMath.abs(deltaAnom.getReal())  < thresholdAngles.getReal()) {
                 return current;
             }
         }
         throw new OrekitException(OrekitMessages.UNABLE_TO_COMPUTE_BROUWER_LYDDANE_MEAN_PARAMETERS, i);
     }
 
 
     /** {@inheritDoc} */
     public FieldKeplerianOrbit<T> propagateOrbit(final FieldAbsoluteDate<T> date, final T[] parameters) {
         // compute Cartesian parameters, taking derivatives into account
         // to make sure velocity and acceleration are consistent
         final FieldBLModel<T> current = models.get(date);
         final FieldUnivariateDerivative2<T>[] propOrb_parameters = current.propagateParameters(date, parameters);
         return new FieldKeplerianOrbit<T>(propOrb_parameters[0].getValue(), propOrb_parameters[1].getValue(),
                                           propOrb_parameters[2].getValue(), propOrb_parameters[3].getValue(),
                                           propOrb_parameters[4].getValue(), propOrb_parameters[5].getValue(),
                                           PositionAngle.MEAN, current.mean.getFrame(), date, mu);
     }
 
     /**
      * Get the value of the M2 drag parameter.
      * @return the value of the M2 drag parameter
      */
     public double getM2() {
         return M2Driver.getValue();
     }
 
     /** Local class for Brouwer-Lyddane model. */
     private static class FieldBLModel<T extends CalculusFieldElement<T>> {
 
         /** Mean orbit. */
         private final FieldKeplerianOrbit<T> mean;
 
         /** Constant mass. */
         private final T mass;
 
         // CHECKSTYLE: stop JavadocVariable check
 
         // preprocessed values
 
         // Constant for secular terms l'', g'', h''
         // l standing for true anomaly, g for perigee argument and h for raan
         private final T xnotDot;
         private final T n;
         private final T lt;
         private final T gt;
         private final T ht;
 
 
         // Long periodT
         private final T dei3sg;
         private final T de2sg;
         private final T deisg;
         private final T de;
 
 
         private final T dlgs2g;
         private final T dlgc3g;
         private final T dlgcg;
 
 
         private final T dh2sgcg;
         private final T dhsgcg;
         private final T dhcg;
 
 
         // Short perioTs
         private final T aC;
         private final T aCbis;
         private final T ac2g2f;
 
 
         private final T eC;
         private final T ecf;
         private final T e2cf;
         private final T e3cf;
         private final T ec2f2g;
         private final T ecfc2f2g;
         private final T e2cfc2f2g;
         private final T e3cfc2f2g;
         private final T ec2gf;
         private final T ec2g3f;
 
 
         private final T ide;
         private final T isfs2f2g;
         private final T icfc2f2g;
         private final T ic2f2g;
 
 
         private final T glf;
         private final T gll;
         private final T glsf;
         private final T glosf;
         private final T gls2f2g;
         private final T gls2gf;
         private final T glos2gf;
         private final T gls2g3f;
         private final T glos2g3f;
 
 
         private final T hf;
         private final T hl;
         private final T hsf;
         private final T hcfs2g2f;
         private final T hs2g2f;
         private final T hsfc2g2f;
 
 
         private final T edls2g;
         private final T edlcg;
         private final T edlc3g;
         private final T edlsf;
         private final T edls2gf;
         private final T edls2g3f;
 
         // Drag terms
         private final T aRate;
         private final T eRate;
 
         // CHECKSTYLE: resume JavadocVariable check
 
         /** Create a model for specified mean orbit.
          * @param mean mean Fieldorbit
          * @param mass constant mass
          * @param referenceRadius reference radius of the central body attraction model (m)
          * @param mu central attraction coefficient (m³/s²)
          * @param ck0 un-normalized zonal coefficients
          */
         FieldBLModel(final FieldKeplerianOrbit<T> mean, final T mass,
                 final double referenceRadius, final T mu, final double[] ck0) {
 
             this.mean = mean;
             this.mass = mass;
             final T one  = mass.getField().getOne();
 
             final T app = mean.getA();
             xnotDot = mu.divide(app).sqrt().divide(app);
 
             // preliminary processing
             final T q = app.divide(referenceRadius).reciprocal();
             T ql = q.multiply(q);
             final T y2 = ql.multiply(-0.5 * ck0[2]);
 
             n = ((mean.getE().multiply(mean.getE()).negate()).add(1.0)).sqrt();
             final T n2 = n.multiply(n);
             final T n3 = n2.multiply(n);
             final T n4 = n2.multiply(n2);
             final T n6 = n4.multiply(n2);
             final T n8 = n4.multiply(n4);
             final T n10 = n8.multiply(n2);
 
             final T yp2 = y2.divide(n4);
             ql = ql.multiply(q);
             final T yp3 = ql.multiply(ck0[3]).divide(n6);
             ql = ql.multiply(q);
             final T yp4 = ql.multiply(0.375 * ck0[4]).divide(n8);
             ql = ql.multiply(q);
             final T yp5 = ql.multiply(ck0[5]).divide(n10);
 
 
             final FieldSinCos<T> sc = FastMath.sinCos(mean.getI());
             final T sinI1 = sc.sin();
             final T sinI2 = sinI1.multiply(sinI1);
             final T cosI1 = sc.cos();
             final T cosI2 = cosI1.multiply(cosI1);
             final T cosI3 = cosI2.multiply(cosI1);
             final T cosI4 = cosI2.multiply(cosI2);
             final T cosI6 = cosI4.multiply(cosI2);
             final T C5c2 = T2(cosI1).reciprocal();
             final T C3c2 = cosI2.multiply(3.0).subtract(1.0);
 
             final T epp = mean.getE();
             final T epp2 = epp.multiply(epp);
             final T epp3 = epp2.multiply(epp);
             final T epp4 = epp2.multiply(epp2);
 
             if (epp.getReal() >= 1) {
                 // Only for elliptical (e < 1) orbits
                 throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL,
                                           mean.getE().getReal());
             }
 
             // secular multiplicative
             lt = one.add(yp2.multiply(n).multiply(C3c2).multiply(1.5)).
                      add(yp2.multiply(0.09375).multiply(yp2).multiply(n).multiply(n2.multiply(25.0).add(n.multiply(16.0)).add(-15.0).
                              add(cosI2.multiply(n2.multiply(-90.0).add(n.multiply(-96.0)).add(30.0))).
                              add(cosI4.multiply(n2.multiply(25.0).add(n.multiply(144.0)).add(105.0))))).
                      add(yp4.multiply(0.9375).multiply(n).multiply(epp2).multiply(cosI4.multiply(35.0).add(cosI2.multiply(-30.0)).add(3.0)));
 
             gt = yp2.multiply(-1.5).multiply(C5c2).
                      add(yp2.multiply(0.09375).multiply(yp2).multiply(n2.multiply(25.0).add(n.multiply(24.0)).add(-35.0).
                             add(cosI2.multiply(n2.multiply(-126.0).add(n.multiply(-192.0)).add(90.0))).
                             add(cosI4.multiply(n2.multiply(45.0).add(n.multiply(360.0)).add(385.0))))).
                      add(yp4.multiply(0.3125).multiply(n2.multiply(-9.0).add(21.0).
                             add(cosI2.multiply(n2.multiply(126.0).add(-270.0))).
                             add(cosI4.multiply(n2.multiply(-189.0).add(385.0)))));
 
             ht = yp2.multiply(-3.0).multiply(cosI1).
                      add(yp2.multiply(0.375).multiply(yp2).multiply(cosI1.multiply(n2.multiply(9.0).add(n.multiply(12.0)).add(-5.0)).
                                                                     add(cosI3.multiply(n2.multiply(-5.0).add(n.multiply(-36.0)).add(-35.0))))).
                      add(yp4.multiply(1.25).multiply(cosI1).multiply(n2.multiply(-3.0).add(5.0)).multiply(cosI2.multiply(-7.0).add(3.0)));
 
             final T cA = one.subtract(cosI2.multiply(11.0)).subtract(cosI4.multiply(40.0).divide(C5c2));
             final T cB = one.subtract(cosI2.multiply(3.0)).subtract(cosI4.multiply(8.0).divide(C5c2));
             final T cC = one.subtract(cosI2.multiply(9.0)).subtract(cosI4.multiply(24.0).divide(C5c2));
             final T cD = one.subtract(cosI2.multiply(5.0)).subtract(cosI4.multiply(16.0).divide(C5c2));
 
             final T qyp2_4 = yp2.multiply(3.0).multiply(yp2).multiply(cA).
                              subtract(yp4.multiply(10.0).multiply(cB));
             final T qyp52 = cosI1.multiply(epp3).multiply(cD.multiply(0.5).divide(sinI1).
                                                           add(sinI1.multiply(cosI4.divide(C5c2).divide(C5c2).multiply(80.0).
                                                                              add(cosI2.divide(C5c2).multiply(32.0).
                                                                              add(5.0)))));
             final T qyp22 = epp2.add(2.0).subtract(epp2.multiply(3.0).add(2.0).multiply(11.0).multiply(cosI2)).
                             subtract(epp2.multiply(5.0).add(2.0).multiply(40.0).multiply(cosI4.divide(C5c2))).
                             subtract(epp2.multiply(400.0).multiply(cosI6).divide(C5c2).divide(C5c2));
             final T qyp42 = one.divide(5.0).multiply(qyp22.
                                                      add(one.multiply(4.0).multiply(epp2.
                                                                                     add(2.0).
                                                                                     subtract(cosI2.multiply(epp2.multiply(3.0).add(2.0))))));
             final T qyp52bis = cosI1.multiply(sinI1).multiply(epp).multiply(epp2.multiply(3.0).add(4.0)).
                                                                    multiply(cosI4.divide(C5c2).divide(C5c2).multiply(40.0).
                                                                             add(cosI2.divide(C5c2).multiply(16.0)).
                                                                             add(3.0));
            // long periodic multiplicative
             dei3sg =  yp5.divide(yp2).multiply(35.0 / 96.0).multiply(epp2).multiply(n2).multiply(cD).multiply(sinI1);
             de2sg = qyp2_4.divide(yp2).multiply(epp).multiply(n2).multiply(-1.0 / 12.0);
             deisg = sinI1.multiply(yp5.multiply(-35.0 / 128.0).divide(yp2).multiply(epp2).multiply(n2).multiply(cD).
                             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)))));
             de = epp2.multiply(n2).multiply(qyp2_4).divide(24.0).divide(yp2);
 
             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));
             dlgs2g = yp2.multiply(48.0).reciprocal().multiply(yp2.multiply(-3.0).multiply(yp2).multiply(qyp22).
                             add(yp4.multiply(10.0).multiply(qyp42))).
                             add(n3.divide(yp2).multiply(qyp2_4).divide(24.0));
             dlgc3g =  yp5.multiply(35.0 / 384.0).divide(yp2).multiply(n3).multiply(epp).multiply(cD).multiply(sinI1).
                             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)))));
             dlgcg = yp3.negate().multiply(cosI2).multiply(epp).divide(yp2.multiply(sinI1).multiply(4.0)).
                     add(yp5.divide(yp2).multiply(0.078125).multiply(cC).multiply(cosI2.divide(sinI1).multiply(epp.negate()).multiply(epp2.multiply(3.0).add(4.0)).
                                                                     add(sinI1.multiply(epp2).multiply(epp2.multiply(9.0).add(26.0)))).
                     subtract(yp5.divide(yp2).multiply(0.46875).multiply(qyp52bis).multiply(cosI1)).
                     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))).
                     add(yp5.divide(yp2).multiply(0.078125).multiply(n2).multiply(cC).multiply(qyp52quotient).multiply(sinI1)));
             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)).
                             subtract(yp4.multiply(10.0).multiply(cosI4.divide(sinI2).multiply(40.0).add(cosI2.divide(sinI1).multiply(16.0)).add(3.0)));
             dh2sgcg = yp5.divide(yp2).multiply(qyp52).multiply(35.0 / 144.0);
             dhsgcg = qyp24.multiply(cosI1).multiply(epp2.negate()).divide(yp2.multiply(12.0));
             dhcg = yp5.divide(yp2).multiply(qyp52).multiply(-35.0 / 576.0).
                    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))))).
                    add(yp5.multiply(qyp52bis).multiply(1.875).divide(yp2.multiply(4.0)));
 
             // short periodic multiplicative
             aC = yp2.negate().multiply(C3c2).multiply(app).divide(n3);
             aCbis = y2.multiply(app).multiply(C3c2);
             ac2g2f = y2.multiply(app).multiply(sinI2).multiply(3.0);
 
             T qe = y2.multiply(C3c2).multiply(0.5).multiply(n2).divide(n6);
             eC = qe.multiply(epp).divide(n3.add(1.0)).multiply(epp2.multiply(epp2.subtract(3.0)).add(3.0));
             ecf = qe.multiply(3.0);
             e2cf = qe.multiply(3.0).multiply(epp);
             e3cf = qe.multiply(epp2);
             qe = y2.multiply(0.5).multiply(n2).multiply(3.0).multiply(cosI2.negate().add(1.0)).divide(n6);
             ec2f2g = qe.multiply(epp);
             ecfc2f2g = qe.multiply(3.0);
             e2cfc2f2g = qe.multiply(3.0).multiply(epp);
             e3cfc2f2g = qe.multiply(epp2);
             qe = yp2.multiply(-0.5).multiply(n2).multiply(cosI2.negate().add(1.0));
             ec2gf = qe.multiply(3.0);
             ec2g3f = qe;
 
             T qi = yp2.multiply(epp).multiply(cosI1).multiply(sinI1);
             ide = cosI1.multiply(epp.negate()).divide(sinI1.multiply(n2));
             isfs2f2g = qi;
             icfc2f2g = qi.multiply(2.0);
             qi = yp2.multiply(cosI1).multiply(sinI1);
             ic2f2g = qi.multiply(1.5);
 
             T qgl1 = yp2.multiply(0.25);
             T qgl2 =  yp2.multiply(epp).multiply(n2).multiply(0.25).divide(n.add(1.0));
             glf = qgl1.multiply(C5c2).multiply(-6.0);
             gll = qgl1.multiply(C5c2).multiply(6.0);
             glsf = qgl1.multiply(C5c2).multiply(-6.0).multiply(epp).
                    add(qgl2.multiply(C3c2).multiply(2.0));
             glosf = qgl2.multiply(C3c2).multiply(2.0);
             qgl1 = qgl1.multiply(cosI2.multiply(-5.0).add(3.0));
             qgl2 = qgl2.multiply(3.0).multiply(cosI2.negate().add(1.0));
             gls2f2g = qgl1.multiply(3.0);
             gls2gf = qgl1.multiply(3.0).multiply(epp).
                      add(qgl2);
             glos2gf = qgl2.negate();
             gls2g3f = qgl1.multiply(epp).
                       add(qgl2.multiply(1.0 / 3.0));
             glos2g3f = qgl2;
 
             final T qh = yp2.multiply(cosI1).multiply(3.0);
             hf = qh.negate();
             hl = qh;
             hsf = qh.multiply(epp).negate();
             hcfs2g2f = yp2.multiply(cosI1).multiply(epp).multiply(2.0);
             hs2g2f = yp2.multiply(cosI1).multiply(1.5);
             hsfc2g2f = yp2.multiply(cosI1).multiply(epp).negate();
 
             final T qedl = yp2.multiply(n3).multiply(-0.25);
             edls2g = qyp2_4.multiply(1.0 / 24.0).multiply(epp).multiply(n3).divide(yp2);
             edlcg = yp3.divide(yp2).multiply(-0.25).multiply(n3).multiply(sinI1).
                     subtract(yp5.divide(yp2).multiply(0.078125).multiply(n3).multiply(sinI1).multiply(cC).multiply(epp2.multiply(9.0).add(4.0)));
             edlc3g = yp5.divide(yp2).multiply(n3).multiply(epp2).multiply(cD).multiply(sinI1).multiply(35.0 / 384.0);
             edlsf = qedl.multiply(C3c2).multiply(2.0);
             edls2gf = qedl.multiply(3.0).multiply(cosI2.negate().add(1.0));
             edls2g3f = qedl.multiply(1.0 / 3.0);
 
             // secular rates of the mean semi-major axis and eccentricity
             // Eq. 2.41 and Eq. 2.45 of Phipps' 1992 thesis
             aRate = app.multiply(-4.0).divide(xnotDot.multiply(3.0));
             eRate = epp.multiply(n).multiply(n).multiply(-4.0).divide(xnotDot.multiply(3.0));
 
         }
 
         /**
          * Accurate computation of E - e sin(E).
          *
          * @param E eccentric anomaly
          * @return E - e sin(E)
          */
         private FieldUnivariateDerivative2<T> eMeSinE(final FieldUnivariateDerivative2<T> E) {
             FieldUnivariateDerivative2<T> x = E.sin().multiply(mean.getE().negate().add(1.0));
             final FieldUnivariateDerivative2<T> mE2 = E.negate().multiply(E);
             FieldUnivariateDerivative2<T> term = E;
             FieldUnivariateDerivative2<T> d    = E.getField().getZero();
             // the inequality test below IS intentional and should NOT be replaced by a check with a small tolerance
             for (FieldUnivariateDerivative2<T> x0 = d.add(Double.NaN); !Double.valueOf(x.getValue().getReal()).equals(Double.valueOf(x0.getValue().getReal()));) {
                 d = d.add(2);
                 term = term.multiply(mE2.divide(d.multiply(d.add(1))));
                 x0 = x;
                 x = x.subtract(term);
             }
             return x;
         }
 
         /**
          * Gets eccentric anomaly from mean anomaly.
          * <p>The algorithm used to solve the Kepler equation has been published in:
          * "Procedures for  solving Kepler's Equation", A. W. Odell and R. H. Gooding,
          * Celestial Mechanics 38 (1986) 307-334</p>
          * <p>It has been copied from the OREKIT library (KeplerianOrbit class).</p>
          *
          * @param mk the mean anomaly (rad)
          * @return the eccentric anomaly (rad)
          */
         private FieldUnivariateDerivative2<T> getEccentricAnomaly(final FieldUnivariateDerivative2<T> mk) {
             final double k1 = 3 * FastMath.PI + 2;
             final double k2 = FastMath.PI - 1;
             final double k3 = 6 * FastMath.PI - 1;
             final double A  = 3.0 * k2 * k2 / k1;
             final double B  = k3 * k3 / (6.0 * k1);
 
             final T zero = mean.getE().getField().getZero();
 
             // reduce M to [-PI PI] interval
             final FieldUnivariateDerivative2<T> reducedM = new FieldUnivariateDerivative2<T>(MathUtils.normalizeAngle(mk.getValue(), zero ),
                                                                              mk.getFirstDerivative(),
                                                                              mk.getSecondDerivative());
 
             // compute start value according to A. W. Odell and R. H. Gooding S12 starter
             FieldUnivariateDerivative2<T> ek;
             if (reducedM.getValue().abs().getReal() < 1.0 / 6.0) {
                 if (reducedM.getValue().abs().getReal() < Precision.SAFE_MIN) {
                     // this is an Orekit change to the S12 starter.
                     // If reducedM is 0.0, the derivative of cbrt is infinite which induces NaN appearing later in
                     // the computation. As in this case E and M are almost equal, we initialize ek with reducedM
                     ek = reducedM;
                 } else {
                     // this is the standard S12 starter
                     ek = reducedM.add(reducedM.multiply(6).cbrt().subtract(reducedM).multiply(mean.getE()));
                 }
             } else {
                 if (reducedM.getValue().getReal() < 0) {
                     final FieldUnivariateDerivative2<T> w = reducedM.add(FastMath.PI);
                     ek = reducedM.add(w.multiply(-A).divide(w.subtract(B)).subtract(FastMath.PI).subtract(reducedM).multiply(mean.getE()));
                 } else {
                     final FieldUnivariateDerivative2<T> minusW = reducedM.subtract(FastMath.PI);
                     ek = reducedM.add(minusW.multiply(A).divide(minusW.add(B)).add(FastMath.PI).subtract(reducedM).multiply(mean.getE()));
                 }
             }
 
             final T e1 = mean.getE().negate().add(1.0);
             final boolean noCancellationRisk = (e1.add(ek.getValue().multiply(ek.getValue())).getReal() / 6) >= 0.1;
 
             // perform two iterations, each consisting of one Halley step and one Newton-Raphson step
             for (int j = 0; j < 2; ++j) {
                 final FieldUnivariateDerivative2<T> f;
                 FieldUnivariateDerivative2<T> fd;
                 final FieldUnivariateDerivative2<T> fdd  = ek.sin().multiply(mean.getE());
                 final FieldUnivariateDerivative2<T> fddd = ek.cos().multiply(mean.getE());
                 if (noCancellationRisk) {
                     f  = ek.subtract(fdd).subtract(reducedM);
                     fd = fddd.subtract(1).negate();
                 } else {
                     f  = eMeSinE(ek).subtract(reducedM);
                     final FieldUnivariateDerivative2<T> s = ek.multiply(0.5).sin();
                     fd = s.multiply(s).multiply(mean.getE().multiply(2.0)).add(e1);
                 }
                 final FieldUnivariateDerivative2<T> dee = f.multiply(fd).divide(f.multiply(0.5).multiply(fdd).subtract(fd.multiply(fd)));
 
                 // update eccentric anomaly, using expressions that limit underflow problems
                 final FieldUnivariateDerivative2<T> w = fd.add(dee.multiply(0.5).multiply(fdd.add(dee.multiply(fdd).divide(3))));
                 fd = fd.add(dee.multiply(fdd.add(dee.multiply(0.5).multiply(fdd))));
                 ek = ek.subtract(f.subtract(dee.multiply(fd.subtract(w))).divide(fd));
             }
 
             // expand the result back to original range
             ek = ek.add(mk.getValue().subtract(reducedM.getValue()));
 
             // Returns the eccentric anomaly
             return ek;
         }
 
         /**
          * This method is used in Brouwer-Lyddane model to avoid singularity at the
          * critical inclination (i = 63.4°).
          * <p>
          * This method, based on Warren Phipps's 1992 thesis (Eq. 2.47 and 2.48),
          * approximate the factor (1.0 - 5.0 * cos²(inc))^-1 (causing the singularity)
          * by a function, named T2 in the thesis.
          * </p>
          * @param cosInc cosine of the mean inclination
          * @return an approximation of (1.0 - 5.0 * cos²(inc))^-1 term
          */
         private T T2(final T cosInc) {
 
             // X = (1.0 - 5.0 * cos²(inc))
             final T x  = cosInc.multiply(cosInc).multiply(-5.0).add(1.0);
             final T x2 = x.multiply(x);
 
             // Eq. 2.48
             T sum = x.getField().getZero();
             for (int i = 0; i <= 12; i++) {
                 final double sign = i % 2 == 0 ? +1.0 : -1.0;
                 sum = sum.add(FastMath.pow(x2, i).multiply(FastMath.pow(BETA, i)).multiply(sign).divide(CombinatoricsUtils.factorialDouble(i + 1)));
             }
 
             // Right term of equation 2.47
             T product = x.getField().getOne();
             for (int i = 0; i <= 10; i++) {
                 product = product.multiply(FastMath.exp(x2.multiply(BETA).multiply(FastMath.scalb(-1.0, i))).add(1.0));
             }
 
             // Return (Eq. 2.47)
             return x.multiply(BETA).multiply(sum).multiply(product);
 
         }
 
         /** Extrapolate an orbit up to a specific target date.
          * @param date target date for the orbit
          * @param parameters model parameters
          * @return propagated parameters
          */
         public FieldUnivariateDerivative2<T>[] propagateParameters(final FieldAbsoluteDate<T> date, final T[] parameters) {
 
             // Field
             final Field<T> field = date.getField();
             final T one  = field.getOne();
             final T zero = field.getZero();
 
             // Empirical drag coefficient M2
             final T m2 = parameters[0];
 
             // Keplerian evolution
             final FieldUnivariateDerivative2<T> dt = new FieldUnivariateDerivative2<>(date.durationFrom(mean.getDate()), one, zero);
             final FieldUnivariateDerivative2<T> xnot = dt.multiply(xnotDot);
 
             //____________________________________
             // secular effects
 
             // mean mean anomaly
             final FieldUnivariateDerivative2<T> dtM2  = dt.multiply(m2);
             final FieldUnivariateDerivative2<T> dt2M2 = dt.multiply(dtM2);
             final FieldUnivariateDerivative2<T> lpp = new FieldUnivariateDerivative2<T>(MathUtils.normalizeAngle(mean.getMeanAnomaly().add(lt.multiply(xnot.getValue())).add(dt2M2.getValue()),
                                                                                         one.getPi()),
                                                                                         lt.multiply(xnotDot).add(dtM2.multiply(2.0).getValue()),
                                                                                         m2.multiply(2.0));
             // mean argument of perigee
             final FieldUnivariateDerivative2<T> gpp = new FieldUnivariateDerivative2<T>(MathUtils.normalizeAngle(mean.getPerigeeArgument().add(gt.multiply(xnot.getValue())),
                                                                                         one.getPi()),
                                                                                         gt.multiply(xnotDot),
                                                                                         zero);
             // mean longitude of ascending node
             final FieldUnivariateDerivative2<T> hpp = new FieldUnivariateDerivative2<T>(MathUtils.normalizeAngle(mean.getRightAscensionOfAscendingNode().add(ht.multiply(xnot.getValue())),
                                                                                         one.getPi()),
                                                                                         ht.multiply(xnotDot),
                                                                                         zero);
 
             // ________________________________________________
             // secular rates of the mean semi-major axis and eccentricity
 
             // semi-major axis
             final FieldUnivariateDerivative2<T> appDrag = dt.multiply(aRate.multiply(m2));
 
             // eccentricity
             final FieldUnivariateDerivative2<T> eppDrag = dt.multiply(eRate.multiply(m2));
 
             //____________________________________
             // Long periodical terms
             final FieldUnivariateDerivative2<T> cg1 = gpp.cos();
             final FieldUnivariateDerivative2<T> sg1 = gpp.sin();
             final FieldUnivariateDerivative2<T> c2g = cg1.multiply(cg1).subtract(sg1.multiply(sg1));
             final FieldUnivariateDerivative2<T> s2g = cg1.multiply(sg1).add(sg1.multiply(cg1));
             final FieldUnivariateDerivative2<T> c3g = c2g.multiply(cg1).subtract(s2g.multiply(sg1));
             final FieldUnivariateDerivative2<T> sg2 = sg1.multiply(sg1);
             final FieldUnivariateDerivative2<T> sg3 = sg1.multiply(sg2);
 
 
             // de eccentricity
             final FieldUnivariateDerivative2<T> d1e = sg3.multiply(dei3sg).
                                                add(sg1.multiply(deisg)).
                                                add(sg2.multiply(de2sg)).
                                                add(de);
 
             // l' + g'
             final FieldUnivariateDerivative2<T> lp_p_gp = s2g.multiply(dlgs2g).
                                                add(c3g.multiply(dlgc3g)).
                                                add(cg1.multiply(dlgcg)).
                                                add(lpp).
                                                add(gpp);
 
             // h'
             final FieldUnivariateDerivative2<T> hp = sg2.multiply(cg1).multiply(dh2sgcg).
                                                add(sg1.multiply(cg1).multiply(dhsgcg)).
                                                add(cg1.multiply(dhcg)).
                                                add(hpp);
 
             // Short periodical terms
             // eccentric anomaly
             final FieldUnivariateDerivative2<T> Ep = getEccentricAnomaly(lpp);
             final FieldUnivariateDerivative2<T> cf1 = (Ep.cos().subtract(mean.getE())).divide(Ep.cos().multiply(mean.getE().negate()).add(1.0));
             final FieldUnivariateDerivative2<T> sf1 = (Ep.sin().multiply(n)).divide(Ep.cos().multiply(mean.getE().negate()).add(1.0));
             final FieldUnivariateDerivative2<T> f = FastMath.atan2(sf1, cf1);
 
             final FieldUnivariateDerivative2<T> c2f = cf1.multiply(cf1).subtract(sf1.multiply(sf1));
             final FieldUnivariateDerivative2<T> s2f = cf1.multiply(sf1).add(sf1.multiply(cf1));
             final FieldUnivariateDerivative2<T> c3f = c2f.multiply(cf1).subtract(s2f.multiply(sf1));
             final FieldUnivariateDerivative2<T> s3f = c2f.multiply(sf1).add(s2f.multiply(cf1));
             final FieldUnivariateDerivative2<T> cf2 = cf1.multiply(cf1);
             final FieldUnivariateDerivative2<T> cf3 = cf1.multiply(cf2);
 
             final FieldUnivariateDerivative2<T> c2g1f = cf1.multiply(c2g).subtract(sf1.multiply(s2g));
             final FieldUnivariateDerivative2<T> c2g2f = c2f.multiply(c2g).subtract(s2f.multiply(s2g));
             final FieldUnivariateDerivative2<T> c2g3f = c3f.multiply(c2g).subtract(s3f.multiply(s2g));
             final FieldUnivariateDerivative2<T> s2g1f = cf1.multiply(s2g).add(c2g.multiply(sf1));
             final FieldUnivariateDerivative2<T> s2g2f = c2f.multiply(s2g).add(c2g.multiply(s2f));
             final FieldUnivariateDerivative2<T> s2g3f = c3f.multiply(s2g).add(c2g.multiply(s3f));
 
             final FieldUnivariateDerivative2<T> eE = (Ep.cos().multiply(mean.getE().negate()).add(1.0)).reciprocal();
             final FieldUnivariateDerivative2<T> eE3 = eE.multiply(eE).multiply(eE);
             final FieldUnivariateDerivative2<T> sigma = eE.multiply(n.multiply(n)).multiply(eE).add(eE);
 
             // Semi-major axis
             final FieldUnivariateDerivative2<T> a = eE3.multiply(aCbis).add(appDrag.add(mean.getA())).
                                             add(aC).
                                             add(eE3.multiply(c2g2f).multiply(ac2g2f));
 
             // Eccentricity
             final FieldUnivariateDerivative2<T> e = d1e.add(eppDrag.add(mean.getE())).
                                             add(eC).
                                             add(cf1.multiply(ecf)).
                                             add(cf2.multiply(e2cf)).
                                             add(cf3.multiply(e3cf)).
                                             add(c2g2f.multiply(ec2f2g)).
                                             add(c2g2f.multiply(cf1).multiply(ecfc2f2g)).
                                             add(c2g2f.multiply(cf2).multiply(e2cfc2f2g)).
                                             add(c2g2f.multiply(cf3).multiply(e3cfc2f2g)).
                                             add(c2g1f.multiply(ec2gf)).
                                             add(c2g3f.multiply(ec2g3f));
 
             // Inclination
             final FieldUnivariateDerivative2<T> i = d1e.multiply(ide).
                                             add(mean.getI()).
                                             add(sf1.multiply(s2g2f.multiply(isfs2f2g))).
                                             add(cf1.multiply(c2g2f.multiply(icfc2f2g))).
                                             add(c2g2f.multiply(ic2f2g));
 
             // Argument of perigee + True anomaly
             final FieldUnivariateDerivative2<T> g_p_l = lp_p_gp.add(f.multiply(glf)).
                                              add(lpp.multiply(gll)).
                                              add(sf1.multiply(glsf)).
                                              add(sigma.multiply(sf1).multiply(glosf)).
                                              add(s2g2f.multiply(gls2f2g)).
                                              add(s2g1f.multiply(gls2gf)).
                                              add(sigma.multiply(s2g1f).multiply(glos2gf)).
                                              add(s2g3f.multiply(gls2g3f)).
                                              add(sigma.multiply(s2g3f).multiply(glos2g3f));
 
 
             // Longitude of ascending node
             final FieldUnivariateDerivative2<T> h = hp.add(f.multiply(hf)).
                                             add(lpp.multiply(hl)).
                                             add(sf1.multiply(hsf)).
                                             add(cf1.multiply(s2g2f).multiply(hcfs2g2f)).
                                             add(s2g2f.multiply(hs2g2f)).
                                             add(c2g2f.multiply(sf1).multiply(hsfc2g2f));
 
             final FieldUnivariateDerivative2<T> edl = s2g.multiply(edls2g).
                                             add(cg1.multiply(edlcg)).
                                             add(c3g.multiply(edlc3g)).
                                             add(sf1.multiply(edlsf)).
                                             add(s2g1f.multiply(edls2gf)).
                                             add(s2g3f.multiply(edls2g3f)).
                                             add(sf1.multiply(sigma).multiply(edlsf)).
                                             add(s2g1f.multiply(sigma).multiply(edls2gf.negate())).
                                             add(s2g3f.multiply(sigma).multiply(edls2g3f.multiply(3.0)));
 
             final FieldUnivariateDerivative2<T> A = e.multiply(lpp.cos()).subtract(edl.multiply(lpp.sin()));
             final FieldUnivariateDerivative2<T> B = e.multiply(lpp.sin()).add(edl.multiply(lpp.cos()));
 
             // True anomaly
             final FieldUnivariateDerivative2<T> l = FastMath.atan2(B, A);
 
             // Argument of perigee
             final FieldUnivariateDerivative2<T> g = g_p_l.subtract(l);
 
             final FieldUnivariateDerivative2<T>[] FTD = MathArrays.buildArray(g.getField(), 6);
             FTD[0] = a;
             FTD[1] = e;
             FTD[2] = i;
             FTD[3] = g;
             FTD[4] = h;
             FTD[5] = l;
             return FTD;
         }
     }
 
     /** {@inheritDoc} */
     @Override
     protected T getMass(final FieldAbsoluteDate<T> date) {
         return models.get(date).mass;
     }
 
     /** {@inheritDoc} */
     @Override
     protected List<ParameterDriver> getParametersDrivers() {
         return Collections.singletonList(M2Driver);
     }
 
 }