FieldOrbit.java

  1. /* Copyright 2002-2019 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (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.orbits;



  21. import org.hipparchus.RealFieldElement;
  22. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  23. import org.hipparchus.linear.FieldDecompositionSolver;
  24. import org.hipparchus.linear.FieldLUDecomposition;
  25. import org.hipparchus.linear.FieldMatrix;
  26. import org.hipparchus.linear.MatrixUtils;
  27. import org.hipparchus.util.FastMath;
  28. import org.hipparchus.util.MathArrays;
  29. import org.orekit.errors.OrekitIllegalArgumentException;
  30. import org.orekit.errors.OrekitInternalError;
  31. import org.orekit.errors.OrekitMessages;
  32. import org.orekit.frames.Frame;
  33. import org.orekit.frames.Transform;
  34. import org.orekit.time.FieldAbsoluteDate;
  35. import org.orekit.time.FieldTimeInterpolable;
  36. import org.orekit.time.FieldTimeShiftable;
  37. import org.orekit.time.FieldTimeStamped;
  38. import org.orekit.utils.FieldPVCoordinates;
  39. import org.orekit.utils.FieldPVCoordinatesProvider;
  40. import org.orekit.utils.TimeStampedFieldPVCoordinates;
  41. import org.orekit.utils.TimeStampedPVCoordinates;

  43. /**
  44.  * This class handles orbital parameters.

  46.  * <p>
  47.  * For user convenience, both the Cartesian and the equinoctial elements
  48.  * are provided by this class, regardless of the canonical representation
  49.  * implemented in the derived class (which may be classical Keplerian
  50.  * elements for example).
  51.  * </p>
  52.  * <p>
  53.  * The parameters are defined in a frame specified by the user. It is important
  54.  * to make sure this frame is consistent: it probably is inertial and centered
  55.  * on the central body. This information is used for example by some
  56.  * force models.
  57.  * </p>
  58.  * <p>
  59.  * Instance of this class are guaranteed to be immutable.
  60.  * </p>
  61.  * @author Luc Maisonobe
  62.  * @author Guylaine Prat
  63.  * @author Fabien Maussion
  64.  * @author V&eacute;ronique Pommier-Maurussane
  65.  * @since 9.0
  66.  */
  67. public abstract class FieldOrbit<T extends RealFieldElement<T>>
  68.     implements FieldPVCoordinatesProvider<T>, FieldTimeStamped<T>, FieldTimeShiftable<FieldOrbit<T>, T>, FieldTimeInterpolable<FieldOrbit<T>, T> {

  70.     /** Frame in which are defined the orbital parameters. */
  71.     private final Frame frame;

  73.     /** Date of the orbital parameters. */
  74.     private final FieldAbsoluteDate<T> date;

  76.     /** Value of mu used to compute position and velocity (m³/s²). */
  77.     private final double mu;

  79.     /** Computed PVCoordinates. */
  80.     private transient TimeStampedFieldPVCoordinates<T> pvCoordinates;

  82.     /** Jacobian of the orbital parameters with mean angle with respect to the Cartesian coordinates. */
  83.     private transient T[][] jacobianMeanWrtCartesian;

  85.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with mean angle. */
  86.     private transient T[][] jacobianWrtParametersMean;

  88.     /** Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian coordinates. */
  89.     private transient T[][] jacobianEccentricWrtCartesian;

  91.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with eccentric angle. */
  92.     private transient T[][] jacobianWrtParametersEccentric;

  94.     /** Jacobian of the orbital parameters with true angle with respect to the Cartesian coordinates. */
  95.     private transient T[][] jacobianTrueWrtCartesian;

  97.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with true angle. */
  98.     private transient T[][] jacobianWrtParametersTrue;

  100.     /** Default constructor.
  101.      * Build a new instance with arbitrary default elements.
  102.      * @param frame the frame in which the parameters are defined
  103.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  104.      * @param date date of the orbital parameters
  105.      * @param mu central attraction coefficient (m^3/s^2)
  106.      * @exception IllegalArgumentException if frame is not a {@link
  107.      * Frame#isPseudoInertial pseudo-inertial frame}
  108.      */
  109.     protected FieldOrbit(final Frame frame, final FieldAbsoluteDate<T> date, final double mu)
  110.         throws IllegalArgumentException {
  111.         ensurePseudoInertialFrame(frame);
  112.         this.date                      = date;
  113.         this.mu                        = mu;
  114.         this.pvCoordinates             = null;
  115.         this.frame                     = frame;
  116.         jacobianMeanWrtCartesian       = null;
  117.         jacobianWrtParametersMean      = null;
  118.         jacobianEccentricWrtCartesian  = null;
  119.         jacobianWrtParametersEccentric = null;
  120.         jacobianTrueWrtCartesian       = null;
  121.         jacobianWrtParametersTrue      = null;
  122.     }

  124.     /** Set the orbit from Cartesian parameters.
  125.      *
  126.      * <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
  127.      * {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
  128.      * use {@code mu} and the position to compute the acceleration, including
  129.      * {@link #shiftedBy(RealFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
  130.      *
  131.      * @param FieldPVCoordinates the position and velocity in the inertial frame
  132.      * @param frame the frame in which the {@link TimeStampedPVCoordinates} are defined
  133.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  134.      * @param mu central attraction coefficient (m^3/s^2)
  135.      * @exception IllegalArgumentException if frame is not a {@link
  136.      * Frame#isPseudoInertial pseudo-inertial frame}
  137.      */
  138.     protected FieldOrbit(final TimeStampedFieldPVCoordinates<T> FieldPVCoordinates, final Frame frame, final double mu)
  139.         throws IllegalArgumentException {
  140.         ensurePseudoInertialFrame(frame);
  141.         this.date = FieldPVCoordinates.getDate();
  142.         this.mu = mu;
  143.         if (FieldPVCoordinates.getAcceleration().getNormSq().getReal() == 0.0) {
  144.             // the acceleration was not provided,
  145.             // compute it from Newtonian attraction
  146.             final T r2 = FieldPVCoordinates.getPosition().getNormSq();
  147.             final T r3 = r2.multiply(r2.sqrt());
  148.             this.pvCoordinates = new TimeStampedFieldPVCoordinates<>(FieldPVCoordinates.getDate(),
  149.                                                                      FieldPVCoordinates.getPosition(),
  150.                                                                      FieldPVCoordinates.getVelocity(),
  151.                                                                      new FieldVector3D<>(r3.reciprocal().multiply(-mu), FieldPVCoordinates.getPosition()));
  152.         } else {
  153.             this.pvCoordinates = FieldPVCoordinates;
  154.         }
  155.         this.frame = frame;
  156.     }

  158.     /** Check if Cartesian coordinates include non-Keplerian acceleration.
  159.      * @param pva Cartesian coordinates
  160.      * @param mu central attraction coefficient
  161.      * @param <T> type of the field elements
  162.      * @return true if Cartesian coordinates include non-Keplerian acceleration
  163.      */
  164.     protected static <T extends RealFieldElement<T>> boolean hasNonKeplerianAcceleration(final FieldPVCoordinates<T> pva, final double mu) {

  166.         final FieldVector3D<T> a = pva.getAcceleration();
  167.         if (a == null) {
  168.             return false;
  169.         }

  171.         final FieldVector3D<T> p = pva.getPosition();
  172.         final T r2 = p.getNormSq();
  173.         final T r  = r2.sqrt();
  174.         final FieldVector3D<T> keplerianAcceleration = new FieldVector3D<>(r.multiply(r2).reciprocal().multiply(-mu), p);
  175.         if (a.getNorm().getReal() > 1.0e-9 * keplerianAcceleration.getNorm().getReal()) {
  176.             // we have a relevant acceleration, we can compute derivatives
  177.             return true;
  178.         } else {
  179.             // the provided acceleration is either too small to be reliable (probably even 0), or NaN
  180.             return false;
  181.         }

  183.     }

  185.     /** Get the orbit type.
  186.      * @return orbit type
  187.      */
  188.     public abstract OrbitType getType();

  190.     /** Ensure the defining frame is a pseudo-inertial frame.
  191.      * @param frame frame to check
  192.      * @exception IllegalArgumentException if frame is not a {@link
  193.      * Frame#isPseudoInertial pseudo-inertial frame}
  194.      */
  195.     private static void ensurePseudoInertialFrame(final Frame frame)
  196.         throws IllegalArgumentException {
  197.         if (!frame.isPseudoInertial()) {
  198.             throw new OrekitIllegalArgumentException(OrekitMessages.NON_PSEUDO_INERTIAL_FRAME,
  199.                                                      frame.getName());
  200.         }
  201.     }

  203.     /** Get the frame in which the orbital parameters are defined.
  204.      * @return frame in which the orbital parameters are defined
  205.      */
  206.     public Frame getFrame() {
  207.         return frame;
  208.     }

  210.     /**Transforms the FieldOrbit instance into an Orbit instance.
  211.      * @return Orbit instance with same properties
  212.      */
  213.     public abstract Orbit toOrbit();

  215.     /** Get the semi-major axis.
  216.      * <p>Note that the semi-major axis is considered negative for hyperbolic orbits.</p>
  217.      * @return semi-major axis (m)
  218.      */
  219.     public abstract T getA();

  221.     /** Get the semi-major axis derivative.
  222.      * <p>Note that the semi-major axis is considered negative for hyperbolic orbits.</p>
  223.      * <p>
  224.      * If the orbit was created without derivatives, the value returned is null.
  225.      * </p>
  226.      * @return semi-major axis  derivative (m/s)
  227.      */
  228.     public abstract T getADot();

  230.     /** Get the first component of the equinoctial eccentricity vector.
  231.      * @return first component of the equinoctial eccentricity vector
  232.      */
  233.     public abstract T getEquinoctialEx();

  235.     /** Get the first component of the equinoctial eccentricity vector.
  236.      * <p>
  237.      * If the orbit was created without derivatives, the value returned is null.
  238.      * </p>
  239.      * @return first component of the equinoctial eccentricity vector
  240.      */
  241.     public abstract T getEquinoctialExDot();

  243.     /** Get the second component of the equinoctial eccentricity vector.
  244.      * @return second component of the equinoctial eccentricity vector
  245.      */
  246.     public abstract T getEquinoctialEy();

  248.     /** Get the second component of the equinoctial eccentricity vector.
  249.      * <p>
  250.      * If the orbit was created without derivatives, the value returned is null.
  251.      * </p>
  252.      * @return second component of the equinoctial eccentricity vector
  253.      */
  254.     public abstract T getEquinoctialEyDot();

  256.     /** Get the first component of the inclination vector.
  257.      * @return first component of the inclination vector
  258.      */
  259.     public abstract T getHx();

  261.     /** Get the first component of the inclination vector derivative.
  262.      * <p>
  263.      * If the orbit was created without derivatives, the value returned is null.
  264.      * </p>
  265.      * @return first component of the inclination vector derivative
  266.      */
  267.     public abstract T getHxDot();

  269.     /** Get the second component of the inclination vector.
  270.      * @return second component of the inclination vector
  271.      */
  272.     public abstract T getHy();

  274.     /** Get the second component of the inclination vector derivative.
  275.      * @return second component of the inclination vector derivative
  276.      */
  277.     public abstract T getHyDot();

  279.     /** Get the eccentric longitude argument.
  280.      * @return E + ω + Ω eccentric longitude argument (rad)
  281.      */
  282.     public abstract T getLE();

  284.     /** Get the eccentric longitude argument derivative.
  285.      * <p>
  286.      * If the orbit was created without derivatives, the value returned is null.
  287.      * </p>
  288.      * @return d(E + ω + Ω)/dt eccentric longitude argument derivative (rad/s)
  289.      */
  290.     public abstract T getLEDot();

  292.     /** Get the true longitude argument.
  293.      * @return v + ω + Ω true longitude argument (rad)
  294.      */
  295.     public abstract T getLv();

  297.     /** Get the true longitude argument derivative.
  298.      * <p>
  299.      * If the orbit was created without derivatives, the value returned is null.
  300.      * </p>
  301.      * @return d(v + ω + Ω)/dt true longitude argument derivative (rad/s)
  302.      */
  303.     public abstract T getLvDot();

  305.     /** Get the mean longitude argument.
  306.      * @return M + ω + Ω mean longitude argument (rad)
  307.      */
  308.     public abstract T getLM();

  310.     /** Get the mean longitude argument derivative.
  311.      * <p>
  312.      * If the orbit was created without derivatives, the value returned is null.
  313.      * </p>
  314.      * @return d(M + ω + Ω)/dt mean longitude argument derivative (rad/s)
  315.      */
  316.     public abstract T getLMDot();

  318.     // Additional orbital elements

  320.     /** Get the eccentricity.
  321.      * @return eccentricity
  322.      */
  323.     public abstract T getE();

  325.     /** Get the eccentricity derivative.
  326.      * <p>
  327.      * If the orbit was created without derivatives, the value returned is null.
  328.      * </p>
  329.      * @return eccentricity derivative
  330.      */
  331.     public abstract T getEDot();

  333.     /** Get the inclination.
  334.      * <p>
  335.      * If the orbit was created without derivatives, the value returned is null.
  336.      * </p>
  337.      * @return inclination (rad)
  338.      */
  339.     public abstract T getI();

  341.     /** Get the inclination derivative.
  342.      * @return inclination derivative (rad/s)
  343.      */
  344.     public abstract T getIDot();

  346.     /** Get the central acceleration constant.
  347.      * @return central acceleration constant
  348.      */

  350.     /** Check if orbit includes derivatives.
  351.      * @return true if orbit includes derivatives
  352.      * @see #getADot()
  353.      * @see #getEquinoctialExDot()
  354.      * @see #getEquinoctialEyDot()
  355.      * @see #getHxDot()
  356.      * @see #getHyDot()
  357.      * @see #getLEDot()
  358.      * @see #getLvDot()
  359.      * @see #getLMDot()
  360.      * @see #getEDot()
  361.      * @see #getIDot()
  362.      * @since 9.0
  363.      */
  364.     public abstract boolean hasDerivatives();

  366.     public double getMu() {
  367.         return mu;
  368.     }

  370.     /** Get the Keplerian period.
  371.      * <p>The Keplerian period is computed directly from semi major axis
  372.      * and central acceleration constant.</p>
  373.      * @return Keplerian period in seconds, or positive infinity for hyperbolic orbits
  374.      */
  375.     public T getKeplerianPeriod() {
  376.         final T a = getA();
  377.         return (a.getReal() < 0) ? getA().getField().getZero().add(Double.POSITIVE_INFINITY) : a.multiply(2 * FastMath.PI).multiply(a.divide(mu).sqrt());
  378.     }

  380.     /** Get the Keplerian mean motion.
  381.      * <p>The Keplerian mean motion is computed directly from semi major axis
  382.      * and central acceleration constant.</p>
  383.      * @return Keplerian mean motion in radians per second
  384.      */
  385.     public T getKeplerianMeanMotion() {
  386.         final T absA = getA().abs();
  387.         return absA.reciprocal().multiply(mu).sqrt().divide(absA);
  388.     }

  390.     /** Get the date of orbital parameters.
  391.      * @return date of the orbital parameters
  392.      */
  393.     public FieldAbsoluteDate<T> getDate() {
  394.         return date;
  395.     }

  397.     /** Get the {@link TimeStampedPVCoordinates} in a specified frame.
  398.      * @param outputFrame frame in which the position/velocity coordinates shall be computed
  399.      * @return FieldPVCoordinates in the specified output frame
  400.           * @see #getPVCoordinates()
  401.      */
  402.     public TimeStampedFieldPVCoordinates<T> getPVCoordinates(final Frame outputFrame) {
  403.         if (pvCoordinates == null) {
  404.             pvCoordinates = initPVCoordinates();
  405.         }

  407.         // If output frame requested is the same as definition frame,
  408.         // PV coordinates are returned directly
  409.         if (outputFrame == frame) {
  410.             return pvCoordinates;
  411.         }

  413.         // Else, PV coordinates are transformed to output frame
  414.         final Transform t = frame.getTransformTo(outputFrame, date.toAbsoluteDate()); //TODO CHECK THIS
  415.         return t.transformPVCoordinates(pvCoordinates);
  416.     }

  418.     /** {@inheritDoc} */
  419.     public TimeStampedFieldPVCoordinates<T> getPVCoordinates(final FieldAbsoluteDate<T> otherDate, final Frame otherFrame) {
  420.         return shiftedBy(otherDate.durationFrom(getDate())).getPVCoordinates(otherFrame);
  421.     }


  424.     /** Get the {@link TimeStampedPVCoordinates} in definition frame.
  425.      * @return FieldPVCoordinates in the definition frame
  426.      * @see #getPVCoordinates(Frame)
  427.      */
  428.     public TimeStampedFieldPVCoordinates<T> getPVCoordinates() {
  429.         if (pvCoordinates == null) {
  430.             pvCoordinates = initPVCoordinates();

  432.         }
  433.         return pvCoordinates;
  434.     }

  436.     /** Compute the position/velocity coordinates from the canonical parameters.
  437.      * @return computed position/velocity coordinates
  438.      */
  439.     protected abstract TimeStampedFieldPVCoordinates<T> initPVCoordinates();

  441.     /** Get a time-shifted orbit.
  442.      * <p>
  443.      * The orbit can be slightly shifted to close dates. This shift is based on
  444.      * a simple Keplerian model. It is <em>not</em> intended as a replacement
  445.      * for proper orbit and attitude propagation but should be sufficient for
  446.      * small time shifts or coarse accuracy.
  447.      * </p>
  448.      * @param dt time shift in seconds
  449.      * @return a new orbit, shifted with respect to the instance (which is immutable)
  450.      */
  451.     public abstract FieldOrbit<T> shiftedBy(T dt);

  453.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  454.      * <p>
  455.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  456.      * respect to Cartesian coordinate j. This means each row corresponds to one orbital parameter
  457.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  458.      * </p>
  459.      * @param type type of the position angle to use
  460.      * @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
  461.      * is larger than 6x6, only the 6x6 upper left corner will be modified
  462.      */
  463.     public void getJacobianWrtCartesian(final PositionAngle type, final T[][] jacobian) {

  465.         final T[][] cachedJacobian;
  466.         synchronized (this) {
  467.             switch (type) {
  468.                 case MEAN :
  469.                     if (jacobianMeanWrtCartesian == null) {
  470.                         // first call, we need to compute the Jacobian and cache it
  471.                         jacobianMeanWrtCartesian = computeJacobianMeanWrtCartesian();
  472.                     }
  473.                     cachedJacobian = jacobianMeanWrtCartesian;
  474.                     break;
  475.                 case ECCENTRIC :
  476.                     if (jacobianEccentricWrtCartesian == null) {
  477.                         // first call, we need to compute the Jacobian and cache it
  478.                         jacobianEccentricWrtCartesian = computeJacobianEccentricWrtCartesian();
  479.                     }
  480.                     cachedJacobian = jacobianEccentricWrtCartesian;
  481.                     break;
  482.                 case TRUE :
  483.                     if (jacobianTrueWrtCartesian == null) {
  484.                         // first call, we need to compute the Jacobian and cache it
  485.                         jacobianTrueWrtCartesian = computeJacobianTrueWrtCartesian();
  486.                     }
  487.                     cachedJacobian = jacobianTrueWrtCartesian;
  488.                     break;
  489.                 default :
  490.                     throw new OrekitInternalError(null);
  491.             }
  492.         }

  494.         // fill the user provided array
  495.         for (int i = 0; i < cachedJacobian.length; ++i) {
  496.             System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
  497.         }

  499.     }

  501.     /** Compute the Jacobian of the Cartesian parameters with respect to the orbital parameters.
  502.      * <p>
  503.      * Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i of the orbit with
  504.      * respect to orbital parameter j. This means each row corresponds to one Cartesian coordinate
  505.      * x, y, z, xdot, ydot, zdot whereas columns 0 to 5 correspond to the orbital parameters.
  506.      * </p>
  507.      * @param type type of the position angle to use
  508.      * @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
  509.      * is larger than 6x6, only the 6x6 upper left corner will be modified
  510.      */
  511.     public void getJacobianWrtParameters(final PositionAngle type, final T[][] jacobian) {

  513.         final T[][] cachedJacobian;
  514.         synchronized (this) {
  515.             switch (type) {
  516.                 case MEAN :
  517.                     if (jacobianWrtParametersMean == null) {
  518.                         // first call, we need to compute the Jacobian and cache it
  519.                         jacobianWrtParametersMean = createInverseJacobian(type);
  520.                     }
  521.                     cachedJacobian = jacobianWrtParametersMean;
  522.                     break;
  523.                 case ECCENTRIC :
  524.                     if (jacobianWrtParametersEccentric == null) {
  525.                         // first call, we need to compute the Jacobian and cache it
  526.                         jacobianWrtParametersEccentric = createInverseJacobian(type);
  527.                     }
  528.                     cachedJacobian = jacobianWrtParametersEccentric;
  529.                     break;
  530.                 case TRUE :
  531.                     if (jacobianWrtParametersTrue == null) {
  532.                         // first call, we need to compute the Jacobian and cache it
  533.                         jacobianWrtParametersTrue = createInverseJacobian(type);
  534.                     }
  535.                     cachedJacobian = jacobianWrtParametersTrue;
  536.                     break;
  537.                 default :
  538.                     throw new OrekitInternalError(null);
  539.             }
  540.         }

  542.         // fill the user-provided array
  543.         for (int i = 0; i < cachedJacobian.length; ++i) {
  544.             System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
  545.         }

  547.     }

  549.     /** Create an inverse Jacobian.
  550.      * @param type type of the position angle to use
  551.      * @return inverse Jacobian
  552.      */
  553.     private T[][] createInverseJacobian(final PositionAngle type) {

  555.         // get the direct Jacobian
  556.         final T[][] directJacobian = MathArrays.buildArray(getA().getField(), 6, 6);
  557.         getJacobianWrtCartesian(type, directJacobian);

  559.         // invert the direct Jacobian
  560.         final FieldMatrix<T> matrix = MatrixUtils.createFieldMatrix(directJacobian);
  561.         final FieldDecompositionSolver<T> solver = new FieldLUDecomposition<>(matrix).getSolver();
  562.         return solver.getInverse().getData();

  564.     }

  566.     /** Compute the Jacobian of the orbital parameters with mean angle with respect to the Cartesian parameters.
  567.      * <p>
  568.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  569.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  570.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  571.      * </p>
  572.      * @return 6x6 Jacobian matrix
  573.      * @see #computeJacobianEccentricWrtCartesian()
  574.      * @see #computeJacobianTrueWrtCartesian()
  575.      */
  576.     protected abstract T[][] computeJacobianMeanWrtCartesian();

  578.     /** Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.
  579.      * <p>
  580.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  581.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  582.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  583.      * </p>
  584.      * @return 6x6 Jacobian matrix
  585.      * @see #computeJacobianMeanWrtCartesian()
  586.      * @see #computeJacobianTrueWrtCartesian()
  587.      */
  588.     protected abstract T[][] computeJacobianEccentricWrtCartesian();

  590.     /** Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.
  591.      * <p>
  592.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  593.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  594.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  595.      * </p>
  596.      * @return 6x6 Jacobian matrix
  597.      * @see #computeJacobianMeanWrtCartesian()
  598.      * @see #computeJacobianEccentricWrtCartesian()
  599.      */
  600.     protected abstract T[][] computeJacobianTrueWrtCartesian();

  602.     /** Add the contribution of the Keplerian motion to parameters derivatives
  603.      * <p>
  604.      * This method is used by integration-based propagators to evaluate the part of Keplerian
  605.      * motion to evolution of the orbital state.
  606.      * </p>
  607.      * @param type type of the position angle in the state
  608.      * @param gm attraction coefficient to use
  609.      * @param pDot array containing orbital state derivatives to update (the Keplerian
  610.      * part must be <em>added</em> to the array components, as the array may already
  611.      * contain some non-zero elements corresponding to non-Keplerian parts)
  612.      */
  613.     public abstract void addKeplerContribution(PositionAngle type, double gm, T[] pDot);

  615.         /** Fill a Jacobian half row with a single vector.
  616.      * @param a coefficient of the vector
  617.      * @param v vector
  618.      * @param row Jacobian matrix row
  619.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  620.      */

  622.     protected void fillHalfRow(final T a, final FieldVector3D<T> v, final T[] row, final int j) {
  623.         row[j]     = a.multiply(v.getX());
  624.         row[j + 1] = a.multiply(v.getY());
  625.         row[j + 2] = a.multiply(v.getZ());
  626.     }

  628.     /** Fill a Jacobian half row with a linear combination of vectors.
  629.      * @param a1 coefficient of the first vector
  630.      * @param v1 first vector
  631.      * @param a2 coefficient of the second vector
  632.      * @param v2 second vector
  633.      * @param row Jacobian matrix row
  634.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  635.      */
  636.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
  637.                                       final T[] row, final int j) {
  638.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX());
  639.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY());
  640.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ());
  641. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX()));
  642. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY()));
  643. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ()));
  644.     }

  646.     /** Fill a Jacobian half row with a linear combination of vectors.
  647.      * @param a1 coefficient of the first vector
  648.      * @param v1 first vector
  649.      * @param a2 coefficient of the second vector
  650.      * @param v2 second vector
  651.      * @param a3 coefficient of the third vector
  652.      * @param v3 third vector
  653.      * @param row Jacobian matrix row
  654.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  655.      */
  656.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1,
  657.                                final T a2, final FieldVector3D<T> v2,
  658.                                final T a3, final FieldVector3D<T> v3,
  659.                                       final T[] row, final int j) {
  660.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX());
  661.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY());
  662.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ());



  666. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX()));
  667. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY()));
  668. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ()));
  669.     }

  671.     /** Fill a Jacobian half row with a linear combination of vectors.
  672.      * @param a1 coefficient of the first vector
  673.      * @param v1 first vector
  674.      * @param a2 coefficient of the second vector
  675.      * @param v2 second vector
  676.      * @param a3 coefficient of the third vector
  677.      * @param v3 third vector
  678.      * @param a4 coefficient of the fourth vector
  679.      * @param v4 fourth vector
  680.      * @param row Jacobian matrix row
  681.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  682.      */
  683.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
  684.                                       final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
  685.                                       final T[] row, final int j) {
  686.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX());
  687.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY());
  688.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ());
  689. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX()));
  690. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY()));
  691. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ()));
  692.     }

  694.     /** Fill a Jacobian half row with a linear combination of vectors.
  695.      * @param a1 coefficient of the first vector
  696.      * @param v1 first vector
  697.      * @param a2 coefficient of the second vector
  698.      * @param v2 second vector
  699.      * @param a3 coefficient of the third vector
  700.      * @param v3 third vector
  701.      * @param a4 coefficient of the fourth vector
  702.      * @param v4 fourth vector
  703.      * @param a5 coefficient of the fifth vector
  704.      * @param v5 fifth vector
  705.      * @param row Jacobian matrix row
  706.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  707.      */
  708.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
  709.                                       final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
  710.                                       final T a5, final FieldVector3D<T> v5,
  711.                                       final T[] row, final int j) {
  712.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX()).add(a5.multiply(v5.getX()));
  713.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY()).add(a5.multiply(v5.getY()));
  714.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ()).add(a5.multiply(v5.getZ()));

  716. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX())).add(a5.multiply(v5.getX()));
  717. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY())).add(a5.multiply(v5.getY()));
  718. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ())).add(a5.multiply(v5.getZ()));
  719.     }

  721.     /** Fill a Jacobian half row with a linear combination of vectors.
  722.      * @param a1 coefficient of the first vector
  723.      * @param v1 first vector
  724.      * @param a2 coefficient of the second vector
  725.      * @param v2 second vector
  726.      * @param a3 coefficient of the third vector
  727.      * @param v3 third vector
  728.      * @param a4 coefficient of the fourth vector
  729.      * @param v4 fourth vector
  730.      * @param a5 coefficient of the fifth vector
  731.      * @param v5 fifth vector
  732.      * @param a6 coefficient of the sixth vector
  733.      * @param v6 sixth vector
  734.      * @param row Jacobian matrix row
  735.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  736.      */
  737.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
  738.                                       final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
  739.                                       final T a5, final FieldVector3D<T> v5, final T a6, final FieldVector3D<T> v6,
  740.                                       final T[] row, final int j) {
  741.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX()).add(a1.linearCombination(a5, v5.getX(), a6, v6.getX()));
  742.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY()).add(a1.linearCombination(a5, v5.getY(), a6, v6.getY()));
  743.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ()).add(a1.linearCombination(a5, v5.getZ(), a6, v6.getZ()));


  746. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX())).add(a5.multiply(v5.getX())).add(a6.multiply(v6.getX()));
  747. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY())).add(a5.multiply(v5.getY())).add(a6.multiply(v6.getY()));
  748. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ())).add(a5.multiply(v5.getZ())).add(a6.multiply(v6.getZ()));
  749.     }


  752. }
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