EcksteinHechlerPropagator.java

  1. /* Copyright 2002-2024 CS GROUP
  2.  * Licensed to CS GROUP (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.propagation.analytical;

  19. import java.io.Serializable;

  21. import org.hipparchus.analysis.differentiation.UnivariateDerivative2;
  22. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  23. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  24. import org.hipparchus.linear.RealMatrix;
  25. import org.hipparchus.util.FastMath;
  26. import org.hipparchus.util.MathUtils;
  27. import org.hipparchus.util.SinCos;
  28. import org.orekit.attitudes.AttitudeProvider;
  29. import org.orekit.attitudes.FrameAlignedProvider;
  30. import org.orekit.errors.OrekitException;
  31. import org.orekit.errors.OrekitMessages;
  32. import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider;
  33. import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics;
  34. import org.orekit.orbits.CartesianOrbit;
  35. import org.orekit.orbits.CircularOrbit;
  36. import org.orekit.orbits.Orbit;
  37. import org.orekit.orbits.OrbitType;
  38. import org.orekit.orbits.PositionAngleType;
  39. import org.orekit.propagation.AbstractMatricesHarvester;
  40. import org.orekit.propagation.PropagationType;
  41. import org.orekit.propagation.SpacecraftState;
  42. import org.orekit.time.AbsoluteDate;
  43. import org.orekit.utils.DoubleArrayDictionary;
  44. import org.orekit.utils.TimeSpanMap;
  45. import org.orekit.utils.TimeStampedPVCoordinates;

  47. /** This class propagates a {@link org.orekit.propagation.SpacecraftState}
  48.  *  using the analytical Eckstein-Hechler model.
  49.  * <p>The Eckstein-Hechler model is suited for near circular orbits
  50.  * (e &lt; 0.1, with poor accuracy between 0.005 and 0.1) and inclination
  51.  * neither equatorial (direct or retrograde) nor critical (direct or
  52.  * retrograde).</p>
  53.  * <p>
  54.  * Note that before version 7.0, there was a large inconsistency in the generated
  55.  * orbits, and it was fixed as of version 7.0 of Orekit, with a visible side effect.
  56.  * The problems is that if the circular parameters produced by the Eckstein-Hechler
  57.  * model are used to build an orbit considered to be osculating, the velocity deduced
  58.  * from this orbit was <em>inconsistent with the position evolution</em>! The reason is
  59.  * that the model includes non-Keplerian effects but it does not include a corresponding
  60.  * circular/Cartesian conversion. As a consequence, all subsequent computation involving
  61.  * velocity were wrong. This includes attitude modes like yaw compensation and Doppler
  62.  * effect. As this effect was considered serious enough and as accurate velocities were
  63.  * considered important, the propagator now generates {@link CartesianOrbit Cartesian
  64.  * orbits} which are built in a special way to ensure consistency throughout propagation.
  65.  * A side effect is that if circular parameters are rebuilt by user from these propagated
  66.  * Cartesian orbit, the circular parameters will generally <em>not</em> match the initial
  67.  * orbit (differences in semi-major axis can exceed 120 m). The position however <em>will</em>
  68.  * match to sub-micrometer level, and this position will be identical to the positions
  69.  * that were generated by previous versions (in other words, the internals of the models
  70.  * have not been changed, only the output parameters have been changed). The correctness
  71.  * of the initialization has been assessed and is good, as it allows the subsequent orbit
  72.  * to remain close to a numerical reference orbit.
  73.  * </p>
  74.  * <p>
  75.  * If users need a more definitive initialization of an Eckstein-Hechler propagator, they
  76.  * should consider using a {@link org.orekit.propagation.conversion.PropagatorConverter
  77.  * propagator converter} to initialize their Eckstein-Hechler propagator using a complete
  78.  * sample instead of just a single initial orbit.
  79.  * </p>
  80.  * @see Orbit
  81.  * @author Guylaine Prat
  82.  */
  83. public class EcksteinHechlerPropagator extends AbstractAnalyticalPropagator {

  85.     /** Default convergence threshold for mean parameters conversion. */
  86.     private static final double EPSILON_DEFAULT = 1.0e-11;

  88.     /** Default value for maxIterations. */
  89.     private static final int MAX_ITERATIONS_DEFAULT = 100;

  91.     /** Initial Eckstein-Hechler model. */
  92.     private EHModel initialModel;

  94.     /** All models. */
  95.     private transient TimeSpanMap<EHModel> models;

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

  100.     /** Central attraction coefficient (m³/s²). */
  101.     private double mu;

  103.     /** Un-normalized zonal coefficients. */
  104.     private double[] ck0;

  106.     /** Build a propagator from orbit and potential provider.
  107.      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
  108.      *
  109.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  110.      *
  111.      * @param initialOrbit initial orbit
  112.      * @param provider for un-normalized zonal coefficients
  113.      * @see #EcksteinHechlerPropagator(Orbit, AttitudeProvider,
  114.      * UnnormalizedSphericalHarmonicsProvider)
  115.      * @see #EcksteinHechlerPropagator(Orbit, UnnormalizedSphericalHarmonicsProvider,
  116.      *                                 PropagationType)
  117.      */
  118.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  119.                                      final UnnormalizedSphericalHarmonicsProvider provider) {
  120.         this(initialOrbit, FrameAlignedProvider.of(initialOrbit.getFrame()),
  121.              DEFAULT_MASS, provider, provider.onDate(initialOrbit.getDate()));
  122.     }

  124.     /**
  125.      * Private helper constructor.
  126.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  127.      * @param initialOrbit initial orbit
  128.      * @param attitude attitude provider
  129.      * @param mass spacecraft mass
  130.      * @param provider for un-normalized zonal coefficients
  131.      * @param harmonics {@code provider.onDate(initialOrbit.getDate())}
  132.      * @see #EcksteinHechlerPropagator(Orbit, AttitudeProvider, double,
  133.      *                                 UnnormalizedSphericalHarmonicsProvider,
  134.      *                                 UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics,
  135.      *                                 PropagationType)
  136.      */
  137.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  138.                                      final AttitudeProvider attitude,
  139.                                      final double mass,
  140.                                      final UnnormalizedSphericalHarmonicsProvider provider,
  141.                                      final UnnormalizedSphericalHarmonics harmonics) {
  142.         this(initialOrbit, attitude, mass, provider.getAe(), provider.getMu(),
  143.              harmonics.getUnnormalizedCnm(2, 0),
  144.              harmonics.getUnnormalizedCnm(3, 0),
  145.              harmonics.getUnnormalizedCnm(4, 0),
  146.              harmonics.getUnnormalizedCnm(5, 0),
  147.              harmonics.getUnnormalizedCnm(6, 0));
  148.     }

  150.     /** Build a propagator from orbit and potential.
  151.      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
  152.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  153.      * are related to both the normalized coefficients
  154.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  155.      *  and the J<sub>n</sub> one as follows:</p>
  156.      *
  157.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  158.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  159.      *
  160.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  161.      *
  162.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  163.      *
  164.      * @param initialOrbit initial orbit
  165.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  166.      * @param mu central attraction coefficient (m³/s²)
  167.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  168.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  169.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  170.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  171.      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
  172.      * @see org.orekit.utils.Constants
  173.      * @see #EcksteinHechlerPropagator(Orbit, AttitudeProvider, double, double, double,
  174.      * double, double, double, double, double)
  175.      */
  176.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  177.                                      final double referenceRadius, final double mu,
  178.                                      final double c20, final double c30, final double c40,
  179.                                      final double c50, final double c60) {
  180.         this(initialOrbit, FrameAlignedProvider.of(initialOrbit.getFrame()),
  181.              DEFAULT_MASS, referenceRadius, mu, c20, c30, c40, c50, c60);
  182.     }

  184.     /** Build a propagator from orbit, mass and potential provider.
  185.      * <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
  186.      *
  187.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  188.      *
  189.      * @param initialOrbit initial orbit
  190.      * @param mass spacecraft mass
  191.      * @param provider for un-normalized zonal coefficients
  192.      * @see #EcksteinHechlerPropagator(Orbit, AttitudeProvider, double,
  193.      * UnnormalizedSphericalHarmonicsProvider)
  194.      */
  195.     public EcksteinHechlerPropagator(final Orbit initialOrbit, final double mass,
  196.                                      final UnnormalizedSphericalHarmonicsProvider provider) {
  197.         this(initialOrbit, FrameAlignedProvider.of(initialOrbit.getFrame()),
  198.              mass, provider, provider.onDate(initialOrbit.getDate()));
  199.     }

  201.     /** Build a propagator from orbit, mass and potential.
  202.      * <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
  203.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  204.      * are related to both the normalized coefficients
  205.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  206.      *  and the J<sub>n</sub> one as follows:</p>
  207.      *
  208.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  209.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  210.      *
  211.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  212.      *
  213.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  214.      *
  215.      * @param initialOrbit initial orbit
  216.      * @param mass spacecraft mass
  217.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  218.      * @param mu central attraction coefficient (m³/s²)
  219.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  220.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  221.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  222.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  223.      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
  224.      * @see #EcksteinHechlerPropagator(Orbit, AttitudeProvider, double, double, double,
  225.      * double, double, double, double, double)
  226.      */
  227.     public EcksteinHechlerPropagator(final Orbit initialOrbit, final double mass,
  228.                                      final double referenceRadius, final double mu,
  229.                                      final double c20, final double c30, final double c40,
  230.                                      final double c50, final double c60) {
  231.         this(initialOrbit, FrameAlignedProvider.of(initialOrbit.getFrame()),
  232.              mass, referenceRadius, mu, c20, c30, c40, c50, c60);
  233.     }

  235.     /** Build a propagator from orbit, attitude provider and potential provider.
  236.      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
  237.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  238.      * @param initialOrbit initial orbit
  239.      * @param attitudeProv attitude provider
  240.      * @param provider for un-normalized zonal coefficients
  241.      */
  242.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  243.                                      final AttitudeProvider attitudeProv,
  244.                                      final UnnormalizedSphericalHarmonicsProvider provider) {
  245.         this(initialOrbit, attitudeProv, DEFAULT_MASS, provider, provider.onDate(initialOrbit.getDate()));
  246.     }

  248.     /** Build a propagator from orbit, attitude provider and potential.
  249.      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
  250.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  251.      * are related to both the normalized coefficients
  252.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  253.      *  and the J<sub>n</sub> one as follows:</p>
  254.      *
  255.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  256.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  257.      *
  258.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  259.      *
  260.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  261.      *
  262.      * @param initialOrbit initial orbit
  263.      * @param attitudeProv attitude provider
  264.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  265.      * @param mu central attraction coefficient (m³/s²)
  266.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  267.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  268.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  269.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  270.      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
  271.      */
  272.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  273.                                      final AttitudeProvider attitudeProv,
  274.                                      final double referenceRadius, final double mu,
  275.                                      final double c20, final double c30, final double c40,
  276.                                      final double c50, final double c60) {
  277.         this(initialOrbit, attitudeProv, DEFAULT_MASS, referenceRadius, mu, c20, c30, c40, c50, c60);
  278.     }

  280.     /** Build a propagator from orbit, attitude provider, mass and potential provider.
  281.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  282.      * @param initialOrbit initial orbit
  283.      * @param attitudeProv attitude provider
  284.      * @param mass spacecraft mass
  285.      * @param provider for un-normalized zonal coefficients
  286.      * @see #EcksteinHechlerPropagator(Orbit, AttitudeProvider, double,
  287.      *                                 UnnormalizedSphericalHarmonicsProvider, PropagationType)
  288.      */
  289.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  290.                                      final AttitudeProvider attitudeProv,
  291.                                      final double mass,
  292.                                      final UnnormalizedSphericalHarmonicsProvider provider) {
  293.         this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate()));
  294.     }

  296.     /** Build a propagator from orbit, attitude provider, mass and potential.
  297.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  298.      * are related to both the normalized coefficients
  299.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  300.      *  and the J<sub>n</sub> one as follows:</p>
  301.      *
  302.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  303.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  304.      *
  305.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  306.      *
  307.      * <p>Using this constructor, an initial osculating orbit is considered.</p>
  308.      *
  309.      * @param initialOrbit initial orbit
  310.      * @param attitudeProv attitude provider
  311.      * @param mass spacecraft mass
  312.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  313.      * @param mu central attraction coefficient (m³/s²)
  314.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  315.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  316.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  317.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  318.      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
  319.      * @see #EcksteinHechlerPropagator(Orbit, AttitudeProvider, double, double, double,
  320.      *                                 double, double, double, double, double, PropagationType)
  321.      */
  322.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  323.                                      final AttitudeProvider attitudeProv,
  324.                                      final double mass,
  325.                                      final double referenceRadius, final double mu,
  326.                                      final double c20, final double c30, final double c40,
  327.                                      final double c50, final double c60) {
  328.         this(initialOrbit, attitudeProv, mass, referenceRadius, mu, c20, c30, c40, c50, c60,
  329.              PropagationType.OSCULATING);
  330.     }


  333.     /** Build a propagator from orbit and potential provider.
  334.      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
  335.      *
  336.      * <p>Using this constructor, it is possible to define the initial orbit as
  337.      * a mean Eckstein-Hechler orbit or an osculating one.</p>
  338.      *
  339.      * @param initialOrbit initial orbit
  340.      * @param provider for un-normalized zonal coefficients
  341.      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
  342.      * @since 10.2
  343.      */
  344.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  345.                                      final UnnormalizedSphericalHarmonicsProvider provider,
  346.                                      final PropagationType initialType) {
  347.         this(initialOrbit, FrameAlignedProvider.of(initialOrbit.getFrame()),
  348.              DEFAULT_MASS, provider, provider.onDate(initialOrbit.getDate()), initialType);
  349.     }

  351.     /** Build a propagator from orbit, attitude provider, mass and potential provider.
  352.      * <p>Using this constructor, it is possible to define the initial orbit as
  353.      * a mean Eckstein-Hechler orbit or an osculating one.</p>
  354.      * @param initialOrbit initial orbit
  355.      * @param attitudeProv attitude provider
  356.      * @param mass spacecraft mass
  357.      * @param provider for un-normalized zonal coefficients
  358.      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
  359.      * @since 10.2
  360.      */
  361.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  362.                                      final AttitudeProvider attitudeProv,
  363.                                      final double mass,
  364.                                      final UnnormalizedSphericalHarmonicsProvider provider,
  365.                                      final PropagationType initialType) {
  366.         this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate()), initialType);
  367.     }

  369.     /**
  370.      * Private helper constructor.
  371.      * <p>Using this constructor, it is possible to define the initial orbit as
  372.      * a mean Eckstein-Hechler orbit or an osculating one.</p>
  373.      * @param initialOrbit initial orbit
  374.      * @param attitude attitude provider
  375.      * @param mass spacecraft mass
  376.      * @param provider for un-normalized zonal coefficients
  377.      * @param harmonics {@code provider.onDate(initialOrbit.getDate())}
  378.      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
  379.      * @since 10.2
  380.      */
  381.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  382.                                      final AttitudeProvider attitude,
  383.                                      final double mass,
  384.                                      final UnnormalizedSphericalHarmonicsProvider provider,
  385.                                      final UnnormalizedSphericalHarmonics harmonics,
  386.                                      final PropagationType initialType) {
  387.         this(initialOrbit, attitude, mass, provider.getAe(), provider.getMu(),
  388.              harmonics.getUnnormalizedCnm(2, 0),
  389.              harmonics.getUnnormalizedCnm(3, 0),
  390.              harmonics.getUnnormalizedCnm(4, 0),
  391.              harmonics.getUnnormalizedCnm(5, 0),
  392.              harmonics.getUnnormalizedCnm(6, 0),
  393.              initialType);
  394.     }

  396.     /** Build a propagator from orbit, attitude provider, mass and potential.
  397.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  398.      * are related to both the normalized coefficients
  399.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  400.      *  and the J<sub>n</sub> one as follows:</p>
  401.      *
  402.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  403.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  404.      *
  405.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  406.      *
  407.      * <p>Using this constructor, it is possible to define the initial orbit as
  408.      * a mean Eckstein-Hechler orbit or an osculating one.</p>
  409.      *
  410.      * @param initialOrbit initial orbit
  411.      * @param attitudeProv attitude provider
  412.      * @param mass spacecraft mass
  413.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  414.      * @param mu central attraction coefficient (m³/s²)
  415.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  416.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  417.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  418.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  419.      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
  420.      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
  421.      * @since 10.2
  422.      */
  423.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  424.                                      final AttitudeProvider attitudeProv,
  425.                                      final double mass,
  426.                                      final double referenceRadius, final double mu,
  427.                                      final double c20, final double c30, final double c40,
  428.                                      final double c50, final double c60,
  429.                                      final PropagationType initialType) {
  430.         this(initialOrbit, attitudeProv, mass, referenceRadius, mu,
  431.              c20, c30, c40, c50, c60, initialType, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
  432.     }

  434.     /** Build a propagator from orbit, attitude provider, mass and potential.
  435.      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
  436.      * are related to both the normalized coefficients
  437.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  438.      *  and the J<sub>n</sub> one as follows:</p>
  439.      *
  440.      * <p> C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
  441.      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
  442.      *
  443.      * <p> C<sub>n,0</sub> = -J<sub>n</sub>
  444.      *
  445.      * <p>Using this constructor, it is possible to define the initial orbit as
  446.      * a mean Eckstein-Hechler orbit or an osculating one.</p>
  447.      *
  448.      * @param initialOrbit initial orbit
  449.      * @param attitudeProv attitude provider
  450.      * @param mass spacecraft mass
  451.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  452.      * @param mu central attraction coefficient (m³/s²)
  453.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  454.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  455.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  456.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  457.      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
  458.      * @param epsilon convergence threshold for mean parameters conversion
  459.      * @param maxIterations maximum iterations for mean parameters conversion
  460.      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
  461.      * @since 11.2
  462.      */
  463.     public EcksteinHechlerPropagator(final Orbit initialOrbit,
  464.                                      final AttitudeProvider attitudeProv,
  465.                                      final double mass,
  466.                                      final double referenceRadius, final double mu,
  467.                                      final double c20, final double c30, final double c40,
  468.                                      final double c50, final double c60,
  469.                                      final PropagationType initialType,
  470.                                      final double epsilon, final int maxIterations) {
  471.         super(attitudeProv);

  473.         // store model coefficients
  474.         this.referenceRadius = referenceRadius;
  475.         this.mu  = mu;
  476.         this.ck0 = new double[] {
  477.             0.0, 0.0, c20, c30, c40, c50, c60
  478.         };

  480.         // compute mean parameters if needed
  481.         // transform into circular adapted parameters used by the Eckstein-Hechler model
  482.         resetInitialState(new SpacecraftState(initialOrbit,
  483.                                               attitudeProv.getAttitude(initialOrbit,
  484.                                                                        initialOrbit.getDate(),
  485.                                                                        initialOrbit.getFrame()),
  486.                                               mass),
  487.                           initialType, epsilon, maxIterations);

  489.     }

  491.     /** Conversion from osculating to mean orbit.
  492.      * <p>
  493.      * Compute mean orbit <b>in a Eckstein-Hechler sense</b>, corresponding to the
  494.      * osculating SpacecraftState in input.
  495.      * </p>
  496.      * <p>
  497.      * Since the osculating orbit is obtained with the computation of
  498.      * short-periodic variation, the resulting output will depend on
  499.      * the gravity field parameterized in input.
  500.      * </p>
  501.      * <p>
  502.      * The computation is done through a fixed-point iteration process.
  503.      * </p>
  504.      * @param osculating osculating orbit to convert
  505.      * @param provider for un-normalized zonal coefficients
  506.      * @param harmonics {@code provider.onDate(osculating.getDate())}
  507.      * @return mean orbit in a Eckstein-Hechler sense
  508.      * @since 11.2
  509.      */
  510.     public static CircularOrbit computeMeanOrbit(final Orbit osculating,
  511.                                                  final UnnormalizedSphericalHarmonicsProvider provider,
  512.                                                  final UnnormalizedSphericalHarmonics harmonics) {
  513.         return computeMeanOrbit(osculating, provider, harmonics, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
  514.     }

  516.     /** Conversion from osculating to mean orbit.
  517.      * <p>
  518.      * Compute mean orbit <b>in a Eckstein-Hechler sense</b>, corresponding to the
  519.      * osculating SpacecraftState in input.
  520.      * </p>
  521.      * <p>
  522.      * Since the osculating orbit is obtained with the computation of
  523.      * short-periodic variation, the resulting output will depend on
  524.      * the gravity field parameterized in input.
  525.      * </p>
  526.      * <p>
  527.      * The computation is done through a fixed-point iteration process.
  528.      * </p>
  529.      * @param osculating osculating orbit to convert
  530.      * @param provider for un-normalized zonal coefficients
  531.      * @param harmonics {@code provider.onDate(osculating.getDate())}
  532.      * @param epsilon convergence threshold for mean parameters conversion
  533.      * @param maxIterations maximum iterations for mean parameters conversion
  534.      * @return mean orbit in a Eckstein-Hechler sense
  535.      * @since 11.2
  536.      */
  537.     public static CircularOrbit computeMeanOrbit(final Orbit osculating,
  538.                                                  final UnnormalizedSphericalHarmonicsProvider provider,
  539.                                                  final UnnormalizedSphericalHarmonics harmonics,
  540.                                                  final double epsilon, final int maxIterations) {
  541.         return computeMeanOrbit(osculating,
  542.                                 provider.getAe(), provider.getMu(),
  543.                                 harmonics.getUnnormalizedCnm(2, 0),
  544.                                 harmonics.getUnnormalizedCnm(3, 0),
  545.                                 harmonics.getUnnormalizedCnm(4, 0),
  546.                                 harmonics.getUnnormalizedCnm(5, 0),
  547.                                 harmonics.getUnnormalizedCnm(6, 0),
  548.                                 epsilon, maxIterations);
  549.     }

  551.     /** Conversion from osculating to mean orbit.
  552.      * <p>
  553.      * Compute mean orbit <b>in a Eckstein-Hechler sense</b>, corresponding to the
  554.      * osculating SpacecraftState in input.
  555.      * </p>
  556.      * <p>
  557.      * Since the osculating orbit is obtained with the computation of
  558.      * short-periodic variation, the resulting output will depend on
  559.      * the gravity field parameterized in input.
  560.      * </p>
  561.      * <p>
  562.      * The computation is done through a fixed-point iteration process.
  563.      * </p>
  564.      * @param osculating osculating orbit to convert
  565.      * @param referenceRadius reference radius of the Earth for the potential model (m)
  566.      * @param mu central attraction coefficient (m³/s²)
  567.      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
  568.      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
  569.      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
  570.      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
  571.      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
  572.      * @param epsilon convergence threshold for mean parameters conversion
  573.      * @param maxIterations maximum iterations for mean parameters conversion
  574.      * @return mean orbit in a Eckstein-Hechler sense
  575.      * @since 11.2
  576.      */
  577.     public static CircularOrbit computeMeanOrbit(final Orbit osculating,
  578.                                                  final double referenceRadius, final double mu,
  579.                                                  final double c20, final double c30, final double c40,
  580.                                                  final double c50, final double c60,
  581.                                                  final double epsilon, final int maxIterations) {
  582.         final EcksteinHechlerPropagator propagator =
  583.                         new EcksteinHechlerPropagator(osculating,
  584.                                                       FrameAlignedProvider.of(osculating.getFrame()),
  585.                                                       DEFAULT_MASS,
  586.                                                       referenceRadius, mu, c20, c30, c40, c50, c60,
  587.                                                       PropagationType.OSCULATING, epsilon, maxIterations);
  588.         return propagator.initialModel.mean;
  589.     }

  591.     /** {@inheritDoc}
  592.      * <p>The new initial state to consider
  593.      * must be defined with an osculating orbit.</p>
  594.      * @see #resetInitialState(SpacecraftState, PropagationType)
  595.      */
  596.     public void resetInitialState(final SpacecraftState state) {
  597.         resetInitialState(state, PropagationType.OSCULATING);
  598.     }

  600.     /** Reset the propagator initial state.
  601.      * @param state new initial state to consider
  602.      * @param stateType mean Eckstein-Hechler orbit or osculating orbit
  603.      * @since 10.2
  604.      */
  605.     public void resetInitialState(final SpacecraftState state, final PropagationType stateType) {
  606.         resetInitialState(state, stateType, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
  607.     }

  609.     /** Reset the propagator initial state.
  610.      * @param state new initial state to consider
  611.      * @param stateType mean Eckstein-Hechler orbit or osculating orbit
  612.      * @param epsilon convergence threshold for mean parameters conversion
  613.      * @param maxIterations maximum iterations for mean parameters conversion
  614.      * @since 11.2
  615.      */
  616.     public void resetInitialState(final SpacecraftState state, final PropagationType stateType,
  617.                                   final double epsilon, final int maxIterations) {
  618.         super.resetInitialState(state);
  619.         final CircularOrbit circular = (CircularOrbit) OrbitType.CIRCULAR.convertType(state.getOrbit());
  620.         this.initialModel = (stateType == PropagationType.MEAN) ?
  621.                              new EHModel(circular, state.getMass(), referenceRadius, mu, ck0) :
  622.                              computeMeanParameters(circular, state.getMass(), epsilon, maxIterations);
  623.         this.models = new TimeSpanMap<EHModel>(initialModel);
  624.     }

  626.     /** {@inheritDoc} */
  627.     protected void resetIntermediateState(final SpacecraftState state, final boolean forward) {
  628.         resetIntermediateState(state, forward, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
  629.     }

  631.     /** Reset an intermediate state.
  632.      * @param state new intermediate state to consider
  633.      * @param forward if true, the intermediate state is valid for
  634.      * propagations after itself
  635.      * @param epsilon convergence threshold for mean parameters conversion
  636.      * @param maxIterations maximum iterations for mean parameters conversion
  637.      * @since 11.2
  638.      */
  639.     protected void resetIntermediateState(final SpacecraftState state, final boolean forward,
  640.                                           final double epsilon, final int maxIterations) {
  641.         final EHModel newModel = computeMeanParameters((CircularOrbit) OrbitType.CIRCULAR.convertType(state.getOrbit()),
  642.                                                        state.getMass(), epsilon, maxIterations);
  643.         if (forward) {
  644.             models.addValidAfter(newModel, state.getDate(), false);
  645.         } else {
  646.             models.addValidBefore(newModel, state.getDate(), false);
  647.         }
  648.         stateChanged(state);
  649.     }


  652.     /** Compute mean parameters according to the Eckstein-Hechler analytical model.
  653.      * @param osculating osculating orbit
  654.      * @param mass constant mass
  655.      * @param epsilon convergence threshold for mean parameters conversion
  656.      * @param maxIterations maximum iterations for mean parameters conversion
  657.      * @return Eckstein-Hechler mean model
  658.      */
  659.     private EHModel computeMeanParameters(final CircularOrbit osculating, final double mass,
  660.                                           final double epsilon, final int maxIterations) {

  662.         // sanity check
  663.         if (osculating.getA() < referenceRadius) {
  664.             throw new OrekitException(OrekitMessages.TRAJECTORY_INSIDE_BRILLOUIN_SPHERE,
  665.                                       osculating.getA());
  666.         }

  668.         // rough initialization of the mean parameters
  669.         EHModel current = new EHModel(osculating, mass, referenceRadius, mu, ck0);

  671.         // threshold for each parameter
  672.         final double thresholdA      = epsilon * (1 + FastMath.abs(current.mean.getA()));
  673.         final double thresholdE      = epsilon * (1 + current.mean.getE());
  674.         final double thresholdAngles = epsilon * MathUtils.TWO_PI;

  676.         int i = 0;
  677.         while (i++ < maxIterations) {

  679.             // recompute the osculating parameters from the current mean parameters
  680.             final UnivariateDerivative2[] parameters = current.propagateParameters(current.mean.getDate());

  682.             // adapted parameters residuals
  683.             final double deltaA      = osculating.getA()          - parameters[0].getValue();
  684.             final double deltaEx     = osculating.getCircularEx() - parameters[1].getValue();
  685.             final double deltaEy     = osculating.getCircularEy() - parameters[2].getValue();
  686.             final double deltaI      = osculating.getI()          - parameters[3].getValue();
  687.             final double deltaRAAN   = MathUtils.normalizeAngle(osculating.getRightAscensionOfAscendingNode() -
  688.                                                                 parameters[4].getValue(),
  689.                                                                 0.0);
  690.             final double deltaAlphaM = MathUtils.normalizeAngle(osculating.getAlphaM() - parameters[5].getValue(), 0.0);

  692.             // update mean parameters
  693.             current = new EHModel(new CircularOrbit(current.mean.getA()          + deltaA,
  694.                                                     current.mean.getCircularEx() + deltaEx,
  695.                                                     current.mean.getCircularEy() + deltaEy,
  696.                                                     current.mean.getI()          + deltaI,
  697.                                                     current.mean.getRightAscensionOfAscendingNode() + deltaRAAN,
  698.                                                     current.mean.getAlphaM()     + deltaAlphaM,
  699.                                                     PositionAngleType.MEAN,
  700.                                                     current.mean.getFrame(),
  701.                                                     current.mean.getDate(), mu),
  702.                                   mass, referenceRadius, mu, ck0);

  704.             // check convergence
  705.             if (FastMath.abs(deltaA)      < thresholdA &&
  706.                 FastMath.abs(deltaEx)     < thresholdE &&
  707.                 FastMath.abs(deltaEy)     < thresholdE &&
  708.                 FastMath.abs(deltaI)      < thresholdAngles &&
  709.                 FastMath.abs(deltaRAAN)   < thresholdAngles &&
  710.                 FastMath.abs(deltaAlphaM) < thresholdAngles) {
  711.                 return current;
  712.             }

  714.         }

  716.         throw new OrekitException(OrekitMessages.UNABLE_TO_COMPUTE_ECKSTEIN_HECHLER_MEAN_PARAMETERS, i);

  718.     }

  720.     /** {@inheritDoc} */
  721.     public CartesianOrbit propagateOrbit(final AbsoluteDate date) {
  722.         // compute Cartesian parameters, taking derivatives into account
  723.         // to make sure velocity and acceleration are consistent
  724.         final EHModel current = models.get(date);
  725.         return new CartesianOrbit(toCartesian(date, current.propagateParameters(date)),
  726.                                   current.mean.getFrame(), mu);
  727.     }

  729.     /**
  730.      * Get the central attraction coefficient μ.
  731.      * @return mu central attraction coefficient (m³/s²)
  732.      * @since 11.1
  733.      */
  734.     public double getMu() {
  735.         return mu;
  736.     }

  738.     /**
  739.      * Get the un-normalized zonal coefficients.
  740.      * @return the un-normalized zonal coefficients
  741.      * @since 11.1
  742.      */
  743.     public double[] getCk0() {
  744.         return ck0.clone();
  745.     }

  747.     /**
  748.      * Get the reference radius of the central body attraction model.
  749.      * @return the reference radius in meters
  750.      * @since 11.1
  751.      */
  752.     public double getReferenceRadius() {
  753.         return referenceRadius;
  754.     }

  756.     /** {@inheritDoc} */
  757.     @Override
  758.     protected AbstractMatricesHarvester createHarvester(final String stmName, final RealMatrix initialStm,
  759.                                                         final DoubleArrayDictionary initialJacobianColumns) {
  760.         // Create the harvester
  761.         final EcksteinHechlerHarvester harvester = new EcksteinHechlerHarvester(this, stmName, initialStm, initialJacobianColumns);
  762.         // Update the list of additional state provider
  763.         addAdditionalStateProvider(harvester);
  764.         // Return the configured harvester
  765.         return harvester;
  766.     }

  768.     /** Local class for Eckstein-Hechler model, with fixed mean parameters. */
  769.     private static class EHModel implements Serializable {

  771.         /** Serializable UID. */
  772.         private static final long serialVersionUID = 20160115L;

  774.         /** Mean orbit. */
  775.         private final CircularOrbit mean;

  777.         /** Constant mass. */
  778.         private final double mass;

  780.         // CHECKSTYLE: stop JavadocVariable check

  782.         // preprocessed values
  783.         private final double xnotDot;
  784.         private final double rdpom;
  785.         private final double rdpomp;
  786.         private final double eps1;
  787.         private final double eps2;
  788.         private final double xim;
  789.         private final double ommD;
  790.         private final double rdl;
  791.         private final double aMD;

  793.         private final double kh;
  794.         private final double kl;

  796.         private final double ax1;
  797.         private final double ay1;
  798.         private final double as1;
  799.         private final double ac2;
  800.         private final double axy3;
  801.         private final double as3;
  802.         private final double ac4;
  803.         private final double as5;
  804.         private final double ac6;

  806.         private final double ex1;
  807.         private final double exx2;
  808.         private final double exy2;
  809.         private final double ex3;
  810.         private final double ex4;

  812.         private final double ey1;
  813.         private final double eyx2;
  814.         private final double eyy2;
  815.         private final double ey3;
  816.         private final double ey4;

  818.         private final double rx1;
  819.         private final double ry1;
  820.         private final double r2;
  821.         private final double r3;
  822.         private final double rl;

  824.         private final double iy1;
  825.         private final double ix1;
  826.         private final double i2;
  827.         private final double i3;
  828.         private final double ih;

  830.         private final double lx1;
  831.         private final double ly1;
  832.         private final double l2;
  833.         private final double l3;
  834.         private final double ll;

  836.         // CHECKSTYLE: resume JavadocVariable check

  838.         /** Create a model for specified mean orbit.
  839.          * @param mean mean orbit
  840.          * @param mass constant mass
  841.          * @param referenceRadius reference radius of the central body attraction model (m)
  842.          * @param mu central attraction coefficient (m³/s²)
  843.          * @param ck0 un-normalized zonal coefficients
  844.          */
  845.         EHModel(final CircularOrbit mean, final double mass,
  846.                 final double referenceRadius, final double mu, final double[] ck0) {

  848.             this.mean            = mean;
  849.             this.mass            = mass;

  851.             // preliminary processing
  852.             double q = referenceRadius / mean.getA();
  853.             double ql = q * q;
  854.             final double g2 = ck0[2] * ql;
  855.             ql *= q;
  856.             final double g3 = ck0[3] * ql;
  857.             ql *= q;
  858.             final double g4 = ck0[4] * ql;
  859.             ql *= q;
  860.             final double g5 = ck0[5] * ql;
  861.             ql *= q;
  862.             final double g6 = ck0[6] * ql;

  864.             final SinCos sc    = FastMath.sinCos(mean.getI());
  865.             final double cosI1 = sc.cos();
  866.             final double sinI1 = sc.sin();
  867.             final double sinI2 = sinI1 * sinI1;
  868.             final double sinI4 = sinI2 * sinI2;
  869.             final double sinI6 = sinI2 * sinI4;

  871.             if (sinI2 < 1.0e-10) {
  872.                 throw new OrekitException(OrekitMessages.ALMOST_EQUATORIAL_ORBIT,
  873.                                           FastMath.toDegrees(mean.getI()));
  874.             }

  876.             if (FastMath.abs(sinI2 - 4.0 / 5.0) < 1.0e-3) {
  877.                 throw new OrekitException(OrekitMessages.ALMOST_CRITICALLY_INCLINED_ORBIT,
  878.                                           FastMath.toDegrees(mean.getI()));
  879.             }

  881.             if (mean.getE() > 0.1) {
  882.                 // if 0.005 < e < 0.1 no error is triggered, but accuracy is poor
  883.                 throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL,
  884.                                           mean.getE());
  885.             }

  887.             xnotDot = FastMath.sqrt(mu / mean.getA()) / mean.getA();

  889.             rdpom = -0.75 * g2 * (4.0 - 5.0 * sinI2);
  890.             rdpomp = 7.5 * g4 * (1.0 - 31.0 / 8.0 * sinI2 + 49.0 / 16.0 * sinI4) -
  891.                     13.125 * g6 * (1.0 - 8.0 * sinI2 + 129.0 / 8.0 * sinI4 - 297.0 / 32.0 * sinI6);

  893.             q = 3.0 / (32.0 * rdpom);
  894.             eps1 = q * g4 * sinI2 * (30.0 - 35.0 * sinI2) -
  895.                     175.0 * q * g6 * sinI2 * (1.0 - 3.0 * sinI2 + 2.0625 * sinI4);
  896.             q = 3.0 * sinI1 / (8.0 * rdpom);
  897.             eps2 = q * g3 * (4.0 - 5.0 * sinI2) - q * g5 * (10.0 - 35.0 * sinI2 + 26.25 * sinI4);

  899.             xim = mean.getI();
  900.             ommD = cosI1 * (1.50    * g2 - 2.25 * g2 * g2 * (2.5 - 19.0 / 6.0 * sinI2) +
  901.                             0.9375  * g4 * (7.0 * sinI2 - 4.0) +
  902.                             3.28125 * g6 * (2.0 - 9.0 * sinI2 + 8.25 * sinI4));

  904.             rdl = 1.0 - 1.50 * g2 * (3.0 - 4.0 * sinI2);
  905.             aMD = rdl +
  906.                     2.25 * g2 * g2 * (9.0 - 263.0 / 12.0 * sinI2 + 341.0 / 24.0 * sinI4) +
  907.                     15.0 / 16.0 * g4 * (8.0 - 31.0 * sinI2 + 24.5 * sinI4) +
  908.                     105.0 / 32.0 * g6 * (-10.0 / 3.0 + 25.0 * sinI2 - 48.75 * sinI4 + 27.5 * sinI6);

  910.             final double qq = -1.5 * g2 / rdl;
  911.             final double qA   = 0.75 * g2 * g2 * sinI2;
  912.             final double qB   = 0.25 * g4 * sinI2;
  913.             final double qC   = 105.0 / 16.0 * g6 * sinI2;
  914.             final double qD   = -0.75 * g3 * sinI1;
  915.             final double qE   = 3.75 * g5 * sinI1;
  916.             kh = 0.375 / rdpom;
  917.             kl = kh / sinI1;

  919.             ax1 = qq * (2.0 - 3.5 * sinI2);
  920.             ay1 = qq * (2.0 - 2.5 * sinI2);
  921.             as1 = qD * (4.0 - 5.0 * sinI2) +
  922.                   qE * (2.625 * sinI4 - 3.5 * sinI2 + 1.0);
  923.             ac2 = qq * sinI2 +
  924.                   qA * 7.0 * (2.0 - 3.0 * sinI2) +
  925.                   qB * (15.0 - 17.5 * sinI2) +
  926.                   qC * (3.0 * sinI2 - 1.0 - 33.0 / 16.0 * sinI4);
  927.             axy3 = qq * 3.5 * sinI2;
  928.             as3 = qD * 5.0 / 3.0 * sinI2 +
  929.                   qE * 7.0 / 6.0 * sinI2 * (1.0 - 1.125 * sinI2);
  930.             ac4 = qA * sinI2 +
  931.                   qB * 4.375 * sinI2 +
  932.                   qC * 0.75 * (1.1 * sinI4 - sinI2);

  934.             as5 = qE * 21.0 / 80.0 * sinI4;

  936.             ac6 = qC * -11.0 / 80.0 * sinI4;

  938.             ex1 = qq * (1.0 - 1.25 * sinI2);
  939.             exx2 = qq * 0.5 * (3.0 - 5.0 * sinI2);
  940.             exy2 = qq * (2.0 - 1.5 * sinI2);
  941.             ex3 = qq * 7.0 / 12.0 * sinI2;
  942.             ex4 = qq * 17.0 / 8.0 * sinI2;

  944.             ey1 = qq * (1.0 - 1.75 * sinI2);
  945.             eyx2 = qq * (1.0 - 3.0 * sinI2);
  946.             eyy2 = qq * (2.0 * sinI2 - 1.5);
  947.             ey3 = qq * 7.0 / 12.0 * sinI2;
  948.             ey4 = qq * 17.0 / 8.0 * sinI2;

  950.             q  = -qq * cosI1;
  951.             rx1 =  3.5 * q;
  952.             ry1 = -2.5 * q;
  953.             r2 = -0.5 * q;
  954.             r3 =  7.0 / 6.0 * q;
  955.             rl = g3 * cosI1 * (4.0 - 15.0 * sinI2) -
  956.                  2.5 * g5 * cosI1 * (4.0 - 42.0 * sinI2 + 52.5 * sinI4);

  958.             q = 0.5 * qq * sinI1 * cosI1;
  959.             iy1 =  q;
  960.             ix1 = -q;
  961.             i2 =  q;
  962.             i3 =  q * 7.0 / 3.0;
  963.             ih = -g3 * cosI1 * (4.0 - 5.0 * sinI2) +
  964.                  2.5 * g5 * cosI1 * (4.0 - 14.0 * sinI2 + 10.5 * sinI4);

  966.             lx1 = qq * (7.0 - 77.0 / 8.0 * sinI2);
  967.             ly1 = qq * (55.0 / 8.0 * sinI2 - 7.50);
  968.             l2 = qq * (1.25 * sinI2 - 0.5);
  969.             l3 = qq * (77.0 / 24.0 * sinI2 - 7.0 / 6.0);
  970.             ll = g3 * (53.0 * sinI2 - 4.0 - 57.5 * sinI4) +
  971.                  2.5 * g5 * (4.0 - 96.0 * sinI2 + 269.5 * sinI4 - 183.75 * sinI6);

  973.         }

  975.         /** Extrapolate an orbit up to a specific target date.
  976.          * @param date target date for the orbit
  977.          * @return propagated parameters
  978.          */
  979.         public UnivariateDerivative2[] propagateParameters(final AbsoluteDate date) {

  981.             // Keplerian evolution
  982.             final UnivariateDerivative2 dt = new UnivariateDerivative2(date.durationFrom(mean.getDate()), 1.0, 0.0);
  983.             final UnivariateDerivative2 xnot = dt.multiply(xnotDot);

  985.             // secular effects

  987.             // eccentricity
  988.             final UnivariateDerivative2 x   = xnot.multiply(rdpom + rdpomp);
  989.             final UnivariateDerivative2 cx  = x.cos();
  990.             final UnivariateDerivative2 sx  = x.sin();
  991.             final UnivariateDerivative2 exm = cx.multiply(mean.getCircularEx()).
  992.                                               add(sx.multiply(eps2 - (1.0 - eps1) * mean.getCircularEy()));
  993.             final UnivariateDerivative2 eym = sx.multiply((1.0 + eps1) * mean.getCircularEx()).
  994.                                               add(cx.multiply(mean.getCircularEy() - eps2)).
  995.                                               add(eps2);

  997.             // no secular effect on inclination

  999.             // right ascension of ascending node
  1000.             final UnivariateDerivative2 omm = new UnivariateDerivative2(MathUtils.normalizeAngle(mean.getRightAscensionOfAscendingNode() + ommD * xnot.getValue(),
  1001.                                                                                                FastMath.PI),
  1002.                                                                       ommD * xnotDot,
  1003.                                                                       0.0);

  1005.             // latitude argument
  1006.             final UnivariateDerivative2 xlm = new UnivariateDerivative2(MathUtils.normalizeAngle(mean.getAlphaM() + aMD * xnot.getValue(),
  1007.                                                                                                  FastMath.PI),
  1008.                                                                         aMD * xnotDot,
  1009.                                                                         0.0);

  1011.             // periodical terms
  1012.             final UnivariateDerivative2 cl1 = xlm.cos();
  1013.             final UnivariateDerivative2 sl1 = xlm.sin();
  1014.             final UnivariateDerivative2 cl2 = cl1.multiply(cl1).subtract(sl1.multiply(sl1));
  1015.             final UnivariateDerivative2 sl2 = cl1.multiply(sl1).add(sl1.multiply(cl1));
  1016.             final UnivariateDerivative2 cl3 = cl2.multiply(cl1).subtract(sl2.multiply(sl1));
  1017.             final UnivariateDerivative2 sl3 = cl2.multiply(sl1).add(sl2.multiply(cl1));
  1018.             final UnivariateDerivative2 cl4 = cl3.multiply(cl1).subtract(sl3.multiply(sl1));
  1019.             final UnivariateDerivative2 sl4 = cl3.multiply(sl1).add(sl3.multiply(cl1));
  1020.             final UnivariateDerivative2 cl5 = cl4.multiply(cl1).subtract(sl4.multiply(sl1));
  1021.             final UnivariateDerivative2 sl5 = cl4.multiply(sl1).add(sl4.multiply(cl1));
  1022.             final UnivariateDerivative2 cl6 = cl5.multiply(cl1).subtract(sl5.multiply(sl1));

  1024.             final UnivariateDerivative2 qh  = eym.subtract(eps2).multiply(kh);
  1025.             final UnivariateDerivative2 ql  = exm.multiply(kl);

  1027.             final UnivariateDerivative2 exmCl1 = exm.multiply(cl1);
  1028.             final UnivariateDerivative2 exmSl1 = exm.multiply(sl1);
  1029.             final UnivariateDerivative2 eymCl1 = eym.multiply(cl1);
  1030.             final UnivariateDerivative2 eymSl1 = eym.multiply(sl1);
  1031.             final UnivariateDerivative2 exmCl2 = exm.multiply(cl2);
  1032.             final UnivariateDerivative2 exmSl2 = exm.multiply(sl2);
  1033.             final UnivariateDerivative2 eymCl2 = eym.multiply(cl2);
  1034.             final UnivariateDerivative2 eymSl2 = eym.multiply(sl2);
  1035.             final UnivariateDerivative2 exmCl3 = exm.multiply(cl3);
  1036.             final UnivariateDerivative2 exmSl3 = exm.multiply(sl3);
  1037.             final UnivariateDerivative2 eymCl3 = eym.multiply(cl3);
  1038.             final UnivariateDerivative2 eymSl3 = eym.multiply(sl3);
  1039.             final UnivariateDerivative2 exmCl4 = exm.multiply(cl4);
  1040.             final UnivariateDerivative2 exmSl4 = exm.multiply(sl4);
  1041.             final UnivariateDerivative2 eymCl4 = eym.multiply(cl4);
  1042.             final UnivariateDerivative2 eymSl4 = eym.multiply(sl4);

  1044.             // semi major axis
  1045.             final UnivariateDerivative2 rda = exmCl1.multiply(ax1).
  1046.                                               add(eymSl1.multiply(ay1)).
  1047.                                               add(sl1.multiply(as1)).
  1048.                                               add(cl2.multiply(ac2)).
  1049.                                               add(exmCl3.add(eymSl3).multiply(axy3)).
  1050.                                               add(sl3.multiply(as3)).
  1051.                                               add(cl4.multiply(ac4)).
  1052.                                               add(sl5.multiply(as5)).
  1053.                                               add(cl6.multiply(ac6));

  1055.             // eccentricity
  1056.             final UnivariateDerivative2 rdex = cl1.multiply(ex1).
  1057.                                                add(exmCl2.multiply(exx2)).
  1058.                                                add(eymSl2.multiply(exy2)).
  1059.                                                add(cl3.multiply(ex3)).
  1060.                                                add(exmCl4.add(eymSl4).multiply(ex4));
  1061.             final UnivariateDerivative2 rdey = sl1.multiply(ey1).
  1062.                                                add(exmSl2.multiply(eyx2)).
  1063.                                                add(eymCl2.multiply(eyy2)).
  1064.                                                add(sl3.multiply(ey3)).
  1065.                                                add(exmSl4.subtract(eymCl4).multiply(ey4));

  1067.             // ascending node
  1068.             final UnivariateDerivative2 rdom = exmSl1.multiply(rx1).
  1069.                                                add(eymCl1.multiply(ry1)).
  1070.                                                add(sl2.multiply(r2)).
  1071.                                                add(eymCl3.subtract(exmSl3).multiply(r3)).
  1072.                                                add(ql.multiply(rl));

  1074.             // inclination
  1075.             final UnivariateDerivative2 rdxi = eymSl1.multiply(iy1).
  1076.                                                add(exmCl1.multiply(ix1)).
  1077.                                                add(cl2.multiply(i2)).
  1078.                                                add(exmCl3.add(eymSl3).multiply(i3)).
  1079.                                                add(qh.multiply(ih));

  1081.             // latitude argument
  1082.             final UnivariateDerivative2 rdxl = exmSl1.multiply(lx1).
  1083.                                                add(eymCl1.multiply(ly1)).
  1084.                                                add(sl2.multiply(l2)).
  1085.                                                add(exmSl3.subtract(eymCl3).multiply(l3)).
  1086.                                                add(ql.multiply(ll));

  1088.             // osculating parameters
  1089.             return new UnivariateDerivative2[] {
  1090.                 rda.add(1.0).multiply(mean.getA()),
  1091.                 rdex.add(exm),
  1092.                 rdey.add(eym),
  1093.                 rdxi.add(xim),
  1094.                 rdom.add(omm),
  1095.                 rdxl.add(xlm)
  1096.             };

  1098.         }

  1100.     }

  1102.     /** Convert circular parameters <em>with derivatives</em> to Cartesian coordinates.
  1103.      * @param date date of the orbital parameters
  1104.      * @param parameters circular parameters (a, ex, ey, i, raan, alphaM)
  1105.      * @return Cartesian coordinates consistent with values and derivatives
  1106.      */
  1107.     private TimeStampedPVCoordinates toCartesian(final AbsoluteDate date, final UnivariateDerivative2[] parameters) {

  1109.         // evaluate coordinates in the orbit canonical reference frame
  1110.         final UnivariateDerivative2 cosOmega = parameters[4].cos();
  1111.         final UnivariateDerivative2 sinOmega = parameters[4].sin();
  1112.         final UnivariateDerivative2 cosI     = parameters[3].cos();
  1113.         final UnivariateDerivative2 sinI     = parameters[3].sin();
  1114.         final UnivariateDerivative2 alphaE   = meanToEccentric(parameters[5], parameters[1], parameters[2]);
  1115.         final UnivariateDerivative2 cosAE    = alphaE.cos();
  1116.         final UnivariateDerivative2 sinAE    = alphaE.sin();
  1117.         final UnivariateDerivative2 ex2      = parameters[1].square();
  1118.         final UnivariateDerivative2 ey2      = parameters[2].square();
  1119.         final UnivariateDerivative2 exy      = parameters[1].multiply(parameters[2]);
  1120.         final UnivariateDerivative2 q        = ex2.add(ey2).subtract(1).negate().sqrt();
  1121.         final UnivariateDerivative2 beta     = q.add(1).reciprocal();
  1122.         final UnivariateDerivative2 bx2      = beta.multiply(ex2);
  1123.         final UnivariateDerivative2 by2      = beta.multiply(ey2);
  1124.         final UnivariateDerivative2 bxy      = beta.multiply(exy);
  1125.         final UnivariateDerivative2 u        = bxy.multiply(sinAE).subtract(parameters[1].add(by2.subtract(1).multiply(cosAE)));
  1126.         final UnivariateDerivative2 v        = bxy.multiply(cosAE).subtract(parameters[2].add(bx2.subtract(1).multiply(sinAE)));
  1127.         final UnivariateDerivative2 x        = parameters[0].multiply(u);
  1128.         final UnivariateDerivative2 y        = parameters[0].multiply(v);

  1130.         // canonical orbit reference frame
  1131.         final FieldVector3D<UnivariateDerivative2> p =
  1132.                 new FieldVector3D<>(x.multiply(cosOmega).subtract(y.multiply(cosI.multiply(sinOmega))),
  1133.                                     x.multiply(sinOmega).add(y.multiply(cosI.multiply(cosOmega))),
  1134.                                     y.multiply(sinI));

  1136.         // dispatch derivatives
  1137.         final Vector3D p0 = new Vector3D(p.getX().getValue(),
  1138.                                          p.getY().getValue(),
  1139.                                          p.getZ().getValue());
  1140.         final Vector3D p1 = new Vector3D(p.getX().getFirstDerivative(),
  1141.                                          p.getY().getFirstDerivative(),
  1142.                                          p.getZ().getFirstDerivative());
  1143.         final Vector3D p2 = new Vector3D(p.getX().getSecondDerivative(),
  1144.                                          p.getY().getSecondDerivative(),
  1145.                                          p.getZ().getSecondDerivative());
  1146.         return new TimeStampedPVCoordinates(date, p0, p1, p2);

  1148.     }

  1150.     /** Computes the eccentric latitude argument from the mean latitude argument.
  1151.      * @param alphaM = M + Ω mean latitude argument (rad)
  1152.      * @param ex e cos(Ω), first component of circular eccentricity vector
  1153.      * @param ey e sin(Ω), second component of circular eccentricity vector
  1154.      * @return the eccentric latitude argument.
  1155.      */
  1156.     private UnivariateDerivative2 meanToEccentric(final UnivariateDerivative2 alphaM,
  1157.                                                   final UnivariateDerivative2 ex,
  1158.                                                   final UnivariateDerivative2 ey) {
  1159.         // Generalization of Kepler equation to circular parameters
  1160.         // with alphaE = PA + E and
  1161.         //      alphaM = PA + M = alphaE - ex.sin(alphaE) + ey.cos(alphaE)
  1162.         UnivariateDerivative2 alphaE        = alphaM;
  1163.         UnivariateDerivative2 shift         = alphaM.getField().getZero();
  1164.         UnivariateDerivative2 alphaEMalphaM = alphaM.getField().getZero();
  1165.         UnivariateDerivative2 cosAlphaE     = alphaE.cos();
  1166.         UnivariateDerivative2 sinAlphaE     = alphaE.sin();
  1167.         int                 iter          = 0;
  1168.         do {
  1169.             final UnivariateDerivative2 f2 = ex.multiply(sinAlphaE).subtract(ey.multiply(cosAlphaE));
  1170.             final UnivariateDerivative2 f1 = alphaM.getField().getOne().subtract(ex.multiply(cosAlphaE)).subtract(ey.multiply(sinAlphaE));
  1171.             final UnivariateDerivative2 f0 = alphaEMalphaM.subtract(f2);

  1173.             final UnivariateDerivative2 f12 = f1.multiply(2);
  1174.             shift = f0.multiply(f12).divide(f1.multiply(f12).subtract(f0.multiply(f2)));

  1176.             alphaEMalphaM  = alphaEMalphaM.subtract(shift);
  1177.             alphaE         = alphaM.add(alphaEMalphaM);
  1178.             cosAlphaE      = alphaE.cos();
  1179.             sinAlphaE      = alphaE.sin();

  1181.         } while (++iter < 50 && FastMath.abs(shift.getValue()) > 1.0e-12);

  1183.         return alphaE;

  1185.     }

  1187.     /** {@inheritDoc} */
  1188.     protected double getMass(final AbsoluteDate date) {
  1189.         return models.get(date).mass;
  1190.     }

  1192. }
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