NumericalPropagator.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.numerical;

  19. import java.util.ArrayList;
  20. import java.util.Arrays;
  21. import java.util.Collections;
  22. import java.util.List;

  24. import org.hipparchus.exception.LocalizedCoreFormats;
  25. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  26. import org.hipparchus.linear.MatrixUtils;
  27. import org.hipparchus.linear.QRDecomposition;
  28. import org.hipparchus.linear.RealMatrix;
  29. import org.hipparchus.ode.ODEIntegrator;
  30. import org.hipparchus.util.FastMath;
  31. import org.hipparchus.util.Precision;
  32. import org.orekit.annotation.DefaultDataContext;
  33. import org.orekit.attitudes.Attitude;
  34. import org.orekit.attitudes.AttitudeProvider;
  35. import org.orekit.data.DataContext;
  36. import org.orekit.errors.OrekitException;
  37. import org.orekit.errors.OrekitIllegalArgumentException;
  38. import org.orekit.errors.OrekitInternalError;
  39. import org.orekit.errors.OrekitMessages;
  40. import org.orekit.forces.ForceModel;
  41. import org.orekit.forces.gravity.NewtonianAttraction;
  42. import org.orekit.forces.inertia.InertialForces;
  43. import org.orekit.forces.maneuvers.Maneuver;
  44. import org.orekit.forces.maneuvers.jacobians.Duration;
  45. import org.orekit.forces.maneuvers.jacobians.MedianDate;
  46. import org.orekit.forces.maneuvers.jacobians.TriggerDate;
  47. import org.orekit.forces.maneuvers.trigger.ManeuverTriggers;
  48. import org.orekit.frames.Frame;
  49. import org.orekit.orbits.Orbit;
  50. import org.orekit.orbits.OrbitType;
  51. import org.orekit.orbits.PositionAngleType;
  52. import org.orekit.propagation.AbstractMatricesHarvester;
  53. import org.orekit.propagation.AdditionalStateProvider;
  54. import org.orekit.propagation.MatricesHarvester;
  55. import org.orekit.propagation.PropagationType;
  56. import org.orekit.propagation.Propagator;
  57. import org.orekit.propagation.SpacecraftState;
  58. import org.orekit.propagation.events.EventDetector;
  59. import org.orekit.propagation.events.ParameterDrivenDateIntervalDetector;
  60. import org.orekit.propagation.integration.AbstractIntegratedPropagator;
  61. import org.orekit.propagation.integration.AdditionalDerivativesProvider;
  62. import org.orekit.propagation.integration.StateMapper;
  63. import org.orekit.time.AbsoluteDate;
  64. import org.orekit.utils.AbsolutePVCoordinates;
  65. import org.orekit.utils.DoubleArrayDictionary;
  66. import org.orekit.utils.PVCoordinates;
  67. import org.orekit.utils.ParameterDriver;
  68. import org.orekit.utils.ParameterDriversList;
  69. import org.orekit.utils.ParameterDriversList.DelegatingDriver;
  70. import org.orekit.utils.TimeSpanMap.Span;
  71. import org.orekit.utils.ParameterObserver;
  72. import org.orekit.utils.TimeSpanMap;
  73. import org.orekit.utils.TimeStampedPVCoordinates;

  75. /** This class propagates {@link org.orekit.orbits.Orbit orbits} using
  76.  * numerical integration.
  77.  * <p>Numerical propagation is much more accurate than analytical propagation
  78.  * like for example {@link org.orekit.propagation.analytical.KeplerianPropagator
  79.  * Keplerian} or {@link org.orekit.propagation.analytical.EcksteinHechlerPropagator
  80.  * Eckstein-Hechler}, but requires a few more steps to set up to be used properly.
  81.  * Whereas analytical propagators are configured only thanks to their various
  82.  * constructors and can be used immediately after construction, numerical propagators
  83.  * configuration involve setting several parameters between construction time
  84.  * and propagation time.</p>
  85.  * <p>The configuration parameters that can be set are:</p>
  86.  * <ul>
  87.  *   <li>the initial spacecraft state ({@link #setInitialState(SpacecraftState)})</li>
  88.  *   <li>the central attraction coefficient ({@link #setMu(double)})</li>
  89.  *   <li>the various force models ({@link #addForceModel(ForceModel)},
  90.  *   {@link #removeForceModels()})</li>
  91.  *   <li>the {@link OrbitType type} of orbital parameters to be used for propagation
  92.  *   ({@link #setOrbitType(OrbitType)}),</li>
  93.  *   <li>the {@link PositionAngleType type} of position angle to be used in orbital parameters
  94.  *   to be used for propagation where it is relevant ({@link
  95.  *   #setPositionAngleType(PositionAngleType)}),</li>
  96.  *   <li>whether {@link MatricesHarvester state transition matrices and Jacobians matrices}
  97.  *   should be propagated along with orbital state ({@link
  98.  *   #setupMatricesComputation(String, RealMatrix, DoubleArrayDictionary)}),</li>
  99.  *   <li>whether {@link org.orekit.propagation.integration.AdditionalDerivativesProvider additional derivatives}
  100.  *   should be propagated along with orbital state ({@link
  101.  *   #addAdditionalDerivativesProvider(AdditionalDerivativesProvider)}),</li>
  102.  *   <li>the discrete events that should be triggered during propagation
  103.  *   ({@link #addEventDetector(EventDetector)},
  104.  *   {@link #clearEventsDetectors()})</li>
  105.  *   <li>the binding logic with the rest of the application ({@link #getMultiplexer()})</li>
  106.  * </ul>
  107.  * <p>From these configuration parameters, only the initial state is mandatory. The default
  108.  * propagation settings are in {@link OrbitType#EQUINOCTIAL equinoctial} parameters with
  109.  * {@link PositionAngleType#TRUE true} longitude argument. If the central attraction coefficient
  110.  * is not explicitly specified, the one used to define the initial orbit will be used.
  111.  * However, specifying only the initial state and perhaps the central attraction coefficient
  112.  * would mean the propagator would use only Keplerian forces. In this case, the simpler {@link
  113.  * org.orekit.propagation.analytical.KeplerianPropagator KeplerianPropagator} class would
  114.  * perhaps be more effective.</p>
  115.  * <p>The underlying numerical integrator set up in the constructor may also have its own
  116.  * configuration parameters. Typical configuration parameters for adaptive stepsize integrators
  117.  * are the min, max and perhaps start step size as well as the absolute and/or relative errors
  118.  * thresholds.</p>
  119.  * <p>The state that is seen by the integrator is a simple seven elements double array.
  120.  * The six first elements are either:
  121.  * <ul>
  122.  *   <li>the {@link org.orekit.orbits.EquinoctialOrbit equinoctial orbit parameters} (a, e<sub>x</sub>,
  123.  *   e<sub>y</sub>, h<sub>x</sub>, h<sub>y</sub>, λ<sub>M</sub> or λ<sub>E</sub>
  124.  *   or λ<sub>v</sub>) in meters and radians,</li>
  125.  *   <li>the {@link org.orekit.orbits.KeplerianOrbit Keplerian orbit parameters} (a, e, i, ω, Ω,
  126.  *   M or E or v) in meters and radians,</li>
  127.  *   <li>the {@link org.orekit.orbits.CircularOrbit circular orbit parameters} (a, e<sub>x</sub>, e<sub>y</sub>, i,
  128.  *   Ω, α<sub>M</sub> or α<sub>E</sub> or α<sub>v</sub>) in meters
  129.  *   and radians,</li>
  130.  *   <li>the {@link org.orekit.orbits.CartesianOrbit Cartesian orbit parameters} (x, y, z, v<sub>x</sub>,
  131.  *   v<sub>y</sub>, v<sub>z</sub>) in meters and meters per seconds.
  132.  * </ul>
  133.  * <p> The last element is the mass in kilograms and changes only during thrusters firings
  134.  *
  135.  * <p>The following code snippet shows a typical setting for Low Earth Orbit propagation in
  136.  * equinoctial parameters and true longitude argument:</p>
  137.  * <pre>
  138.  * final double dP       = 0.001;
  139.  * final double minStep  = 0.001;
  140.  * final double maxStep  = 500;
  141.  * final double initStep = 60;
  142.  * final double[][] tolerance = NumericalPropagator.tolerances(dP, orbit, OrbitType.EQUINOCTIAL);
  143.  * AdaptiveStepsizeIntegrator integrator = new DormandPrince853Integrator(minStep, maxStep, tolerance[0], tolerance[1]);
  144.  * integrator.setInitialStepSize(initStep);
  145.  * propagator = new NumericalPropagator(integrator);
  146.  * </pre>
  147.  * <p>By default, at the end of the propagation, the propagator resets the initial state to the final state,
  148.  * thus allowing a new propagation to be started from there without recomputing the part already performed.
  149.  * This behaviour can be chenged by calling {@link #setResetAtEnd(boolean)}.
  150.  * </p>
  151.  * <p>Beware the same instance cannot be used simultaneously by different threads, the class is <em>not</em>
  152.  * thread-safe.</p>
  153.  *
  154.  * @see SpacecraftState
  155.  * @see ForceModel
  156.  * @see org.orekit.propagation.sampling.OrekitStepHandler
  157.  * @see org.orekit.propagation.sampling.OrekitFixedStepHandler
  158.  * @see org.orekit.propagation.integration.IntegratedEphemeris
  159.  * @see TimeDerivativesEquations
  160.  *
  161.  * @author Mathieu Rom&eacute;ro
  162.  * @author Luc Maisonobe
  163.  * @author Guylaine Prat
  164.  * @author Fabien Maussion
  165.  * @author V&eacute;ronique Pommier-Maurussane
  166.  */
  167. public class NumericalPropagator extends AbstractIntegratedPropagator {

  169.     /** Space dimension. */
  170.     private static final int SPACE_DIMENSION = 3;

  172.     /** State dimension. */
  173.     private static final int STATE_DIMENSION = 2 * SPACE_DIMENSION;

  175.     /** Threshold for matrix solving. */
  176.     private static final double THRESHOLD = Precision.SAFE_MIN;

  178.     /** Force models used during the extrapolation of the orbit. */
  179.     private final List<ForceModel> forceModels;

  181.     /** boolean to ignore or not the creation of a NewtonianAttraction. */
  182.     private boolean ignoreCentralAttraction;

  184.     /** Create a new instance of NumericalPropagator, based on orbit definition mu.
  185.      * After creation, the instance is empty, i.e. the attitude provider is set to an
  186.      * unspecified default law and there are no perturbing forces at all.
  187.      * This means that if {@link #addForceModel addForceModel} is not
  188.      * called after creation, the integrated orbit will follow a Keplerian
  189.      * evolution only. The defaults are {@link OrbitType#EQUINOCTIAL}
  190.      * for {@link #setOrbitType(OrbitType) propagation
  191.      * orbit type} and {@link PositionAngleType#TRUE} for {@link
  192.      * #setPositionAngleType(PositionAngleType) position angle type}.
  193.      *
  194.      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
  195.      *
  196.      * @param integrator numerical integrator to use for propagation.
  197.      * @see #NumericalPropagator(ODEIntegrator, AttitudeProvider)
  198.      */
  199.     @DefaultDataContext
  200.     public NumericalPropagator(final ODEIntegrator integrator) {
  201.         this(integrator,
  202.                 Propagator.getDefaultLaw(DataContext.getDefault().getFrames()));
  203.     }

  205.     /** Create a new instance of NumericalPropagator, based on orbit definition mu.
  206.      * After creation, the instance is empty, i.e. the attitude provider is set to an
  207.      * unspecified default law and there are no perturbing forces at all.
  208.      * This means that if {@link #addForceModel addForceModel} is not
  209.      * called after creation, the integrated orbit will follow a Keplerian
  210.      * evolution only. The defaults are {@link OrbitType#EQUINOCTIAL}
  211.      * for {@link #setOrbitType(OrbitType) propagation
  212.      * orbit type} and {@link PositionAngleType#TRUE} for {@link
  213.      * #setPositionAngleType(PositionAngleType) position angle type}.
  214.      * @param integrator numerical integrator to use for propagation.
  215.      * @param attitudeProvider the attitude law.
  216.      * @since 10.1
  217.      */
  218.     public NumericalPropagator(final ODEIntegrator integrator,
  219.                                final AttitudeProvider attitudeProvider) {
  220.         super(integrator, PropagationType.OSCULATING);
  221.         forceModels             = new ArrayList<ForceModel>();
  222.         ignoreCentralAttraction = false;
  223.         initMapper();
  224.         setAttitudeProvider(attitudeProvider);
  225.         clearStepHandlers();
  226.         setOrbitType(OrbitType.EQUINOCTIAL);
  227.         setPositionAngleType(PositionAngleType.TRUE);
  228.     }

  230.     /** Set the flag to ignore or not the creation of a {@link NewtonianAttraction}.
  231.      * @param ignoreCentralAttraction if true, {@link NewtonianAttraction} is <em>not</em>
  232.      * added automatically if missing
  233.      */
  234.     public void setIgnoreCentralAttraction(final boolean ignoreCentralAttraction) {
  235.         this.ignoreCentralAttraction = ignoreCentralAttraction;
  236.     }

  238.      /** Set the central attraction coefficient μ.
  239.       * <p>
  240.       * Setting the central attraction coefficient is
  241.       * equivalent to {@link #addForceModel(ForceModel) add}
  242.       * a {@link NewtonianAttraction} force model.
  243.       * </p>
  244.      * @param mu central attraction coefficient (m³/s²)
  245.      * @see #addForceModel(ForceModel)
  246.      * @see #getAllForceModels()
  247.      */
  248.     public void setMu(final double mu) {
  249.         if (ignoreCentralAttraction) {
  250.             superSetMu(mu);
  251.         } else {
  252.             addForceModel(new NewtonianAttraction(mu));
  253.             superSetMu(mu);
  254.         }
  255.     }

  257.     /** Set the central attraction coefficient μ only in upper class.
  258.      * @param mu central attraction coefficient (m³/s²)
  259.      */
  260.     private void superSetMu(final double mu) {
  261.         super.setMu(mu);
  262.     }

  264.     /** Check if Newtonian attraction force model is available.
  265.      * <p>
  266.      * Newtonian attraction is always the last force model in the list.
  267.      * </p>
  268.      * @return true if Newtonian attraction force model is available
  269.      */
  270.     private boolean hasNewtonianAttraction() {
  271.         final int last = forceModels.size() - 1;
  272.         return last >= 0 && forceModels.get(last) instanceof NewtonianAttraction;
  273.     }

  275.     /** Add a force model.
  276.      * <p>If this method is not called at all, the integrated orbit will follow
  277.      * a Keplerian evolution only.</p>
  278.      * @param model {@link ForceModel} to add (it can be either a perturbing force
  279.      * model or an instance of {@link NewtonianAttraction})
  280.      * @see #removeForceModels()
  281.      * @see #setMu(double)
  282.      */
  283.     public void addForceModel(final ForceModel model) {

  285.         if (model instanceof NewtonianAttraction) {
  286.             // we want to add the central attraction force model

  288.             try {
  289.                 // ensure we are notified of any mu change
  290.                 model.getParametersDrivers().get(0).addObserver(new ParameterObserver() {
  291.                     /** {@inheritDoc} */
  292.                     @Override
  293.                     public void valueSpanMapChanged(final TimeSpanMap<Double> previousValue, final ParameterDriver driver) {
  294.                         superSetMu(driver.getValue());
  295.                     }
  296.                     /** {@inheritDoc} */
  297.                     @Override
  298.                     public void valueChanged(final double previousValue, final ParameterDriver driver, final AbsoluteDate date) {
  299.                         superSetMu(driver.getValue());
  300.                     }
  301.                 });
  302.             } catch (OrekitException oe) {
  303.                 // this should never happen
  304.                 throw new OrekitInternalError(oe);
  305.             }

  307.             if (hasNewtonianAttraction()) {
  308.                 // there is already a central attraction model, replace it
  309.                 forceModels.set(forceModels.size() - 1, model);
  310.             } else {
  311.                 // there are no central attraction model yet, add it at the end of the list
  312.                 forceModels.add(model);
  313.             }
  314.         } else {
  315.             // we want to add a perturbing force model
  316.             if (hasNewtonianAttraction()) {
  317.                 // insert the new force model before Newtonian attraction,
  318.                 // which should always be the last one in the list
  319.                 forceModels.add(forceModels.size() - 1, model);
  320.             } else {
  321.                 // we only have perturbing force models up to now, just append at the end of the list
  322.                 forceModels.add(model);
  323.             }
  324.         }

  326.     }

  328.     /** Remove all force models (except central attraction).
  329.      * <p>Once all perturbing forces have been removed (and as long as no new force
  330.      * model is added), the integrated orbit will follow a Keplerian evolution
  331.      * only.</p>
  332.      * @see #addForceModel(ForceModel)
  333.      */
  334.     public void removeForceModels() {
  335.         final int last = forceModels.size() - 1;
  336.         if (hasNewtonianAttraction()) {
  337.             // preserve the Newtonian attraction model at the end
  338.             final ForceModel newton = forceModels.get(last);
  339.             forceModels.clear();
  340.             forceModels.add(newton);
  341.         } else {
  342.             forceModels.clear();
  343.         }
  344.     }

  346.     /** Get all the force models, perturbing forces and Newtonian attraction included.
  347.      * @return list of perturbing force models, with Newtonian attraction being the
  348.      * last one
  349.      * @see #addForceModel(ForceModel)
  350.      * @see #setMu(double)
  351.      */
  352.     public List<ForceModel> getAllForceModels() {
  353.         return Collections.unmodifiableList(forceModels);
  354.     }

  356.     /** Set propagation orbit type.
  357.      * @param orbitType orbit type to use for propagation, null for
  358.      * propagating using {@link org.orekit.utils.AbsolutePVCoordinates} rather than {@link Orbit}
  359.      */
  360.     public void setOrbitType(final OrbitType orbitType) {
  361.         super.setOrbitType(orbitType);
  362.     }

  364.     /** Get propagation parameter type.
  365.      * @return orbit type used for propagation, null for
  366.      * propagating using {@link org.orekit.utils.AbsolutePVCoordinates} rather than {@link Orbit}
  367.      */
  368.     public OrbitType getOrbitType() {
  369.         return super.getOrbitType();
  370.     }

  372.     /** Set position angle type.
  373.      * <p>
  374.      * The position parameter type is meaningful only if {@link
  375.      * #getOrbitType() propagation orbit type}
  376.      * support it. As an example, it is not meaningful for propagation
  377.      * in {@link OrbitType#CARTESIAN Cartesian} parameters.
  378.      * </p>
  379.      * @param positionAngleType angle type to use for propagation
  380.      */
  381.     public void setPositionAngleType(final PositionAngleType positionAngleType) {
  382.         super.setPositionAngleType(positionAngleType);
  383.     }

  385.     /** Get propagation parameter type.
  386.      * @return angle type to use for propagation
  387.      */
  388.     public PositionAngleType getPositionAngleType() {
  389.         return super.getPositionAngleType();
  390.     }

  392.     /** Set the initial state.
  393.      * @param initialState initial state
  394.      */
  395.     public void setInitialState(final SpacecraftState initialState) {
  396.         resetInitialState(initialState);
  397.     }

  399.     /** {@inheritDoc} */
  400.     public void resetInitialState(final SpacecraftState state) {
  401.         super.resetInitialState(state);
  402.         if (!hasNewtonianAttraction()) {
  403.             // use the state to define central attraction
  404.             setMu(state.getMu());
  405.         }
  406.         setStartDate(state.getDate());
  407.     }

  409.     /** Get the names of the parameters in the matrix returned by {@link MatricesHarvester#getParametersJacobian}.
  410.      * @return names of the parameters (i.e. columns) of the Jacobian matrix
  411.      */
  412.     List<String> getJacobiansColumnsNames() {
  413.         final List<String> columnsNames = new ArrayList<>();
  414.         for (final ForceModel forceModel : getAllForceModels()) {
  415.             for (final ParameterDriver driver : forceModel.getParametersDrivers()) {
  416.                 if (driver.isSelected() && !columnsNames.contains(driver.getNamesSpanMap().getFirstSpan().getData())) {
  417.                     // As driver with same name should have same NamesSpanMap we only check if the first span is present,
  418.                     // if not we add all span names to columnsNames
  419.                     for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
  420.                         columnsNames.add(span.getData());
  421.                     }
  422.                 }
  423.             }
  424.         }
  425.         Collections.sort(columnsNames);
  426.         return columnsNames;
  427.     }

  429.     /** {@inheritDoc} */
  430.     @Override
  431.     protected AbstractMatricesHarvester createHarvester(final String stmName, final RealMatrix initialStm,
  432.                                                         final DoubleArrayDictionary initialJacobianColumns) {
  433.         return new NumericalPropagationHarvester(this, stmName, initialStm, initialJacobianColumns);
  434.     }

  436.     /** {@inheritDoc} */
  437.     @Override
  438.     protected void setUpStmAndJacobianGenerators() {

  440.         final AbstractMatricesHarvester harvester = getHarvester();
  441.         if (harvester != null) {

  443.             // set up the additional equations and additional state providers
  444.             final StateTransitionMatrixGenerator stmGenerator = setUpStmGenerator();
  445.             final List<String> triggersDates = setUpTriggerDatesJacobiansColumns(stmGenerator.getName());
  446.             setUpRegularParametersJacobiansColumns(stmGenerator, triggersDates);

  448.             // as we are now starting the propagation, everything is configured
  449.             // we can freeze the names in the harvester
  450.             harvester.freezeColumnsNames();

  452.         }

  454.     }

  456.     /** Set up the State Transition Matrix Generator.
  457.      * @return State Transition Matrix Generator
  458.      * @since 11.1
  459.      */
  460.     private StateTransitionMatrixGenerator setUpStmGenerator() {

  462.         final AbstractMatricesHarvester harvester = getHarvester();

  464.         // add the STM generator corresponding to the current settings, and setup state accordingly
  465.         StateTransitionMatrixGenerator stmGenerator = null;
  466.         for (final AdditionalDerivativesProvider equations : getAdditionalDerivativesProviders()) {
  467.             if (equations instanceof StateTransitionMatrixGenerator &&
  468.                 equations.getName().equals(harvester.getStmName())) {
  469.                 // the STM generator has already been set up in a previous propagation
  470.                 stmGenerator = (StateTransitionMatrixGenerator) equations;
  471.                 break;
  472.             }
  473.         }
  474.         if (stmGenerator == null) {
  475.             // this is the first time we need the STM generate, create it
  476.             stmGenerator = new StateTransitionMatrixGenerator(harvester.getStmName(), getAllForceModels(), getAttitudeProvider());
  477.             addAdditionalDerivativesProvider(stmGenerator);
  478.         }

  480.         if (!getInitialIntegrationState().hasAdditionalState(harvester.getStmName())) {
  481.             // add the initial State Transition Matrix if it is not already there
  482.             // (perhaps due to a previous propagation)
  483.             setInitialState(stmGenerator.setInitialStateTransitionMatrix(getInitialState(),
  484.                                                                          harvester.getInitialStateTransitionMatrix(),
  485.                                                                          getOrbitType(),
  486.                                                                          getPositionAngleType()));
  487.         }

  489.         return stmGenerator;

  491.     }

  493.     /** Set up the Jacobians columns generator dedicated to trigger dates.
  494.      * @param stmName name of the State Transition Matrix state
  495.      * @return names of the columns corresponding to trigger dates
  496.      * @since 11.1
  497.      */
  498.     private List<String> setUpTriggerDatesJacobiansColumns(final String stmName) {

  500.         final List<String> names = new ArrayList<>();
  501.         for (final ForceModel forceModel : getAllForceModels()) {
  502.             if (forceModel instanceof Maneuver) {
  503.                 final Maneuver maneuver = (Maneuver) forceModel;
  504.                 final ManeuverTriggers maneuverTriggers = maneuver.getManeuverTriggers();

  506.                 maneuverTriggers.getEventDetectors().
  507.                         filter(d -> d instanceof ParameterDrivenDateIntervalDetector).
  508.                         map(d -> (ParameterDrivenDateIntervalDetector) d).
  509.                         forEach(d -> {
  510.                             TriggerDate start;
  511.                             TriggerDate stop;

  513.                             if (d.getStartDriver().isSelected() || d.getMedianDriver().isSelected() || d.getDurationDriver().isSelected()) {
  514.                                 // normally datedriver should have only 1 span but just in case the user defines several span, there will
  515.                                 // be no problem here
  516.                                 for (Span<String> span = d.getStartDriver().getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
  517.                                     start = manageTriggerDate(stmName, maneuver, maneuverTriggers, span.getData(), true, d.getThreshold());
  518.                                     names.add(start.getName());
  519.                                     start = null;
  520.                                 }
  521.                             }
  522.                             if (d.getStopDriver().isSelected() || d.getMedianDriver().isSelected() || d.getDurationDriver().isSelected()) {
  523.                                 // normally datedriver should have only 1 span but just in case the user defines several span, there will
  524.                                 // be no problem here
  525.                                 for (Span<String> span = d.getStopDriver().getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
  526.                                     stop = manageTriggerDate(stmName, maneuver, maneuverTriggers, span.getData(), false, d.getThreshold());
  527.                                     names.add(stop.getName());
  528.                                     stop = null;
  529.                                 }
  530.                             }
  531.                             if (d.getMedianDriver().isSelected()) {
  532.                                 // for first span
  533.                                 Span<String> currentMedianNameSpan = d.getMedianDriver().getNamesSpanMap().getFirstSpan();
  534.                                 MedianDate median =
  535.                                         manageMedianDate(d.getStartDriver().getNamesSpanMap().getFirstSpan().getData(),
  536.                                                 d.getStopDriver().getNamesSpanMap().getFirstSpan().getData(), currentMedianNameSpan.getData());
  537.                                 names.add(median.getName());
  538.                                 // for all span
  539.                                 // normally datedriver should have only 1 span but just in case the user defines several span, there will
  540.                                 // be no problem here. /!\ medianDate driver, startDate driver and stopDate driver must have same span number
  541.                                 for (int spanNumber = 1; spanNumber < d.getMedianDriver().getNamesSpanMap().getSpansNumber(); ++spanNumber) {
  542.                                     currentMedianNameSpan = d.getMedianDriver().getNamesSpanMap().getSpan(currentMedianNameSpan.getEnd());
  543.                                     median =
  544.                                             manageMedianDate(d.getStartDriver().getNamesSpanMap().getSpan(currentMedianNameSpan.getStart()).getData(),
  545.                                                     d.getStopDriver().getNamesSpanMap().getSpan(currentMedianNameSpan.getStart()).getData(),
  546.                                                     currentMedianNameSpan.getData());
  547.                                     names.add(median.getName());

  549.                                 }

  551.                             }
  552.                             if (d.getDurationDriver().isSelected()) {
  553.                                 // for first span
  554.                                 Span<String> currentDurationNameSpan = d.getDurationDriver().getNamesSpanMap().getFirstSpan();
  555.                                 Duration duration =
  556.                                         manageManeuverDuration(d.getStartDriver().getNamesSpanMap().getFirstSpan().getData(),
  557.                                                 d.getStopDriver().getNamesSpanMap().getFirstSpan().getData(), currentDurationNameSpan.getData());
  558.                                 names.add(duration.getName());
  559.                                 // for all span
  560.                                 for (int spanNumber = 1; spanNumber < d.getDurationDriver().getNamesSpanMap().getSpansNumber(); ++spanNumber) {
  561.                                     currentDurationNameSpan = d.getDurationDriver().getNamesSpanMap().getSpan(currentDurationNameSpan.getEnd());
  562.                                     duration =
  563.                                             manageManeuverDuration(d.getStartDriver().getNamesSpanMap().getSpan(currentDurationNameSpan.getStart()).getData(),
  564.                                                     d.getStopDriver().getNamesSpanMap().getSpan(currentDurationNameSpan.getStart()).getData(),
  565.                                                     currentDurationNameSpan.getData());
  566.                                     names.add(duration.getName());

  568.                                 }
  569.                             }
  570.                         });
  571.             }
  572.         }

  574.         return names;

  576.     }

  578.     /** Manage a maneuver trigger date.
  579.      * @param stmName name of the State Transition Matrix state
  580.      * @param maneuver maneuver force model
  581.      * @param mt trigger to which the driver is bound
  582.      * @param driverName name of the date driver
  583.      * @param start if true, the driver is a maneuver start
  584.      * @param threshold event detector threshold
  585.      * @return generator for the date driver
  586.      * @since 11.1
  587.      */
  588.     private TriggerDate manageTriggerDate(final String stmName,
  589.                                           final Maneuver maneuver,
  590.                                           final ManeuverTriggers mt,
  591.                                           final String driverName,
  592.                                           final boolean start,
  593.                                           final double threshold) {

  595.         TriggerDate triggerGenerator = null;

  597.         // check if we already have set up the provider
  598.         for (final AdditionalStateProvider provider : getAdditionalStateProviders()) {
  599.             if (provider instanceof TriggerDate &&
  600.                 provider.getName().equals(driverName)) {
  601.                 // the Jacobian column generator has already been set up in a previous propagation
  602.                 triggerGenerator = (TriggerDate) provider;
  603.                 break;
  604.             }
  605.         }

  607.         if (triggerGenerator == null) {
  608.             // this is the first time we need the Jacobian column generator, create it
  609.             triggerGenerator = new TriggerDate(stmName, driverName, start, maneuver, threshold);
  610.             mt.addResetter(triggerGenerator);
  611.             addAdditionalDerivativesProvider(triggerGenerator.getMassDepletionDelay());
  612.             addAdditionalStateProvider(triggerGenerator);
  613.         }

  615.         if (!getInitialIntegrationState().hasAdditionalState(driverName)) {
  616.             // add the initial Jacobian column if it is not already there
  617.             // (perhaps due to a previous propagation)
  618.             setInitialColumn(triggerGenerator.getMassDepletionDelay().getName(), new double[6]);
  619.             setInitialColumn(driverName, getHarvester().getInitialJacobianColumn(driverName));
  620.         }

  622.         return triggerGenerator;

  624.     }

  626.     /** Manage a maneuver median date.
  627.      * @param startName name of the start driver
  628.      * @param stopName name of the stop driver
  629.      * @param medianName name of the median driver
  630.      * @return generator for the median driver
  631.      * @since 11.1
  632.      */
  633.     private MedianDate manageMedianDate(final String startName, final String stopName, final String medianName) {

  635.         MedianDate medianGenerator = null;

  637.         // check if we already have set up the provider
  638.         for (final AdditionalStateProvider provider : getAdditionalStateProviders()) {
  639.             if (provider instanceof MedianDate &&
  640.                 provider.getName().equals(medianName)) {
  641.                 // the Jacobian column generator has already been set up in a previous propagation
  642.                 medianGenerator = (MedianDate) provider;
  643.                 break;
  644.             }
  645.         }

  647.         if (medianGenerator == null) {
  648.             // this is the first time we need the Jacobian column generator, create it
  649.             medianGenerator = new MedianDate(startName, stopName, medianName);
  650.             addAdditionalStateProvider(medianGenerator);
  651.         }

  653.         if (!getInitialIntegrationState().hasAdditionalState(medianName)) {
  654.             // add the initial Jacobian column if it is not already there
  655.             // (perhaps due to a previous propagation)
  656.             setInitialColumn(medianName, getHarvester().getInitialJacobianColumn(medianName));
  657.         }

  659.         return medianGenerator;

  661.     }

  663.     /** Manage a maneuver duration.
  664.      * @param startName name of the start driver
  665.      * @param stopName name of the stop driver
  666.      * @param durationName name of the duration driver
  667.      * @return generator for the median driver
  668.      * @since 11.1
  669.      */
  670.     private Duration manageManeuverDuration(final String startName, final String stopName, final String durationName) {

  672.         Duration durationGenerator = null;

  674.         // check if we already have set up the provider
  675.         for (final AdditionalStateProvider provider : getAdditionalStateProviders()) {
  676.             if (provider instanceof Duration &&
  677.                 provider.getName().equals(durationName)) {
  678.                 // the Jacobian column generator has already been set up in a previous propagation
  679.                 durationGenerator = (Duration) provider;
  680.                 break;
  681.             }
  682.         }

  684.         if (durationGenerator == null) {
  685.             // this is the first time we need the Jacobian column generator, create it
  686.             durationGenerator = new Duration(startName, stopName, durationName);
  687.             addAdditionalStateProvider(durationGenerator);
  688.         }

  690.         if (!getInitialIntegrationState().hasAdditionalState(durationName)) {
  691.             // add the initial Jacobian column if it is not already there
  692.             // (perhaps due to a previous propagation)
  693.             setInitialColumn(durationName, getHarvester().getInitialJacobianColumn(durationName));
  694.         }

  696.         return durationGenerator;

  698.     }

  700.     /** Set up the Jacobians columns generator for regular parameters.
  701.      * @param stmGenerator generator for the State Transition Matrix
  702.      * @param triggerDates names of the columns already managed as trigger dates
  703.      * @since 11.1
  704.      */
  705.     private void setUpRegularParametersJacobiansColumns(final StateTransitionMatrixGenerator stmGenerator,
  706.                                                         final List<String> triggerDates) {

  708.         // first pass: gather all parameters (excluding trigger dates), binding similar names together
  709.         final ParameterDriversList selected = new ParameterDriversList();
  710.         for (final ForceModel forceModel : getAllForceModels()) {
  711.             for (final ParameterDriver driver : forceModel.getParametersDrivers()) {
  712.                 if (!triggerDates.contains(driver.getNamesSpanMap().getFirstSpan().getData())) {
  713.                     // if the first span is not in triggerdate means that the driver is not a trigger
  714.                     // date and can be selected here
  715.                     selected.add(driver);
  716.                 }
  717.             }
  718.         }

  720.         // second pass: now that shared parameter names are bound together,
  721.         // their selections status have been synchronized, we can filter them
  722.         selected.filter(true);

  724.         // third pass: sort parameters lexicographically
  725.         selected.sort();

  727.         // add the Jacobians column generators corresponding to parameters, and setup state accordingly
  728.         // a new column is needed for each value estimated so for each span of the parameterDriver
  729.         for (final DelegatingDriver driver : selected.getDrivers()) {

  731.             for (Span<String> currentNameSpan = driver.getNamesSpanMap().getFirstSpan(); currentNameSpan != null; currentNameSpan = currentNameSpan.next()) {

  733.                 IntegrableJacobianColumnGenerator generator = null;
  734.                 // check if we already have set up the providers
  735.                 for (final AdditionalDerivativesProvider provider : getAdditionalDerivativesProviders()) {
  736.                     if (provider instanceof IntegrableJacobianColumnGenerator &&
  737.                         provider.getName().equals(currentNameSpan.getData())) {
  738.                         // the Jacobian column generator has already been set up in a previous propagation
  739.                         generator = (IntegrableJacobianColumnGenerator) provider;
  740.                         break;
  741.                     }

  743.                 }

  745.                 if (generator == null) {
  746.                     // this is the first time we need the Jacobian column generator, create it
  747.                     generator = new IntegrableJacobianColumnGenerator(stmGenerator, currentNameSpan.getData());
  748.                     addAdditionalDerivativesProvider(generator);
  749.                 }

  751.                 if (!getInitialIntegrationState().hasAdditionalState(currentNameSpan.getData())) {
  752.                     // add the initial Jacobian column if it is not already there
  753.                     // (perhaps due to a previous propagation)
  754.                     setInitialColumn(currentNameSpan.getData(), getHarvester().getInitialJacobianColumn(currentNameSpan.getData()));
  755.                 }

  757.             }

  759.         }

  761.     }

  763.     /** Add the initial value of the column to the initial state.
  764.      * <p>
  765.      * The initial state must already contain the Cartesian State Transition Matrix.
  766.      * </p>
  767.      * @param columnName name of the column
  768.      * @param dYdQ column of the Jacobian ∂Y/∂qₘ with respect to propagation type,
  769.      * if null (which is the most frequent case), assumed to be 0
  770.      * @since 11.1
  771.      */
  772.     private void setInitialColumn(final String columnName, final double[] dYdQ) {

  774.         final SpacecraftState state = getInitialState();

  776.         if (dYdQ.length != STATE_DIMENSION) {
  777.             throw new OrekitException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
  778.                                       dYdQ.length, STATE_DIMENSION);
  779.         }

  781.         // convert to Cartesian Jacobian
  782.         final double[][] dYdC = new double[STATE_DIMENSION][STATE_DIMENSION];
  783.         getOrbitType().convertType(state.getOrbit()).getJacobianWrtCartesian(getPositionAngleType(), dYdC);
  784.         final double[] column = new QRDecomposition(MatrixUtils.createRealMatrix(dYdC), THRESHOLD).
  785.                         getSolver().
  786.                         solve(MatrixUtils.createRealVector(dYdQ)).
  787.                         toArray();

  789.         // set additional state
  790.         setInitialState(state.addAdditionalState(columnName, column));

  792.     }

  794.     /** {@inheritDoc} */
  795.     @Override
  796.     public TimeStampedPVCoordinates getPVCoordinates(final AbsoluteDate date, final Frame frame) {
  797.         return propagate(date).getPVCoordinates(frame);
  798.     }

  800.     /** {@inheritDoc} */
  801.     @Override
  802.     protected StateMapper createMapper(final AbsoluteDate referenceDate, final double mu,
  803.                                        final OrbitType orbitType, final PositionAngleType positionAngleType,
  804.                                        final AttitudeProvider attitudeProvider, final Frame frame) {
  805.         return new OsculatingMapper(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  806.     }

  808.     /** Internal mapper using directly osculating parameters. */
  809.     private static class OsculatingMapper extends StateMapper {

  811.         /** Simple constructor.
  812.          * <p>
  813.          * The position parameter type is meaningful only if {@link
  814.          * #getOrbitType() propagation orbit type}
  815.          * support it. As an example, it is not meaningful for propagation
  816.          * in {@link OrbitType#CARTESIAN Cartesian} parameters.
  817.          * </p>
  818.          * @param referenceDate reference date
  819.          * @param mu central attraction coefficient (m³/s²)
  820.          * @param orbitType orbit type to use for mapping (can be null for {@link AbsolutePVCoordinates})
  821.          * @param positionAngleType angle type to use for propagation
  822.          * @param attitudeProvider attitude provider
  823.          * @param frame inertial frame
  824.          */
  825.         OsculatingMapper(final AbsoluteDate referenceDate, final double mu,
  826.                          final OrbitType orbitType, final PositionAngleType positionAngleType,
  827.                          final AttitudeProvider attitudeProvider, final Frame frame) {
  828.             super(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  829.         }

  831.         /** {@inheritDoc} */
  832.         public SpacecraftState mapArrayToState(final AbsoluteDate date, final double[] y, final double[] yDot,
  833.                                                final PropagationType type) {
  834.             // the parameter type is ignored for the Numerical Propagator

  836.             final double mass = y[6];
  837.             if (mass <= 0.0) {
  838.                 throw new OrekitException(OrekitMessages.NOT_POSITIVE_SPACECRAFT_MASS, mass);
  839.             }

  841.             if (getOrbitType() == null) {
  842.                 // propagation uses absolute position-velocity-acceleration
  843.                 final Vector3D p = new Vector3D(y[0],    y[1],    y[2]);
  844.                 final Vector3D v = new Vector3D(y[3],    y[4],    y[5]);
  845.                 final Vector3D a;
  846.                 final AbsolutePVCoordinates absPva;
  847.                 if (yDot == null) {
  848.                     absPva = new AbsolutePVCoordinates(getFrame(), new TimeStampedPVCoordinates(date, p, v));
  849.                 } else {
  850.                     a = new Vector3D(yDot[3], yDot[4], yDot[5]);
  851.                     absPva = new AbsolutePVCoordinates(getFrame(), new TimeStampedPVCoordinates(date, p, v, a));
  852.                 }

  854.                 final Attitude attitude = getAttitudeProvider().getAttitude(absPva, date, getFrame());
  855.                 return new SpacecraftState(absPva, attitude, mass);
  856.             } else {
  857.                 // propagation uses regular orbits
  858.                 final Orbit orbit       = getOrbitType().mapArrayToOrbit(y, yDot, getPositionAngleType(), date, getMu(), getFrame());
  859.                 final Attitude attitude = getAttitudeProvider().getAttitude(orbit, date, getFrame());

  861.                 return new SpacecraftState(orbit, attitude, mass);
  862.             }

  864.         }

  866.         /** {@inheritDoc} */
  867.         public void mapStateToArray(final SpacecraftState state, final double[] y, final double[] yDot) {
  868.             if (getOrbitType() == null) {
  869.                 // propagation uses absolute position-velocity-acceleration
  870.                 final Vector3D p = state.getAbsPVA().getPosition();
  871.                 final Vector3D v = state.getAbsPVA().getVelocity();
  872.                 y[0] = p.getX();
  873.                 y[1] = p.getY();
  874.                 y[2] = p.getZ();
  875.                 y[3] = v.getX();
  876.                 y[4] = v.getY();
  877.                 y[5] = v.getZ();
  878.                 y[6] = state.getMass();
  879.             }
  880.             else {
  881.                 getOrbitType().mapOrbitToArray(state.getOrbit(), getPositionAngleType(), y, yDot);
  882.                 y[6] = state.getMass();
  883.             }
  884.         }

  886.     }

  888.     /** {@inheritDoc} */
  889.     protected MainStateEquations getMainStateEquations(final ODEIntegrator integrator) {
  890.         return new Main(integrator);
  891.     }

  893.     /** Internal class for osculating parameters integration. */
  894.     private class Main implements MainStateEquations, TimeDerivativesEquations {

  896.         /** Derivatives array. */
  897.         private final double[] yDot;

  899.         /** Current state. */
  900.         private SpacecraftState currentState;

  902.         /** Jacobian of the orbital parameters with respect to the Cartesian parameters. */
  903.         private double[][] jacobian;

  905.         /** Simple constructor.
  906.          * @param integrator numerical integrator to use for propagation.
  907.          */
  908.         Main(final ODEIntegrator integrator) {

  910.             this.yDot     = new double[7];
  911.             this.jacobian = new double[6][6];

  913.             for (final ForceModel forceModel : forceModels) {
  914.                 forceModel.getEventDetectors().forEach(detector -> setUpEventDetector(integrator, detector));
  915.             }

  917.             if (getOrbitType() == null) {
  918.                 // propagation uses absolute position-velocity-acceleration
  919.                 // we can set Jacobian once and for all
  920.                 for (int i = 0; i < jacobian.length; ++i) {
  921.                     Arrays.fill(jacobian[i], 0.0);
  922.                     jacobian[i][i] = 1.0;
  923.                 }
  924.             }

  926.         }

  928.         /** {@inheritDoc} */
  929.         @Override
  930.         public void init(final SpacecraftState initialState, final AbsoluteDate target) {
  931.             forceModels.forEach(fm -> fm.init(initialState, target));
  932.         }

  934.         /** {@inheritDoc} */
  935.         @Override
  936.         public double[] computeDerivatives(final SpacecraftState state) {

  938.             currentState = state;
  939.             Arrays.fill(yDot, 0.0);
  940.             if (getOrbitType() != null) {
  941.                 // propagation uses regular orbits
  942.                 currentState.getOrbit().getJacobianWrtCartesian(getPositionAngleType(), jacobian);
  943.             }

  945.             // compute the contributions of all perturbing forces,
  946.             // using the Kepler contribution at the end since
  947.             // NewtonianAttraction is always the last instance in the list
  948.             for (final ForceModel forceModel : forceModels) {
  949.                 forceModel.addContribution(state, this);
  950.             }

  952.             if (getOrbitType() == null) {
  953.                 // position derivative is velocity, and was not added above in the force models
  954.                 // (it is added when orbit type is non-null because NewtonianAttraction considers it)
  955.                 final Vector3D velocity = currentState.getPVCoordinates().getVelocity();
  956.                 yDot[0] += velocity.getX();
  957.                 yDot[1] += velocity.getY();
  958.                 yDot[2] += velocity.getZ();
  959.             }


  962.             return yDot.clone();

  964.         }

  966.         /** {@inheritDoc} */
  967.         @Override
  968.         public void addKeplerContribution(final double mu) {
  969.             if (getOrbitType() == null) {
  970.                 // if mu is neither 0 nor NaN, we want to include Newtonian acceleration
  971.                 if (mu > 0) {
  972.                     // velocity derivative is Newtonian acceleration
  973.                     final Vector3D position = currentState.getPosition();
  974.                     final double r2         = position.getNormSq();
  975.                     final double coeff      = -mu / (r2 * FastMath.sqrt(r2));
  976.                     yDot[3] += coeff * position.getX();
  977.                     yDot[4] += coeff * position.getY();
  978.                     yDot[5] += coeff * position.getZ();
  979.                 }

  981.             } else {
  982.                 // propagation uses regular orbits
  983.                 currentState.getOrbit().addKeplerContribution(getPositionAngleType(), mu, yDot);
  984.             }
  985.         }

  987.         /** {@inheritDoc} */
  988.         public void addNonKeplerianAcceleration(final Vector3D gamma) {
  989.             for (int i = 0; i < 6; ++i) {
  990.                 final double[] jRow = jacobian[i];
  991.                 yDot[i] += jRow[3] * gamma.getX() + jRow[4] * gamma.getY() + jRow[5] * gamma.getZ();
  992.             }
  993.         }

  995.         /** {@inheritDoc} */
  996.         @Override
  997.         public void addMassDerivative(final double q) {
  998.             if (q > 0) {
  999.                 throw new OrekitIllegalArgumentException(OrekitMessages.POSITIVE_FLOW_RATE, q);
  1000.             }
  1001.             yDot[6] += q;
  1002.         }

  1004.     }

  1006.     /** Estimate tolerance vectors for integrators when propagating in absolute position-velocity-acceleration.
  1007.      * @param dP user specified position error
  1008.      * @param absPva reference absolute position-velocity-acceleration
  1009.      * @return a two rows array, row 0 being the absolute tolerance error and row 1
  1010.      * being the relative tolerance error
  1011.      * @see NumericalPropagator#tolerances(double, Orbit, OrbitType)
  1012.      */
  1013.     public static double[][] tolerances(final double dP, final AbsolutePVCoordinates absPva) {

  1015.         final double relative = dP / absPva.getPosition().getNorm();
  1016.         final double dV = relative * absPva.getVelocity().getNorm();

  1018.         final double[] absTol = new double[7];
  1019.         final double[] relTol = new double[7];

  1021.         absTol[0] = dP;
  1022.         absTol[1] = dP;
  1023.         absTol[2] = dP;
  1024.         absTol[3] = dV;
  1025.         absTol[4] = dV;
  1026.         absTol[5] = dV;

  1028.         // we set the mass tolerance arbitrarily to 1.0e-6 kg, as mass evolves linearly
  1029.         // with trust, this often has no influence at all on propagation
  1030.         absTol[6] = 1.0e-6;

  1032.         Arrays.fill(relTol, relative);

  1034.         return new double[][] {
  1035.             absTol, relTol
  1036.         };

  1038.     }

  1040.     /** Estimate tolerance vectors for integrators when propagating in orbits.
  1041.      * <p>
  1042.      * The errors are estimated from partial derivatives properties of orbits,
  1043.      * starting from a scalar position error specified by the user.
  1044.      * Considering the energy conservation equation V = sqrt(mu (2/r - 1/a)),
  1045.      * we get at constant energy (i.e. on a Keplerian trajectory):
  1046.      * <pre>
  1047.      * V r² |dV| = mu |dr|
  1048.      * </pre>
  1049.      * <p> So we deduce a scalar velocity error consistent with the position error.
  1050.      * From here, we apply orbits Jacobians matrices to get consistent errors
  1051.      * on orbital parameters.
  1052.      *
  1053.      * <p>
  1054.      * The tolerances are only <em>orders of magnitude</em>, and integrator tolerances
  1055.      * are only local estimates, not global ones. So some care must be taken when using
  1056.      * these tolerances. Setting 1mm as a position error does NOT mean the tolerances
  1057.      * will guarantee a 1mm error position after several orbits integration.
  1058.      * </p>
  1059.      * @param dP user specified position error
  1060.      * @param orbit reference orbit
  1061.      * @param type propagation type for the meaning of the tolerance vectors elements
  1062.      * (it may be different from {@code orbit.getType()})
  1063.      * @return a two rows array, row 0 being the absolute tolerance error and row 1
  1064.      * being the relative tolerance error
  1065.      */
  1066.     public static double[][] tolerances(final double dP, final Orbit orbit, final OrbitType type) {

  1068.         // estimate the scalar velocity error
  1069.         final PVCoordinates pv = orbit.getPVCoordinates();
  1070.         final double r2 = pv.getPosition().getNormSq();
  1071.         final double v  = pv.getVelocity().getNorm();
  1072.         final double dV = orbit.getMu() * dP / (v * r2);

  1074.         return tolerances(dP, dV, orbit, type);

  1076.     }

  1078.     /** Estimate tolerance vectors for integrators when propagating in orbits.
  1079.      * <p>
  1080.      * The errors are estimated from partial derivatives properties of orbits,
  1081.      * starting from scalar position and velocity errors specified by the user.
  1082.      * <p>
  1083.      * The tolerances are only <em>orders of magnitude</em>, and integrator tolerances
  1084.      * are only local estimates, not global ones. So some care must be taken when using
  1085.      * these tolerances. Setting 1mm as a position error does NOT mean the tolerances
  1086.      * will guarantee a 1mm error position after several orbits integration.
  1087.      * </p>
  1088.      * @param dP user specified position error
  1089.      * @param dV user specified velocity error
  1090.      * @param orbit reference orbit
  1091.      * @param type propagation type for the meaning of the tolerance vectors elements
  1092.      * (it may be different from {@code orbit.getType()})
  1093.      * @return a two rows array, row 0 being the absolute tolerance error and row 1
  1094.      * being the relative tolerance error
  1095.      * @since 10.3
  1096.      */
  1097.     public static double[][] tolerances(final double dP, final double dV,
  1098.                                         final Orbit orbit, final OrbitType type) {

  1100.         final double[] absTol = new double[7];
  1101.         final double[] relTol = new double[7];

  1103.         // we set the mass tolerance arbitrarily to 1.0e-6 kg, as mass evolves linearly
  1104.         // with trust, this often has no influence at all on propagation
  1105.         absTol[6] = 1.0e-6;

  1107.         if (type == OrbitType.CARTESIAN) {
  1108.             absTol[0] = dP;
  1109.             absTol[1] = dP;
  1110.             absTol[2] = dP;
  1111.             absTol[3] = dV;
  1112.             absTol[4] = dV;
  1113.             absTol[5] = dV;
  1114.         } else {

  1116.             // convert the orbit to the desired type
  1117.             final double[][] jacobian = new double[6][6];
  1118.             final Orbit converted = type.convertType(orbit);
  1119.             converted.getJacobianWrtCartesian(PositionAngleType.TRUE, jacobian);

  1121.             for (int i = 0; i < 6; ++i) {
  1122.                 final double[] row = jacobian[i];
  1123.                 absTol[i] = FastMath.abs(row[0]) * dP +
  1124.                             FastMath.abs(row[1]) * dP +
  1125.                             FastMath.abs(row[2]) * dP +
  1126.                             FastMath.abs(row[3]) * dV +
  1127.                             FastMath.abs(row[4]) * dV +
  1128.                             FastMath.abs(row[5]) * dV;
  1129.                 if (Double.isNaN(absTol[i])) {
  1130.                     throw new OrekitException(OrekitMessages.SINGULAR_JACOBIAN_FOR_ORBIT_TYPE, type);
  1131.                 }
  1132.             }

  1134.         }

  1136.         Arrays.fill(relTol, dP / FastMath.sqrt(orbit.getPosition().getNormSq()));

  1138.         return new double[][] {
  1139.             absTol, relTol
  1140.         };

  1142.     }

  1144.     /** {@inheritDoc} */
  1145.     @Override
  1146.     protected void beforeIntegration(final SpacecraftState initialState, final AbsoluteDate tEnd) {

  1148.         if (!getFrame().isPseudoInertial()) {

  1150.             // inspect all force models to find InertialForces
  1151.             for (ForceModel force : forceModels) {
  1152.                 if (force instanceof InertialForces) {
  1153.                     return;
  1154.                 }
  1155.             }

  1157.             // throw exception if no inertial forces found
  1158.             throw new OrekitException(OrekitMessages.INERTIAL_FORCE_MODEL_MISSING, getFrame().getName());

  1160.         }

  1162.     }

  1164. }
Created with JaCoCo 0.8.11.202310140853