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.attitudes.AttitudeProviderModifier;
  36. import org.orekit.data.DataContext;
  37. import org.orekit.errors.OrekitException;
  38. import org.orekit.errors.OrekitIllegalArgumentException;
  39. import org.orekit.errors.OrekitInternalError;
  40. import org.orekit.errors.OrekitMessages;
  41. import org.orekit.forces.ForceModel;
  42. import org.orekit.forces.gravity.NewtonianAttraction;
  43. import org.orekit.forces.inertia.InertialForces;
  44. import org.orekit.forces.maneuvers.Maneuver;
  45. import org.orekit.forces.maneuvers.jacobians.Duration;
  46. import org.orekit.forces.maneuvers.jacobians.MedianDate;
  47. import org.orekit.forces.maneuvers.jacobians.TriggerDate;
  48. import org.orekit.forces.maneuvers.trigger.ManeuverTriggers;
  49. import org.orekit.frames.Frame;
  50. import org.orekit.orbits.Orbit;
  51. import org.orekit.orbits.OrbitType;
  52. import org.orekit.orbits.PositionAngleType;
  53. import org.orekit.propagation.AbstractMatricesHarvester;
  54. import org.orekit.propagation.AdditionalStateProvider;
  55. import org.orekit.propagation.MatricesHarvester;
  56. import org.orekit.propagation.PropagationType;
  57. import org.orekit.propagation.Propagator;
  58. import org.orekit.propagation.SpacecraftState;
  59. import org.orekit.propagation.events.EventDetector;
  60. import org.orekit.propagation.events.ParameterDrivenDateIntervalDetector;
  61. import org.orekit.propagation.integration.AbstractIntegratedPropagator;
  62. import org.orekit.propagation.integration.AdditionalDerivativesProvider;
  63. import org.orekit.propagation.integration.StateMapper;
  64. import org.orekit.time.AbsoluteDate;
  65. import org.orekit.utils.AbsolutePVCoordinates;
  66. import org.orekit.utils.DoubleArrayDictionary;
  67. import org.orekit.utils.PVCoordinates;
  68. import org.orekit.utils.ParameterDriver;
  69. import org.orekit.utils.ParameterDriversList;
  70. import org.orekit.utils.ParameterDriversList.DelegatingDriver;
  71. import org.orekit.utils.TimeSpanMap.Span;
  72. import org.orekit.utils.ParameterObserver;
  73. import org.orekit.utils.TimeSpanMap;
  74. import org.orekit.utils.TimeStampedPVCoordinates;

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

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

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

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

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

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

  185.     /**
  186.      * boolean to know if a full attitude (with rates) is needed when computing derivatives for the ODE.
  187.      * since 12.1
  188.      */
  189.     private boolean needFullAttitudeForDerivatives = true;

  191.     /** Create a new instance of NumericalPropagator, based on orbit definition mu.
  192.      * After creation, the instance is empty, i.e. the attitude provider is set to an
  193.      * unspecified default law and there are no perturbing forces at all.
  194.      * This means that if {@link #addForceModel addForceModel} is not
  195.      * called after creation, the integrated orbit will follow a Keplerian
  196.      * evolution only. The defaults are {@link OrbitType#EQUINOCTIAL}
  197.      * for {@link #setOrbitType(OrbitType) propagation
  198.      * orbit type} and {@link PositionAngleType#TRUE} for {@link
  199.      * #setPositionAngleType(PositionAngleType) position angle type}.
  200.      *
  201.      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
  202.      *
  203.      * @param integrator numerical integrator to use for propagation.
  204.      * @see #NumericalPropagator(ODEIntegrator, AttitudeProvider)
  205.      */
  206.     @DefaultDataContext
  207.     public NumericalPropagator(final ODEIntegrator integrator) {
  208.         this(integrator,
  209.                 Propagator.getDefaultLaw(DataContext.getDefault().getFrames()));
  210.     }

  212.     /** Create a new instance of NumericalPropagator, based on orbit definition mu.
  213.      * After creation, the instance is empty, i.e. the attitude provider is set to an
  214.      * unspecified default law and there are no perturbing forces at all.
  215.      * This means that if {@link #addForceModel addForceModel} is not
  216.      * called after creation, the integrated orbit will follow a Keplerian
  217.      * evolution only. The defaults are {@link OrbitType#EQUINOCTIAL}
  218.      * for {@link #setOrbitType(OrbitType) propagation
  219.      * orbit type} and {@link PositionAngleType#TRUE} for {@link
  220.      * #setPositionAngleType(PositionAngleType) position angle type}.
  221.      * @param integrator numerical integrator to use for propagation.
  222.      * @param attitudeProvider the attitude law.
  223.      * @since 10.1
  224.      */
  225.     public NumericalPropagator(final ODEIntegrator integrator,
  226.                                final AttitudeProvider attitudeProvider) {
  227.         super(integrator, PropagationType.OSCULATING);
  228.         forceModels             = new ArrayList<>();
  229.         ignoreCentralAttraction = false;
  230.         initMapper();
  231.         setAttitudeProvider(attitudeProvider);
  232.         clearStepHandlers();
  233.         setOrbitType(OrbitType.EQUINOCTIAL);
  234.         setPositionAngleType(PositionAngleType.TRUE);
  235.     }

  237.     /** Set the flag to ignore or not the creation of a {@link NewtonianAttraction}.
  238.      * @param ignoreCentralAttraction if true, {@link NewtonianAttraction} is <em>not</em>
  239.      * added automatically if missing
  240.      */
  241.     public void setIgnoreCentralAttraction(final boolean ignoreCentralAttraction) {
  242.         this.ignoreCentralAttraction = ignoreCentralAttraction;
  243.     }

  245.      /** Set the central attraction coefficient μ.
  246.       * <p>
  247.       * Setting the central attraction coefficient is
  248.       * equivalent to {@link #addForceModel(ForceModel) add}
  249.       * a {@link NewtonianAttraction} force model.
  250.       * * </p>
  251.       * @param mu central attraction coefficient (m³/s²)
  252.       * @see #addForceModel(ForceModel)
  253.       * @see #getAllForceModels()
  254.       */
  255.     @Override
  256.     public void setMu(final double mu) {
  257.         if (ignoreCentralAttraction) {
  258.             superSetMu(mu);
  259.         } else {
  260.             addForceModel(new NewtonianAttraction(mu));
  261.             superSetMu(mu);
  262.         }
  263.     }

  265.     /** Set the central attraction coefficient μ only in upper class.
  266.      * @param mu central attraction coefficient (m³/s²)
  267.      */
  268.     private void superSetMu(final double mu) {
  269.         super.setMu(mu);
  270.     }

  272.     /** Check if Newtonian attraction force model is available.
  273.      * <p>
  274.      * Newtonian attraction is always the last force model in the list.
  275.      * </p>
  276.      * @return true if Newtonian attraction force model is available
  277.      */
  278.     private boolean hasNewtonianAttraction() {
  279.         final int last = forceModels.size() - 1;
  280.         return last >= 0 && forceModels.get(last) instanceof NewtonianAttraction;
  281.     }

  283.     /** Add a force model.
  284.      * <p>If this method is not called at all, the integrated orbit will follow
  285.      * a Keplerian evolution only.</p>
  286.      * @param model {@link ForceModel} to add (it can be either a perturbing force
  287.      * model or an instance of {@link NewtonianAttraction})
  288.      * @see #removeForceModels()
  289.      * @see #setMu(double)
  290.      */
  291.     public void addForceModel(final ForceModel model) {

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

  296.             try {
  297.                 // ensure we are notified of any mu change
  298.                 model.getParametersDrivers().get(0).addObserver(new ParameterObserver() {
  299.                     /** {@inheritDoc} */
  300.                     @Override
  301.                     public void valueSpanMapChanged(final TimeSpanMap<Double> previousValue, final ParameterDriver driver) {
  302.                         superSetMu(driver.getValue());
  303.                     }
  304.                     /** {@inheritDoc} */
  305.                     @Override
  306.                     public void valueChanged(final double previousValue, final ParameterDriver driver, final AbsoluteDate date) {
  307.                         superSetMu(driver.getValue());
  308.                     }
  309.                 });
  310.             } catch (OrekitException oe) {
  311.                 // this should never happen
  312.                 throw new OrekitInternalError(oe);
  313.             }

  315.             if (hasNewtonianAttraction()) {
  316.                 // there is already a central attraction model, replace it
  317.                 forceModels.set(forceModels.size() - 1, model);
  318.             } else {
  319.                 // there are no central attraction model yet, add it at the end of the list
  320.                 forceModels.add(model);
  321.             }
  322.         } else {
  323.             // we want to add a perturbing force model
  324.             if (hasNewtonianAttraction()) {
  325.                 // insert the new force model before Newtonian attraction,
  326.                 // which should always be the last one in the list
  327.                 forceModels.add(forceModels.size() - 1, model);
  328.             } else {
  329.                 // we only have perturbing force models up to now, just append at the end of the list
  330.                 forceModels.add(model);
  331.             }
  332.         }

  334.     }

  336.     /** Remove all force models (except central attraction).
  337.      * <p>Once all perturbing forces have been removed (and as long as no new force
  338.      * model is added), the integrated orbit will follow a Keplerian evolution
  339.      * only.</p>
  340.      * @see #addForceModel(ForceModel)
  341.      */
  342.     public void removeForceModels() {
  343.         final int last = forceModels.size() - 1;
  344.         if (hasNewtonianAttraction()) {
  345.             // preserve the Newtonian attraction model at the end
  346.             final ForceModel newton = forceModels.get(last);
  347.             forceModels.clear();
  348.             forceModels.add(newton);
  349.         } else {
  350.             forceModels.clear();
  351.         }
  352.     }

  354.     /** Get all the force models, perturbing forces and Newtonian attraction included.
  355.      * @return list of perturbing force models, with Newtonian attraction being the
  356.      * last one
  357.      * @see #addForceModel(ForceModel)
  358.      * @see #setMu(double)
  359.      */
  360.     public List<ForceModel> getAllForceModels() {
  361.         return Collections.unmodifiableList(forceModels);
  362.     }

  364.     /** Set propagation orbit type.
  365.      * @param orbitType orbit type to use for propagation, null for
  366.      * propagating using {@link org.orekit.utils.AbsolutePVCoordinates} rather than {@link Orbit}
  367.      */
  368.     @Override
  369.     public void setOrbitType(final OrbitType orbitType) {
  370.         super.setOrbitType(orbitType);
  371.     }

  373.     /** Get propagation parameter type.
  374.      * @return orbit type used for propagation, null for
  375.      * propagating using {@link org.orekit.utils.AbsolutePVCoordinates} rather than {@link Orbit}
  376.      */
  377.     @Override
  378.     public OrbitType getOrbitType() {
  379.         return super.getOrbitType();
  380.     }

  382.     /** Set position angle type.
  383.      * <p>
  384.      * The position parameter type is meaningful only if {@link
  385.      * #getOrbitType() propagation orbit type}
  386.      * support it. As an example, it is not meaningful for propagation
  387.      * in {@link OrbitType#CARTESIAN Cartesian} parameters.
  388.      * </p>
  389.      * @param positionAngleType angle type to use for propagation
  390.      */
  391.     @Override
  392.     public void setPositionAngleType(final PositionAngleType positionAngleType) {
  393.         super.setPositionAngleType(positionAngleType);
  394.     }

  396.     /** Get propagation parameter type.
  397.      * @return angle type to use for propagation
  398.      */
  399.     @Override
  400.     public PositionAngleType getPositionAngleType() {
  401.         return super.getPositionAngleType();
  402.     }

  404.     /** Set the initial state.
  405.      * @param initialState initial state
  406.      */
  407.     public void setInitialState(final SpacecraftState initialState) {
  408.         resetInitialState(initialState);
  409.     }

  411.     /** {@inheritDoc} */
  412.     @Override
  413.     public void resetInitialState(final SpacecraftState state) {
  414.         super.resetInitialState(state);
  415.         if (!hasNewtonianAttraction()) {
  416.             // use the state to define central attraction
  417.             setMu(state.getMu());
  418.         }
  419.         setStartDate(state.getDate());
  420.     }

  422.     /** Get the names of the parameters in the matrix returned by {@link MatricesHarvester#getParametersJacobian}.
  423.      * @return names of the parameters (i.e. columns) of the Jacobian matrix
  424.      */
  425.     List<String> getJacobiansColumnsNames() {
  426.         final List<String> columnsNames = new ArrayList<>();
  427.         for (final ForceModel forceModel : getAllForceModels()) {
  428.             for (final ParameterDriver driver : forceModel.getParametersDrivers()) {
  429.                 if (driver.isSelected() && !columnsNames.contains(driver.getNamesSpanMap().getFirstSpan().getData())) {
  430.                     // As driver with same name should have same NamesSpanMap we only check if the first span is present,
  431.                     // if not we add all span names to columnsNames
  432.                     for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
  433.                         columnsNames.add(span.getData());
  434.                     }
  435.                 }
  436.             }
  437.         }
  438.         Collections.sort(columnsNames);
  439.         return columnsNames;
  440.     }

  442.     /** {@inheritDoc} */
  443.     @Override
  444.     protected AbstractMatricesHarvester createHarvester(final String stmName, final RealMatrix initialStm,
  445.                                                         final DoubleArrayDictionary initialJacobianColumns) {
  446.         return new NumericalPropagationHarvester(this, stmName, initialStm, initialJacobianColumns);
  447.     }

  449.     /** {@inheritDoc} */
  450.     @Override
  451.     protected void setUpStmAndJacobianGenerators() {

  453.         final AbstractMatricesHarvester harvester = getHarvester();
  454.         if (harvester != null) {

  456.             // set up the additional equations and additional state providers
  457.             final StateTransitionMatrixGenerator stmGenerator = setUpStmGenerator();
  458.             final List<String> triggersDates = setUpTriggerDatesJacobiansColumns(stmGenerator.getName());
  459.             setUpRegularParametersJacobiansColumns(stmGenerator, triggersDates);

  461.             // as we are now starting the propagation, everything is configured
  462.             // we can freeze the names in the harvester
  463.             harvester.freezeColumnsNames();

  465.         }

  467.     }

  469.     /** Set up the State Transition Matrix Generator.
  470.      * @return State Transition Matrix Generator
  471.      * @since 11.1
  472.      */
  473.     private StateTransitionMatrixGenerator setUpStmGenerator() {

  475.         final AbstractMatricesHarvester harvester = getHarvester();

  477.         // add the STM generator corresponding to the current settings, and setup state accordingly
  478.         StateTransitionMatrixGenerator stmGenerator = null;
  479.         for (final AdditionalDerivativesProvider equations : getAdditionalDerivativesProviders()) {
  480.             if (equations instanceof StateTransitionMatrixGenerator &&
  481.                 equations.getName().equals(harvester.getStmName())) {
  482.                 // the STM generator has already been set up in a previous propagation
  483.                 stmGenerator = (StateTransitionMatrixGenerator) equations;
  484.                 break;
  485.             }
  486.         }
  487.         if (stmGenerator == null) {
  488.             // this is the first time we need the STM generate, create it
  489.             stmGenerator = new StateTransitionMatrixGenerator(harvester.getStmName(), getAllForceModels(), getAttitudeProvider());
  490.             addAdditionalDerivativesProvider(stmGenerator);
  491.         }

  493.         if (!getInitialIntegrationState().hasAdditionalState(harvester.getStmName())) {
  494.             // add the initial State Transition Matrix if it is not already there
  495.             // (perhaps due to a previous propagation)
  496.             setInitialState(stmGenerator.setInitialStateTransitionMatrix(getInitialState(),
  497.                                                                          harvester.getInitialStateTransitionMatrix(),
  498.                                                                          getOrbitType(),
  499.                                                                          getPositionAngleType()));
  500.         }

  502.         return stmGenerator;

  504.     }

  506.     /** Set up the Jacobians columns generator dedicated to trigger dates.
  507.      * @param stmName name of the State Transition Matrix state
  508.      * @return names of the columns corresponding to trigger dates
  509.      * @since 11.1
  510.      */
  511.     private List<String> setUpTriggerDatesJacobiansColumns(final String stmName) {

  513.         final List<String> names = new ArrayList<>();
  514.         for (final ForceModel forceModel : getAllForceModels()) {
  515.             if (forceModel instanceof Maneuver) {
  516.                 final Maneuver maneuver = (Maneuver) forceModel;
  517.                 final ManeuverTriggers maneuverTriggers = maneuver.getManeuverTriggers();

  519.                 maneuverTriggers.getEventDetectors().
  520.                         filter(d -> d instanceof ParameterDrivenDateIntervalDetector).
  521.                         map(d -> (ParameterDrivenDateIntervalDetector) d).
  522.                         forEach(d -> {
  523.                             TriggerDate start;
  524.                             TriggerDate stop;

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

  562.                                 }

  564.                             }
  565.                             if (d.getDurationDriver().isSelected()) {
  566.                                 // for first span
  567.                                 Span<String> currentDurationNameSpan = d.getDurationDriver().getNamesSpanMap().getFirstSpan();
  568.                                 Duration duration =
  569.                                         manageManeuverDuration(d.getStartDriver().getNamesSpanMap().getFirstSpan().getData(),
  570.                                                 d.getStopDriver().getNamesSpanMap().getFirstSpan().getData(), currentDurationNameSpan.getData());
  571.                                 names.add(duration.getName());
  572.                                 // for all span
  573.                                 for (int spanNumber = 1; spanNumber < d.getDurationDriver().getNamesSpanMap().getSpansNumber(); ++spanNumber) {
  574.                                     currentDurationNameSpan = d.getDurationDriver().getNamesSpanMap().getSpan(currentDurationNameSpan.getEnd());
  575.                                     duration =
  576.                                             manageManeuverDuration(d.getStartDriver().getNamesSpanMap().getSpan(currentDurationNameSpan.getStart()).getData(),
  577.                                                     d.getStopDriver().getNamesSpanMap().getSpan(currentDurationNameSpan.getStart()).getData(),
  578.                                                     currentDurationNameSpan.getData());
  579.                                     names.add(duration.getName());

  581.                                 }
  582.                             }
  583.                         });
  584.             }
  585.         }

  587.         return names;

  589.     }

  591.     /** Manage a maneuver trigger date.
  592.      * @param stmName name of the State Transition Matrix state
  593.      * @param maneuver maneuver force model
  594.      * @param mt trigger to which the driver is bound
  595.      * @param driverName name of the date driver
  596.      * @param start if true, the driver is a maneuver start
  597.      * @param threshold event detector threshold
  598.      * @return generator for the date driver
  599.      * @since 11.1
  600.      */
  601.     private TriggerDate manageTriggerDate(final String stmName,
  602.                                           final Maneuver maneuver,
  603.                                           final ManeuverTriggers mt,
  604.                                           final String driverName,
  605.                                           final boolean start,
  606.                                           final double threshold) {

  608.         TriggerDate triggerGenerator = null;

  610.         // check if we already have set up the provider
  611.         for (final AdditionalStateProvider provider : getAdditionalStateProviders()) {
  612.             if (provider instanceof TriggerDate &&
  613.                 provider.getName().equals(driverName)) {
  614.                 // the Jacobian column generator has already been set up in a previous propagation
  615.                 triggerGenerator = (TriggerDate) provider;
  616.                 break;
  617.             }
  618.         }

  620.         if (triggerGenerator == null) {
  621.             // this is the first time we need the Jacobian column generator, create it
  622.             triggerGenerator = new TriggerDate(stmName, driverName, start, maneuver, threshold);
  623.             mt.addResetter(triggerGenerator);
  624.             addAdditionalDerivativesProvider(triggerGenerator.getMassDepletionDelay());
  625.             addAdditionalStateProvider(triggerGenerator);
  626.         }

  628.         if (!getInitialIntegrationState().hasAdditionalState(driverName)) {
  629.             // add the initial Jacobian column if it is not already there
  630.             // (perhaps due to a previous propagation)
  631.             setInitialColumn(triggerGenerator.getMassDepletionDelay().getName(), new double[6]);
  632.             setInitialColumn(driverName, getHarvester().getInitialJacobianColumn(driverName));
  633.         }

  635.         return triggerGenerator;

  637.     }

  639.     /** Manage a maneuver median date.
  640.      * @param startName name of the start driver
  641.      * @param stopName name of the stop driver
  642.      * @param medianName name of the median driver
  643.      * @return generator for the median driver
  644.      * @since 11.1
  645.      */
  646.     private MedianDate manageMedianDate(final String startName, final String stopName, final String medianName) {

  648.         MedianDate medianGenerator = null;

  650.         // check if we already have set up the provider
  651.         for (final AdditionalStateProvider provider : getAdditionalStateProviders()) {
  652.             if (provider instanceof MedianDate &&
  653.                 provider.getName().equals(medianName)) {
  654.                 // the Jacobian column generator has already been set up in a previous propagation
  655.                 medianGenerator = (MedianDate) provider;
  656.                 break;
  657.             }
  658.         }

  660.         if (medianGenerator == null) {
  661.             // this is the first time we need the Jacobian column generator, create it
  662.             medianGenerator = new MedianDate(startName, stopName, medianName);
  663.             addAdditionalStateProvider(medianGenerator);
  664.         }

  666.         if (!getInitialIntegrationState().hasAdditionalState(medianName)) {
  667.             // add the initial Jacobian column if it is not already there
  668.             // (perhaps due to a previous propagation)
  669.             setInitialColumn(medianName, getHarvester().getInitialJacobianColumn(medianName));
  670.         }

  672.         return medianGenerator;

  674.     }

  676.     /** Manage a maneuver duration.
  677.      * @param startName name of the start driver
  678.      * @param stopName name of the stop driver
  679.      * @param durationName name of the duration driver
  680.      * @return generator for the median driver
  681.      * @since 11.1
  682.      */
  683.     private Duration manageManeuverDuration(final String startName, final String stopName, final String durationName) {

  685.         Duration durationGenerator = null;

  687.         // check if we already have set up the provider
  688.         for (final AdditionalStateProvider provider : getAdditionalStateProviders()) {
  689.             if (provider instanceof Duration &&
  690.                 provider.getName().equals(durationName)) {
  691.                 // the Jacobian column generator has already been set up in a previous propagation
  692.                 durationGenerator = (Duration) provider;
  693.                 break;
  694.             }
  695.         }

  697.         if (durationGenerator == null) {
  698.             // this is the first time we need the Jacobian column generator, create it
  699.             durationGenerator = new Duration(startName, stopName, durationName);
  700.             addAdditionalStateProvider(durationGenerator);
  701.         }

  703.         if (!getInitialIntegrationState().hasAdditionalState(durationName)) {
  704.             // add the initial Jacobian column if it is not already there
  705.             // (perhaps due to a previous propagation)
  706.             setInitialColumn(durationName, getHarvester().getInitialJacobianColumn(durationName));
  707.         }

  709.         return durationGenerator;

  711.     }

  713.     /** Set up the Jacobians columns generator for regular parameters.
  714.      * @param stmGenerator generator for the State Transition Matrix
  715.      * @param triggerDates names of the columns already managed as trigger dates
  716.      * @since 11.1
  717.      */
  718.     private void setUpRegularParametersJacobiansColumns(final StateTransitionMatrixGenerator stmGenerator,
  719.                                                         final List<String> triggerDates) {

  721.         // first pass: gather all parameters (excluding trigger dates), binding similar names together
  722.         final ParameterDriversList selected = new ParameterDriversList();
  723.         for (final ForceModel forceModel : getAllForceModels()) {
  724.             for (final ParameterDriver driver : forceModel.getParametersDrivers()) {
  725.                 if (!triggerDates.contains(driver.getNamesSpanMap().getFirstSpan().getData())) {
  726.                     // if the first span is not in triggerdate means that the driver is not a trigger
  727.                     // date and can be selected here
  728.                     selected.add(driver);
  729.                 }
  730.             }
  731.         }

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

  737.         // third pass: sort parameters lexicographically
  738.         selected.sort();

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

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

  746.                 IntegrableJacobianColumnGenerator generator = null;
  747.                 // check if we already have set up the providers
  748.                 for (final AdditionalDerivativesProvider provider : getAdditionalDerivativesProviders()) {
  749.                     if (provider instanceof IntegrableJacobianColumnGenerator &&
  750.                         provider.getName().equals(currentNameSpan.getData())) {
  751.                         // the Jacobian column generator has already been set up in a previous propagation
  752.                         generator = (IntegrableJacobianColumnGenerator) provider;
  753.                         break;
  754.                     }

  756.                 }

  758.                 if (generator == null) {
  759.                     // this is the first time we need the Jacobian column generator, create it
  760.                     generator = new IntegrableJacobianColumnGenerator(stmGenerator, currentNameSpan.getData());
  761.                     addAdditionalDerivativesProvider(generator);
  762.                 }

  764.                 if (!getInitialIntegrationState().hasAdditionalState(currentNameSpan.getData())) {
  765.                     // add the initial Jacobian column if it is not already there
  766.                     // (perhaps due to a previous propagation)
  767.                     setInitialColumn(currentNameSpan.getData(), getHarvester().getInitialJacobianColumn(currentNameSpan.getData()));
  768.                 }

  770.             }

  772.         }

  774.     }

  776.     /** Add the initial value of the column to the initial state.
  777.      * <p>
  778.      * The initial state must already contain the Cartesian State Transition Matrix.
  779.      * </p>
  780.      * @param columnName name of the column
  781.      * @param dYdQ column of the Jacobian ∂Y/∂qₘ with respect to propagation type,
  782.      * if null (which is the most frequent case), assumed to be 0
  783.      * @since 11.1
  784.      */
  785.     private void setInitialColumn(final String columnName, final double[] dYdQ) {

  787.         final SpacecraftState state = getInitialState();

  789.         if (dYdQ.length != STATE_DIMENSION) {
  790.             throw new OrekitException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
  791.                                       dYdQ.length, STATE_DIMENSION);
  792.         }

  794.         // convert to Cartesian Jacobian
  795.         final double[][] dYdC = new double[STATE_DIMENSION][STATE_DIMENSION];
  796.         getOrbitType().convertType(state.getOrbit()).getJacobianWrtCartesian(getPositionAngleType(), dYdC);
  797.         final double[] column = new QRDecomposition(MatrixUtils.createRealMatrix(dYdC), THRESHOLD).
  798.                         getSolver().
  799.                         solve(MatrixUtils.createRealVector(dYdQ)).
  800.                         toArray();

  802.         // set additional state
  803.         setInitialState(state.addAdditionalState(columnName, column));

  805.     }

  807.     /** {@inheritDoc} */
  808.     @Override
  809.     protected AttitudeProvider initializeAttitudeProviderForDerivatives() {
  810.         final AttitudeProvider attitudeProvider = getAttitudeProvider();
  811.         return needFullAttitudeForDerivatives ? attitudeProvider :
  812.                 AttitudeProviderModifier.getFrozenAttitudeProvider(attitudeProvider);
  813.     }

  815.     /** {@inheritDoc} */
  816.     @Override
  817.     protected StateMapper createMapper(final AbsoluteDate referenceDate, final double mu,
  818.                                        final OrbitType orbitType, final PositionAngleType positionAngleType,
  819.                                        final AttitudeProvider attitudeProvider, final Frame frame) {
  820.         return new OsculatingMapper(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  821.     }

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

  826.         /** Simple constructor.
  827.          * <p>
  828.          * The position parameter type is meaningful only if {@link
  829.          * #getOrbitType() propagation orbit type}
  830.          * support it. As an example, it is not meaningful for propagation
  831.          * in {@link OrbitType#CARTESIAN Cartesian} parameters.
  832.          * </p>
  833.          * @param referenceDate reference date
  834.          * @param mu central attraction coefficient (m³/s²)
  835.          * @param orbitType orbit type to use for mapping (can be null for {@link AbsolutePVCoordinates})
  836.          * @param positionAngleType angle type to use for propagation
  837.          * @param attitudeProvider attitude provider
  838.          * @param frame inertial frame
  839.          */
  840.         OsculatingMapper(final AbsoluteDate referenceDate, final double mu,
  841.                          final OrbitType orbitType, final PositionAngleType positionAngleType,
  842.                          final AttitudeProvider attitudeProvider, final Frame frame) {
  843.             super(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  844.         }

  846.         /** {@inheritDoc} */
  847.         public SpacecraftState mapArrayToState(final AbsoluteDate date, final double[] y, final double[] yDot,
  848.                                                final PropagationType type) {
  849.             // the parameter type is ignored for the Numerical Propagator

  851.             final double mass = y[6];
  852.             if (mass <= 0.0) {
  853.                 throw new OrekitException(OrekitMessages.NOT_POSITIVE_SPACECRAFT_MASS, mass);
  854.             }

  856.             if (getOrbitType() == null) {
  857.                 // propagation uses absolute position-velocity-acceleration
  858.                 final Vector3D p = new Vector3D(y[0],    y[1],    y[2]);
  859.                 final Vector3D v = new Vector3D(y[3],    y[4],    y[5]);
  860.                 final Vector3D a;
  861.                 final AbsolutePVCoordinates absPva;
  862.                 if (yDot == null) {
  863.                     absPva = new AbsolutePVCoordinates(getFrame(), new TimeStampedPVCoordinates(date, p, v));
  864.                 } else {
  865.                     a = new Vector3D(yDot[3], yDot[4], yDot[5]);
  866.                     absPva = new AbsolutePVCoordinates(getFrame(), new TimeStampedPVCoordinates(date, p, v, a));
  867.                 }

  869.                 final Attitude attitude = getAttitudeProvider().getAttitude(absPva, date, getFrame());
  870.                 return new SpacecraftState(absPva, attitude, mass);
  871.             } else {
  872.                 // propagation uses regular orbits
  873.                 final Orbit orbit       = getOrbitType().mapArrayToOrbit(y, yDot, getPositionAngleType(), date, getMu(), getFrame());
  874.                 final Attitude attitude = getAttitudeProvider().getAttitude(orbit, date, getFrame());

  876.                 return new SpacecraftState(orbit, attitude, mass);
  877.             }

  879.         }

  881.         /** {@inheritDoc} */
  882.         public void mapStateToArray(final SpacecraftState state, final double[] y, final double[] yDot) {
  883.             if (getOrbitType() == null) {
  884.                 // propagation uses absolute position-velocity-acceleration
  885.                 final Vector3D p = state.getAbsPVA().getPosition();
  886.                 final Vector3D v = state.getAbsPVA().getVelocity();
  887.                 y[0] = p.getX();
  888.                 y[1] = p.getY();
  889.                 y[2] = p.getZ();
  890.                 y[3] = v.getX();
  891.                 y[4] = v.getY();
  892.                 y[5] = v.getZ();
  893.                 y[6] = state.getMass();
  894.             }
  895.             else {
  896.                 getOrbitType().mapOrbitToArray(state.getOrbit(), getPositionAngleType(), y, yDot);
  897.                 y[6] = state.getMass();
  898.             }
  899.         }

  901.     }

  903.     /** {@inheritDoc} */
  904.     protected MainStateEquations getMainStateEquations(final ODEIntegrator integrator) {
  905.         return new Main(integrator);
  906.     }

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

  911.         /** Derivatives array. */
  912.         private final double[] yDot;

  914.         /** Current state. */
  915.         private SpacecraftState currentState;

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

  920.         /** Flag keeping track whether Jacobian matrix needs to be recomputed or not. */
  921.         private boolean recomputingJacobian;

  923.         /** Simple constructor.
  924.          * @param integrator numerical integrator to use for propagation.
  925.          */
  926.         Main(final ODEIntegrator integrator) {

  928.             this.yDot     = new double[7];
  929.             this.jacobian = new double[6][6];
  930.             this.recomputingJacobian = true;

  932.             for (final ForceModel forceModel : forceModels) {
  933.                 forceModel.getEventDetectors().forEach(detector -> setUpEventDetector(integrator, detector));
  934.             }

  936.             // default value for Jacobian is identity
  937.             for (int i = 0; i < jacobian.length; ++i) {
  938.                 Arrays.fill(jacobian[i], 0.0);
  939.                 jacobian[i][i] = 1.0;
  940.             }

  942.         }

  944.         /** {@inheritDoc} */
  945.         @Override
  946.         public void init(final SpacecraftState initialState, final AbsoluteDate target) {
  947.             needFullAttitudeForDerivatives = forceModels.stream().anyMatch(ForceModel::dependsOnAttitudeRate);

  949.             forceModels.forEach(fm -> fm.init(initialState, target));

  951.             final int numberOfForces = forceModels.size();
  952.             final OrbitType orbitType = getOrbitType();
  953.             if (orbitType != null && orbitType != OrbitType.CARTESIAN && numberOfForces > 0) {
  954.                 if (numberOfForces > 1) {
  955.                     recomputingJacobian = true;
  956.                 } else {
  957.                     recomputingJacobian = !(forceModels.get(0) instanceof NewtonianAttraction);
  958.                 }
  959.             } else {
  960.                 recomputingJacobian = false;
  961.             }
  962.         }

  964.         /** {@inheritDoc} */
  965.         @Override
  966.         public double[] computeDerivatives(final SpacecraftState state) {

  968.             currentState = state;
  969.             Arrays.fill(yDot, 0.0);
  970.             if (recomputingJacobian) {
  971.                 // propagation uses Jacobian matrix of orbital parameters w.r.t. Cartesian ones
  972.                 currentState.getOrbit().getJacobianWrtCartesian(getPositionAngleType(), jacobian);
  973.             }

  975.             // compute the contributions of all perturbing forces,
  976.             // using the Kepler contribution at the end since
  977.             // NewtonianAttraction is always the last instance in the list
  978.             for (final ForceModel forceModel : forceModels) {
  979.                 forceModel.addContribution(state, this);
  980.             }

  982.             if (getOrbitType() == null) {
  983.                 // position derivative is velocity, and was not added above in the force models
  984.                 // (it is added when orbit type is non-null because NewtonianAttraction considers it)
  985.                 final Vector3D velocity = currentState.getPVCoordinates().getVelocity();
  986.                 yDot[0] += velocity.getX();
  987.                 yDot[1] += velocity.getY();
  988.                 yDot[2] += velocity.getZ();
  989.             }


  992.             return yDot.clone();

  994.         }

  996.         /** {@inheritDoc} */
  997.         @Override
  998.         public void addKeplerContribution(final double mu) {
  999.             if (getOrbitType() == null) {
  1000.                 // if mu is neither 0 nor NaN, we want to include Newtonian acceleration
  1001.                 if (mu > 0) {
  1002.                     // velocity derivative is Newtonian acceleration
  1003.                     final Vector3D position = currentState.getPosition();
  1004.                     final double r2         = position.getNormSq();
  1005.                     final double coeff      = -mu / (r2 * FastMath.sqrt(r2));
  1006.                     yDot[3] += coeff * position.getX();
  1007.                     yDot[4] += coeff * position.getY();
  1008.                     yDot[5] += coeff * position.getZ();
  1009.                 }

  1011.             } else {
  1012.                 // propagation uses regular orbits
  1013.                 currentState.getOrbit().addKeplerContribution(getPositionAngleType(), mu, yDot);
  1014.             }
  1015.         }

  1017.         /** {@inheritDoc} */
  1018.         public void addNonKeplerianAcceleration(final Vector3D gamma) {
  1019.             for (int i = 0; i < 6; ++i) {
  1020.                 final double[] jRow = jacobian[i];
  1021.                 yDot[i] += jRow[3] * gamma.getX() + jRow[4] * gamma.getY() + jRow[5] * gamma.getZ();
  1022.             }
  1023.         }

  1025.         /** {@inheritDoc} */
  1026.         @Override
  1027.         public void addMassDerivative(final double q) {
  1028.             if (q > 0) {
  1029.                 throw new OrekitIllegalArgumentException(OrekitMessages.POSITIVE_FLOW_RATE, q);
  1030.             }
  1031.             yDot[6] += q;
  1032.         }

  1034.     }

  1036.     /** Estimate tolerance vectors for integrators when propagating in absolute position-velocity-acceleration.
  1037.      * @param dP user specified position error
  1038.      * @param absPva reference absolute position-velocity-acceleration
  1039.      * @return a two rows array, row 0 being the absolute tolerance error and row 1
  1040.      * being the relative tolerance error
  1041.      * @see NumericalPropagator#tolerances(double, Orbit, OrbitType)
  1042.      */
  1043.     public static double[][] tolerances(final double dP, final AbsolutePVCoordinates absPva) {

  1045.         final double relative = dP / absPva.getPosition().getNorm();
  1046.         final double dV = relative * absPva.getVelocity().getNorm();

  1048.         final double[] absTol = new double[7];
  1049.         final double[] relTol = new double[7];

  1051.         absTol[0] = dP;
  1052.         absTol[1] = dP;
  1053.         absTol[2] = dP;
  1054.         absTol[3] = dV;
  1055.         absTol[4] = dV;
  1056.         absTol[5] = dV;

  1058.         // we set the mass tolerance arbitrarily to 1.0e-6 kg, as mass evolves linearly
  1059.         // with trust, this often has no influence at all on propagation
  1060.         absTol[6] = 1.0e-6;

  1062.         Arrays.fill(relTol, relative);

  1064.         return new double[][] {
  1065.             absTol, relTol
  1066.         };

  1068.     }

  1070.     /** Estimate tolerance vectors for integrators when propagating in orbits.
  1071.      * <p>
  1072.      * The errors are estimated from partial derivatives properties of orbits,
  1073.      * starting from a scalar position error specified by the user.
  1074.      * Considering the energy conservation equation V = sqrt(mu (2/r - 1/a)),
  1075.      * we get at constant energy (i.e. on a Keplerian trajectory):
  1076.      * <pre>
  1077.      * V r² |dV| = mu |dr|
  1078.      * </pre>
  1079.      * <p> So we deduce a scalar velocity error consistent with the position error.
  1080.      * From here, we apply orbits Jacobians matrices to get consistent errors
  1081.      * on orbital parameters.
  1082.      *
  1083.      * <p>
  1084.      * The tolerances are only <em>orders of magnitude</em>, and integrator tolerances
  1085.      * are only local estimates, not global ones. So some care must be taken when using
  1086.      * these tolerances. Setting 1mm as a position error does NOT mean the tolerances
  1087.      * will guarantee a 1mm error position after several orbits integration.
  1088.      * </p>
  1089.      * @param dP user specified position 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.      */
  1096.     public static double[][] tolerances(final double dP, final Orbit orbit, final OrbitType type) {

  1098.         // estimate the scalar velocity error
  1099.         final PVCoordinates pv = orbit.getPVCoordinates();
  1100.         final double r2 = pv.getPosition().getNormSq();
  1101.         final double v  = pv.getVelocity().getNorm();
  1102.         final double dV = orbit.getMu() * dP / (v * r2);

  1104.         return tolerances(dP, dV, orbit, type);

  1106.     }

  1108.     /** Estimate tolerance vectors for integrators when propagating in orbits.
  1109.      * <p>
  1110.      * The errors are estimated from partial derivatives properties of orbits,
  1111.      * starting from scalar position and velocity errors specified by the user.
  1112.      * <p>
  1113.      * The tolerances are only <em>orders of magnitude</em>, and integrator tolerances
  1114.      * are only local estimates, not global ones. So some care must be taken when using
  1115.      * these tolerances. Setting 1mm as a position error does NOT mean the tolerances
  1116.      * will guarantee a 1mm error position after several orbits integration.
  1117.      * </p>
  1118.      * @param dP user specified position error
  1119.      * @param dV user specified velocity error
  1120.      * @param orbit reference orbit
  1121.      * @param type propagation type for the meaning of the tolerance vectors elements
  1122.      * (it may be different from {@code orbit.getType()})
  1123.      * @return a two rows array, row 0 being the absolute tolerance error and row 1
  1124.      * being the relative tolerance error
  1125.      * @since 10.3
  1126.      */
  1127.     public static double[][] tolerances(final double dP, final double dV,
  1128.                                         final Orbit orbit, final OrbitType type) {

  1130.         final double[] absTol = new double[7];
  1131.         final double[] relTol = new double[7];

  1133.         // we set the mass tolerance arbitrarily to 1.0e-6 kg, as mass evolves linearly
  1134.         // with trust, this often has no influence at all on propagation
  1135.         absTol[6] = 1.0e-6;

  1137.         if (type == OrbitType.CARTESIAN) {
  1138.             absTol[0] = dP;
  1139.             absTol[1] = dP;
  1140.             absTol[2] = dP;
  1141.             absTol[3] = dV;
  1142.             absTol[4] = dV;
  1143.             absTol[5] = dV;
  1144.         } else {

  1146.             // convert the orbit to the desired type
  1147.             final double[][] jacobian = new double[6][6];
  1148.             final Orbit converted = type.convertType(orbit);
  1149.             converted.getJacobianWrtCartesian(PositionAngleType.TRUE, jacobian);

  1151.             for (int i = 0; i < 6; ++i) {
  1152.                 final double[] row = jacobian[i];
  1153.                 absTol[i] = FastMath.abs(row[0]) * dP +
  1154.                             FastMath.abs(row[1]) * dP +
  1155.                             FastMath.abs(row[2]) * dP +
  1156.                             FastMath.abs(row[3]) * dV +
  1157.                             FastMath.abs(row[4]) * dV +
  1158.                             FastMath.abs(row[5]) * dV;
  1159.                 if (Double.isNaN(absTol[i])) {
  1160.                     throw new OrekitException(OrekitMessages.SINGULAR_JACOBIAN_FOR_ORBIT_TYPE, type);
  1161.                 }
  1162.             }

  1164.         }

  1166.         Arrays.fill(relTol, dP / FastMath.sqrt(orbit.getPosition().getNormSq()));

  1168.         return new double[][] {
  1169.             absTol, relTol
  1170.         };

  1172.     }

  1174.     /** {@inheritDoc} */
  1175.     @Override
  1176.     protected void beforeIntegration(final SpacecraftState initialState, final AbsoluteDate tEnd) {

  1178.         if (!getFrame().isPseudoInertial()) {

  1180.             // inspect all force models to find InertialForces
  1181.             for (ForceModel force : forceModels) {
  1182.                 if (force instanceof InertialForces) {
  1183.                     return;
  1184.                 }
  1185.             }

  1187.             // throw exception if no inertial forces found
  1188.             throw new OrekitException(OrekitMessages.INERTIAL_FORCE_MODEL_MISSING, getFrame().getName());

  1190.         }

  1192.     }

  1194. }
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