NumericalPropagator.java

  1. /* Copyright 2002-2019 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.propagation.numerical;

  19. import java.io.NotSerializableException;
  20. import java.io.Serializable;
  21. import java.util.ArrayList;
  22. import java.util.Arrays;
  23. import java.util.Collections;
  24. import java.util.List;

  26. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  27. import org.hipparchus.ode.ODEIntegrator;
  28. import org.hipparchus.util.FastMath;
  29. import org.orekit.attitudes.Attitude;
  30. import org.orekit.attitudes.AttitudeProvider;
  31. import org.orekit.errors.OrekitException;
  32. import org.orekit.errors.OrekitIllegalArgumentException;
  33. import org.orekit.errors.OrekitInternalError;
  34. import org.orekit.errors.OrekitMessages;
  35. import org.orekit.forces.ForceModel;
  36. import org.orekit.forces.gravity.NewtonianAttraction;
  37. import org.orekit.frames.Frame;
  38. import org.orekit.orbits.Orbit;
  39. import org.orekit.orbits.OrbitType;
  40. import org.orekit.orbits.PositionAngle;
  41. import org.orekit.propagation.SpacecraftState;
  42. import org.orekit.propagation.events.EventDetector;
  43. import org.orekit.propagation.integration.AbstractIntegratedPropagator;
  44. import org.orekit.propagation.integration.StateMapper;
  45. import org.orekit.time.AbsoluteDate;
  46. import org.orekit.utils.PVCoordinates;
  47. import org.orekit.utils.ParameterDriver;
  48. import org.orekit.utils.ParameterObserver;
  49. import org.orekit.utils.TimeStampedPVCoordinates;

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

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

  148.     /** Create a new instance of NumericalPropagator, based on orbit definition mu.
  149.      * After creation, the instance is empty, i.e. the attitude provider is set to an
  150.      * unspecified default law and there are no perturbing forces at all.
  151.      * This means that if {@link #addForceModel addForceModel} is not
  152.      * called after creation, the integrated orbit will follow a Keplerian
  153.      * evolution only. The defaults are {@link OrbitType#EQUINOCTIAL}
  154.      * for {@link #setOrbitType(OrbitType) propagation
  155.      * orbit type} and {@link PositionAngle#TRUE} for {@link
  156.      * #setPositionAngleType(PositionAngle) position angle type}.
  157.      * @param integrator numerical integrator to use for propagation.
  158.      */
  159.     public NumericalPropagator(final ODEIntegrator integrator) {
  160.         super(integrator, true);
  161.         forceModels = new ArrayList<ForceModel>();
  162.         initMapper();
  163.         setAttitudeProvider(DEFAULT_LAW);
  164.         setSlaveMode();
  165.         setOrbitType(OrbitType.EQUINOCTIAL);
  166.         setPositionAngleType(PositionAngle.TRUE);
  167.     }

  169.      /** Set the central attraction coefficient μ.
  170.       * <p>
  171.       * Setting the central attraction coefficient is
  172.       * equivalent to {@link #addForceModel(ForceModel) add}
  173.       * a {@link NewtonianAttraction} force model.
  174.       * </p>
  175.      * @param mu central attraction coefficient (m³/s²)
  176.      * @see #addForceModel(ForceModel)
  177.      * @see #getAllForceModels()
  178.      */
  179.     public void setMu(final double mu) {
  180.         addForceModel(new NewtonianAttraction(mu));
  181.     }

  183.     /** Set the central attraction coefficient μ only in upper class.
  184.      * @param mu central attraction coefficient (m³/s²)
  185.      */
  186.     private void superSetMu(final double mu) {
  187.         super.setMu(mu);
  188.     }

  190.     /** Check if Newtonian attraction force model is available.
  191.      * <p>
  192.      * Newtonian attraction is always the last force model in the list.
  193.      * </p>
  194.      * @return true if Newtonian attraction force model is available
  195.      */
  196.     private boolean hasNewtonianAttraction() {
  197.         final int last = forceModels.size() - 1;
  198.         return last >= 0 && forceModels.get(last) instanceof NewtonianAttraction;
  199.     }

  201.     /** Add a force model.
  202.      * <p>If this method is not called at all, the integrated orbit will follow
  203.      * a Keplerian evolution only.</p>
  204.      * @param model {@link ForceModel} to add (it can be either a perturbing force
  205.      * model or an instance of {@link NewtonianAttraction})
  206.      * @see #removeForceModels()
  207.      * @see #setMu(double)
  208.      */
  209.     public void addForceModel(final ForceModel model) {

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

  214.             try {
  215.                 // ensure we are notified of any mu change
  216.                 model.getParametersDrivers()[0].addObserver(new ParameterObserver() {
  217.                     /** {@inheritDoc} */
  218.                     @Override
  219.                     public void valueChanged(final double previousValue, final ParameterDriver driver) {
  220.                         superSetMu(driver.getValue());
  221.                     }
  222.                 });
  223.             } catch (OrekitException oe) {
  224.                 // this should never happen
  225.                 throw new OrekitInternalError(oe);
  226.             }

  228.             if (hasNewtonianAttraction()) {
  229.                 // there is already a central attraction model, replace it
  230.                 forceModels.set(forceModels.size() - 1, model);
  231.             } else {
  232.                 // there are no central attraction model yet, add it at the end of the list
  233.                 forceModels.add(model);
  234.             }
  235.         } else {
  236.             // we want to add a perturbing force model
  237.             if (hasNewtonianAttraction()) {
  238.                 // insert the new force model before Newtonian attraction,
  239.                 // which should always be the last one in the list
  240.                 forceModels.add(forceModels.size() - 1, model);
  241.             } else {
  242.                 // we only have perturbing force models up to now, just append at the end of the list
  243.                 forceModels.add(model);
  244.             }
  245.         }

  247.     }

  249.     /** Remove all force models (except central attraction).
  250.      * <p>Once all perturbing forces have been removed (and as long as no new force
  251.      * model is added), the integrated orbit will follow a Keplerian evolution
  252.      * only.</p>
  253.      * @see #addForceModel(ForceModel)
  254.      */
  255.     public void removeForceModels() {
  256.         final int last = forceModels.size() - 1;
  257.         if (hasNewtonianAttraction()) {
  258.             // preserve the Newtonian attraction model at the end
  259.             final ForceModel newton = forceModels.get(last);
  260.             forceModels.clear();
  261.             forceModels.add(newton);
  262.         } else {
  263.             forceModels.clear();
  264.         }
  265.     }

  267.     /** Get all the force models, perturbing forces and Newtonian attraction included.
  268.      * @return list of perturbing force models, with Newtonian attraction being the
  269.      * last one
  270.      * @see #addForceModel(ForceModel)
  271.      * @see #setMu(double)
  272.      */
  273.     public List<ForceModel> getAllForceModels() {
  274.         return Collections.unmodifiableList(forceModels);
  275.     }

  277.     /** Set propagation orbit type.
  278.      * @param orbitType orbit type to use for propagation
  279.      */
  280.     public void setOrbitType(final OrbitType orbitType) {
  281.         super.setOrbitType(orbitType);
  282.     }

  284.     /** Get propagation parameter type.
  285.      * @return orbit type used for propagation
  286.      */
  287.     public OrbitType getOrbitType() {
  288.         return super.getOrbitType();
  289.     }

  291.     /** Set position angle type.
  292.      * <p>
  293.      * The position parameter type is meaningful only if {@link
  294.      * #getOrbitType() propagation orbit type}
  295.      * support it. As an example, it is not meaningful for propagation
  296.      * in {@link OrbitType#CARTESIAN Cartesian} parameters.
  297.      * </p>
  298.      * @param positionAngleType angle type to use for propagation
  299.      */
  300.     public void setPositionAngleType(final PositionAngle positionAngleType) {
  301.         super.setPositionAngleType(positionAngleType);
  302.     }

  304.     /** Get propagation parameter type.
  305.      * @return angle type to use for propagation
  306.      */
  307.     public PositionAngle getPositionAngleType() {
  308.         return super.getPositionAngleType();
  309.     }

  311.     /** Set the initial state.
  312.      * @param initialState initial state
  313.      */
  314.     public void setInitialState(final SpacecraftState initialState) {
  315.         resetInitialState(initialState);
  316.     }

  318.     /** {@inheritDoc} */
  319.     public void resetInitialState(final SpacecraftState state) {
  320.         super.resetInitialState(state);
  321.         if (!hasNewtonianAttraction()) {
  322.             // use the state to define central attraction
  323.             setMu(state.getMu());
  324.         }
  325.         setStartDate(state.getDate());
  326.     }

  328.     /** {@inheritDoc} */
  329.     public TimeStampedPVCoordinates getPVCoordinates(final AbsoluteDate date, final Frame frame) {
  330.         return propagate(date).getPVCoordinates(frame);
  331.     }

  333.     /** {@inheritDoc} */
  334.     protected StateMapper createMapper(final AbsoluteDate referenceDate, final double mu,
  335.                                        final OrbitType orbitType, final PositionAngle positionAngleType,
  336.                                        final AttitudeProvider attitudeProvider, final Frame frame) {
  337.         return new OsculatingMapper(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  338.     }

  340.     /** Internal mapper using directly osculating parameters. */
  341.     private static class OsculatingMapper extends StateMapper implements Serializable {

  343.         /** Serializable UID. */
  344.         private static final long serialVersionUID = 20130621L;

  346.         /** Simple constructor.
  347.          * <p>
  348.          * The position parameter type is meaningful only if {@link
  349.          * #getOrbitType() propagation orbit type}
  350.          * support it. As an example, it is not meaningful for propagation
  351.          * in {@link OrbitType#CARTESIAN Cartesian} parameters.
  352.          * </p>
  353.          * @param referenceDate reference date
  354.          * @param mu central attraction coefficient (m³/s²)
  355.          * @param orbitType orbit type to use for mapping
  356.          * @param positionAngleType angle type to use for propagation
  357.          * @param attitudeProvider attitude provider
  358.          * @param frame inertial frame
  359.          */
  360.         OsculatingMapper(final AbsoluteDate referenceDate, final double mu,
  361.                          final OrbitType orbitType, final PositionAngle positionAngleType,
  362.                          final AttitudeProvider attitudeProvider, final Frame frame) {
  363.             super(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  364.         }

  366.         /** {@inheritDoc} */
  367.         public SpacecraftState mapArrayToState(final AbsoluteDate date, final double[] y, final double[] yDot,
  368.                                                final boolean meanOnly) {
  369.             // the parameter meanOnly is ignored for the Numerical Propagator

  371.             final double mass = y[6];
  372.             if (mass <= 0.0) {
  373.                 throw new OrekitException(OrekitMessages.SPACECRAFT_MASS_BECOMES_NEGATIVE, mass);
  374.             }

  376.             final Orbit orbit       = getOrbitType().mapArrayToOrbit(y, yDot, getPositionAngleType(), date, getMu(), getFrame());
  377.             final Attitude attitude = getAttitudeProvider().getAttitude(orbit, date, getFrame());

  379.             return new SpacecraftState(orbit, attitude, mass);

  381.         }

  383.         /** {@inheritDoc} */
  384.         public void mapStateToArray(final SpacecraftState state, final double[] y, final double[] yDot) {
  385.             getOrbitType().mapOrbitToArray(state.getOrbit(), getPositionAngleType(), y, yDot);
  386.             y[6] = state.getMass();
  387.         }

  389.         /** Replace the instance with a data transfer object for serialization.
  390.          * @return data transfer object that will be serialized
  391.          * @exception NotSerializableException if the state mapper cannot be serialized (typically for DSST propagator)
  392.          */
  393.         private Object writeReplace() throws NotSerializableException {
  394.             return new DataTransferObject(getReferenceDate(), getMu(), getOrbitType(),
  395.                                           getPositionAngleType(), getAttitudeProvider(), getFrame());
  396.         }

  398.         /** Internal class used only for serialization. */
  399.         private static class DataTransferObject implements Serializable {

  401.             /** Serializable UID. */
  402.             private static final long serialVersionUID = 20130621L;

  404.             /** Reference date. */
  405.             private final AbsoluteDate referenceDate;

  407.             /** Central attraction coefficient (m³/s²). */
  408.             private final double mu;

  410.             /** Orbit type to use for mapping. */
  411.             private final OrbitType orbitType;

  413.             /** Angle type to use for propagation. */
  414.             private final PositionAngle positionAngleType;

  416.             /** Attitude provider. */
  417.             private final AttitudeProvider attitudeProvider;

  419.             /** Inertial frame. */
  420.             private final Frame frame;

  422.             /** Simple constructor.
  423.              * @param referenceDate reference date
  424.              * @param mu central attraction coefficient (m³/s²)
  425.              * @param orbitType orbit type to use for mapping
  426.              * @param positionAngleType angle type to use for propagation
  427.              * @param attitudeProvider attitude provider
  428.              * @param frame inertial frame
  429.              */
  430.             DataTransferObject(final AbsoluteDate referenceDate, final double mu,
  431.                                       final OrbitType orbitType, final PositionAngle positionAngleType,
  432.                                       final AttitudeProvider attitudeProvider, final Frame frame) {
  433.                 this.referenceDate     = referenceDate;
  434.                 this.mu                = mu;
  435.                 this.orbitType         = orbitType;
  436.                 this.positionAngleType = positionAngleType;
  437.                 this.attitudeProvider  = attitudeProvider;
  438.                 this.frame             = frame;
  439.             }

  441.             /** Replace the deserialized data transfer object with a {@link OsculatingMapper}.
  442.              * @return replacement {@link OsculatingMapper}
  443.              */
  444.             private Object readResolve() {
  445.                 return new OsculatingMapper(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  446.             }
  447.         }

  449.     }

  451.     /** {@inheritDoc} */
  452.     protected MainStateEquations getMainStateEquations(final ODEIntegrator integrator) {
  453.         return new Main(integrator);
  454.     }

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

  459.         /** Derivatives array. */
  460.         private final double[] yDot;

  462.         /** Current orbit. */
  463.         private Orbit orbit;

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

  468.         /** Simple constructor.
  469.          * @param integrator numerical integrator to use for propagation.
  470.          */
  471.         Main(final ODEIntegrator integrator) {

  473.             this.yDot     = new double[7];
  474.             this.jacobian = new double[6][6];

  476.             for (final ForceModel forceModel : forceModels) {
  477.                 forceModel.getEventsDetectors().forEach(detector -> setUpEventDetector(integrator, detector));
  478.             }

  480.         }

  482.         /** {@inheritDoc} */
  483.         @Override
  484.         public void init(final SpacecraftState initialState, final AbsoluteDate target) {
  485.             for (final ForceModel forceModel : forceModels) {
  486.                 forceModel.init(initialState, target);
  487.             }
  488.         }

  490.         /** {@inheritDoc} */
  491.         @Override
  492.         public double[] computeDerivatives(final SpacecraftState state) {

  494.             orbit = state.getOrbit();
  495.             Arrays.fill(yDot, 0.0);
  496.             orbit.getJacobianWrtCartesian(getPositionAngleType(), jacobian);

  498.             // compute the contributions of all perturbing forces,
  499.             // using the Kepler contribution at the end since
  500.             // NewtonianAttraction is always the last instance in the list
  501.             for (final ForceModel forceModel : forceModels) {
  502.                 forceModel.addContribution(state, this);
  503.             }

  505.             return yDot.clone();

  507.         }

  509.         /** {@inheritDoc} */
  510.         @Override
  511.         public void addKeplerContribution(final double mu) {
  512.             orbit.addKeplerContribution(getPositionAngleType(), mu, yDot);
  513.         }

  515.         /** {@inheritDoc} */
  516.         public void addNonKeplerianAcceleration(final Vector3D gamma) {
  517.             for (int i = 0; i < 6; ++i) {
  518.                 final double[] jRow = jacobian[i];
  519.                 yDot[i] += jRow[3] * gamma.getX() + jRow[4] * gamma.getY() + jRow[5] * gamma.getZ();
  520.             }
  521.         }

  523.         /** {@inheritDoc} */
  524.         @Override
  525.         public void addMassDerivative(final double q) {
  526.             if (q > 0) {
  527.                 throw new OrekitIllegalArgumentException(OrekitMessages.POSITIVE_FLOW_RATE, q);
  528.             }
  529.             yDot[6] += q;
  530.         }

  532.     }

  534.     /** Estimate tolerance vectors for integrators.
  535.      * <p>
  536.      * The errors are estimated from partial derivatives properties of orbits,
  537.      * starting from a scalar position error specified by the user.
  538.      * Considering the energy conservation equation V = sqrt(mu (2/r - 1/a)),
  539.      * we get at constant energy (i.e. on a Keplerian trajectory):
  540.      * <pre>
  541.      * V² r |dV| = mu |dr|
  542.      * </pre>
  543.      * <p> So we deduce a scalar velocity error consistent with the position error.
  544.      * From here, we apply orbits Jacobians matrices to get consistent errors
  545.      * on orbital parameters.
  546.      *
  547.      * <p>
  548.      * The tolerances are only <em>orders of magnitude</em>, and integrator tolerances
  549.      * are only local estimates, not global ones. So some care must be taken when using
  550.      * these tolerances. Setting 1mm as a position error does NOT mean the tolerances
  551.      * will guarantee a 1mm error position after several orbits integration.
  552.      * </p>
  553.      * @param dP user specified position error
  554.      * @param orbit reference orbit
  555.      * @param type propagation type for the meaning of the tolerance vectors elements
  556.      * (it may be different from {@code orbit.getType()})
  557.      * @return a two rows array, row 0 being the absolute tolerance error and row 1
  558.      * being the relative tolerance error
  559.      */
  560.     public static double[][] tolerances(final double dP, final Orbit orbit, final OrbitType type) {

  562.         // estimate the scalar velocity error
  563.         final PVCoordinates pv = orbit.getPVCoordinates();
  564.         final double r2 = pv.getPosition().getNormSq();
  565.         final double v  = pv.getVelocity().getNorm();
  566.         final double dV = orbit.getMu() * dP / (v * r2);

  568.         final double[] absTol = new double[7];
  569.         final double[] relTol = new double[7];

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

  575.         if (type == OrbitType.CARTESIAN) {
  576.             absTol[0] = dP;
  577.             absTol[1] = dP;
  578.             absTol[2] = dP;
  579.             absTol[3] = dV;
  580.             absTol[4] = dV;
  581.             absTol[5] = dV;
  582.         } else {

  584.             // convert the orbit to the desired type
  585.             final double[][] jacobian = new double[6][6];
  586.             final Orbit converted = type.convertType(orbit);
  587.             converted.getJacobianWrtCartesian(PositionAngle.TRUE, jacobian);

  589.             for (int i = 0; i < 6; ++i) {
  590.                 final double[] row = jacobian[i];
  591.                 absTol[i] = FastMath.abs(row[0]) * dP +
  592.                             FastMath.abs(row[1]) * dP +
  593.                             FastMath.abs(row[2]) * dP +
  594.                             FastMath.abs(row[3]) * dV +
  595.                             FastMath.abs(row[4]) * dV +
  596.                             FastMath.abs(row[5]) * dV;
  597.                 if (Double.isNaN(absTol[i])) {
  598.                     throw new OrekitException(OrekitMessages.SINGULAR_JACOBIAN_FOR_ORBIT_TYPE, type);
  599.                 }
  600.             }

  602.         }

  604.         Arrays.fill(relTol, dP / FastMath.sqrt(r2));

  606.         return new double[][] {
  607.             absTol, relTol
  608.         };

  610.     }

  612. }
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