FieldNumericalPropagator.java
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* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
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*
* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
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package org.orekit.propagation.numerical;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.Field;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.ode.FieldODEIntegrator;
import org.hipparchus.util.MathArrays;
import org.orekit.annotation.DefaultDataContext;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.attitudes.FieldAttitude;
import org.orekit.data.DataContext;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitIllegalArgumentException;
import org.orekit.errors.OrekitInternalError;
import org.orekit.errors.OrekitMessages;
import org.orekit.forces.ForceModel;
import org.orekit.forces.gravity.NewtonianAttraction;
import org.orekit.frames.Frame;
import org.orekit.orbits.FieldOrbit;
import org.orekit.orbits.OrbitType;
import org.orekit.orbits.PositionAngleType;
import org.orekit.propagation.FieldSpacecraftState;
import org.orekit.propagation.PropagationType;
import org.orekit.propagation.Propagator;
import org.orekit.propagation.events.FieldEventDetector;
import org.orekit.propagation.integration.FieldAbstractIntegratedPropagator;
import org.orekit.propagation.integration.FieldStateMapper;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.FieldAbsolutePVCoordinates;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.ParameterDriver;
import org.orekit.utils.ParameterObserver;
import org.orekit.utils.TimeSpanMap;
import org.orekit.utils.TimeStampedFieldPVCoordinates;
/** This class propagates {@link org.orekit.orbits.FieldOrbit orbits} using
* numerical integration.
* <p>Numerical propagation is much more accurate than analytical propagation
* like for example {@link org.orekit.propagation.analytical.KeplerianPropagator
* Keplerian} or {@link org.orekit.propagation.analytical.EcksteinHechlerPropagator
* Eckstein-Hechler}, but requires a few more steps to set up to be used properly.
* Whereas analytical propagators are configured only thanks to their various
* constructors and can be used immediately after construction, numerical propagators
* configuration involve setting several parameters between construction time
* and propagation time.</p>
* <p>The configuration parameters that can be set are:</p>
* <ul>
* <li>the initial spacecraft state ({@link #setInitialState(FieldSpacecraftState)})</li>
* <li>the central attraction coefficient ({@link #setMu(CalculusFieldElement)})</li>
* <li>the various force models ({@link #addForceModel(ForceModel)},
* {@link #removeForceModels()})</li>
* <li>the {@link OrbitType type} of orbital parameters to be used for propagation
* ({@link #setOrbitType(OrbitType)}),
* <li>the {@link PositionAngleType type} of position angle to be used in orbital parameters
* to be used for propagation where it is relevant ({@link
* #setPositionAngleType(PositionAngleType)}),
* <li>whether {@link org.orekit.propagation.integration.FieldAdditionalDerivativesProvider additional derivatives providers}
* should be propagated along with orbital state
* ({@link #addAdditionalDerivativesProvider(org.orekit.propagation.integration.FieldAdditionalDerivativesProvider)}),
* <li>the discrete events that should be triggered during propagation
* ({@link #addEventDetector(FieldEventDetector)},
* {@link #clearEventsDetectors()})</li>
* <li>the binding logic with the rest of the application ({@link #getMultiplexer()})</li>
* </ul>
* <p>From these configuration parameters, only the initial state is mandatory. The default
* propagation settings are in {@link OrbitType#EQUINOCTIAL equinoctial} parameters with
* {@link PositionAngleType#TRUE true} longitude argument. If the central attraction coefficient
* is not explicitly specified, the one used to define the initial orbit will be used.
* However, specifying only the initial state and perhaps the central attraction coefficient
* would mean the propagator would use only Keplerian forces. In this case, the simpler {@link
* org.orekit.propagation.analytical.KeplerianPropagator KeplerianPropagator} class would
* perhaps be more effective.</p>
* <p>The underlying numerical integrator set up in the constructor may also have its own
* configuration parameters. Typical configuration parameters for adaptive stepsize integrators
* are the min, max and perhaps start step size as well as the absolute and/or relative errors
* thresholds.</p>
* <p>The state that is seen by the integrator is a simple seven elements double array.
* The six first elements are either:
* <ul>
* <li>the {@link org.orekit.orbits.FieldEquinoctialOrbit equinoctial orbit parameters} (a, e<sub>x</sub>,
* e<sub>y</sub>, h<sub>x</sub>, h<sub>y</sub>, λ<sub>M</sub> or λ<sub>E</sub>
* or λ<sub>v</sub>) in meters and radians,</li>
* <li>the {@link org.orekit.orbits.FieldKeplerianOrbit Keplerian orbit parameters} (a, e, i, ω, Ω,
* M or E or v) in meters and radians,</li>
* <li>the {@link org.orekit.orbits.FieldCircularOrbit circular orbit parameters} (a, e<sub>x</sub>, e<sub>y</sub>, i,
* Ω, α<sub>M</sub> or α<sub>E</sub> or α<sub>v</sub>) in meters
* and radians,</li>
* <li>the {@link org.orekit.orbits.FieldCartesianOrbit Cartesian orbit parameters} (x, y, z, v<sub>x</sub>,
* v<sub>y</sub>, v<sub>z</sub>) in meters and meters per seconds.
* </ul>
* The last element is the mass in kilograms.
* <p>The following code snippet shows a typical setting for Low Earth Orbit propagation in
* equinoctial parameters and true longitude argument:</p>
* <pre>
* final T zero = field.getZero();
* final T dP = zero.add(0.001);
* final T minStep = zero.add(0.001);
* final T maxStep = zero.add(500);
* final T initStep = zero.add(60);
* final double[][] tolerance = FieldNumericalPropagator.tolerances(dP, orbit, OrbitType.EQUINOCTIAL);
* AdaptiveStepsizeFieldIntegrator<T> integrator = new DormandPrince853FieldIntegrator<>(field, minStep, maxStep, tolerance[0], tolerance[1]);
* integrator.setInitialStepSize(initStep);
* propagator = new FieldNumericalPropagator<>(field, integrator);
* </pre>
* <p>By default, at the end of the propagation, the propagator resets the initial state to the final state,
* thus allowing a new propagation to be started from there without recomputing the part already performed.
* This behaviour can be changed by calling {@link #setResetAtEnd(boolean)}.
* </p>
* <p>Beware the same instance cannot be used simultaneously by different threads, the class is <em>not</em>
* thread-safe.</p>
* @see FieldSpacecraftState
* @see ForceModel
* @see org.orekit.propagation.sampling.FieldOrekitStepHandler
* @see org.orekit.propagation.sampling.FieldOrekitFixedStepHandler
* @see org.orekit.propagation.integration.FieldIntegratedEphemeris
* @see FieldTimeDerivativesEquations
*
* @author Mathieu Roméro
* @author Luc Maisonobe
* @author Guylaine Prat
* @author Fabien Maussion
* @author Véronique Pommier-Maurussane
* @param <T> type of the field elements
*/
public class FieldNumericalPropagator<T extends CalculusFieldElement<T>> extends FieldAbstractIntegratedPropagator<T> {
/** Force models used during the extrapolation of the FieldOrbit<T>, without Jacobians. */
private final List<ForceModel> forceModels;
/** Field used by this class.*/
private final Field<T> field;
/** boolean to ignore or not the creation of a NewtonianAttraction. */
private boolean ignoreCentralAttraction = false;
/** Create a new instance of NumericalPropagator, based on orbit definition mu.
* After creation, the instance is empty, i.e. the attitude provider is set to an
* unspecified default law and there are no perturbing forces at all.
* This means that if {@link #addForceModel addForceModel} is not
* called after creation, the integrated orbit will follow a Keplerian
* evolution only. The defaults are {@link OrbitType#EQUINOCTIAL}
* for {@link #setOrbitType(OrbitType) propagation
* orbit type} and {@link PositionAngleType#TRUE} for {@link
* #setPositionAngleType(PositionAngleType) position angle type}.
*
* <p>This constructor uses the {@link DataContext#getDefault() default data context}.
*
* @param integrator numerical integrator to use for propagation.
* @param field Field used by default
* @see #FieldNumericalPropagator(Field, FieldODEIntegrator, AttitudeProvider)
*/
@DefaultDataContext
public FieldNumericalPropagator(final Field<T> field, final FieldODEIntegrator<T> integrator) {
this(field, integrator, Propagator.getDefaultLaw(DataContext.getDefault().getFrames()));
}
/** Create a new instance of NumericalPropagator, based on orbit definition mu.
* After creation, the instance is empty, i.e. the attitude provider is set to an
* unspecified default law and there are no perturbing forces at all.
* This means that if {@link #addForceModel addForceModel} is not
* called after creation, the integrated orbit will follow a Keplerian
* evolution only. The defaults are {@link OrbitType#EQUINOCTIAL}
* for {@link #setOrbitType(OrbitType) propagation
* orbit type} and {@link PositionAngleType#TRUE} for {@link
* #setPositionAngleType(PositionAngleType) position angle type}.
* @param field Field used by default
* @param integrator numerical integrator to use for propagation.
* @param attitudeProvider attitude law to use.
* @since 10.1
*/
public FieldNumericalPropagator(final Field<T> field,
final FieldODEIntegrator<T> integrator,
final AttitudeProvider attitudeProvider) {
super(field, integrator, PropagationType.OSCULATING);
this.field = field;
forceModels = new ArrayList<>();
initMapper(field);
setAttitudeProvider(attitudeProvider);
setMu(field.getZero().add(Double.NaN));
clearStepHandlers();
setOrbitType(OrbitType.EQUINOCTIAL);
setPositionAngleType(PositionAngleType.TRUE);
}
/** Set the flag to ignore or not the creation of a {@link NewtonianAttraction}.
* @param ignoreCentralAttraction if true, {@link NewtonianAttraction} is <em>not</em>
* added automatically if missing
*/
public void setIgnoreCentralAttraction(final boolean ignoreCentralAttraction) {
this.ignoreCentralAttraction = ignoreCentralAttraction;
}
/** Set the central attraction coefficient μ.
* <p>
* Setting the central attraction coefficient is
* equivalent to {@link #addForceModel(ForceModel) add}
* a {@link NewtonianAttraction} force model.
* </p>
* @param mu central attraction coefficient (m³/s²)
* @see #addForceModel(ForceModel)
* @see #getAllForceModels()
*/
@Override
public void setMu(final T mu) {
if (ignoreCentralAttraction) {
superSetMu(mu);
} else {
addForceModel(new NewtonianAttraction(mu.getReal()));
}
}
/** Set the central attraction coefficient μ only in upper class.
* @param mu central attraction coefficient (m³/s²)
*/
private void superSetMu(final T mu) {
super.setMu(mu);
}
/** Check if Newtonian attraction force model is available.
* <p>
* Newtonian attraction is always the last force model in the list.
* </p>
* @return true if Newtonian attraction force model is available
*/
private boolean hasNewtonianAttraction() {
final int last = forceModels.size() - 1;
return last >= 0 && forceModels.get(last) instanceof NewtonianAttraction;
}
/** Add a force model to the global perturbation model.
* <p>If this method is not called at all, the integrated orbit will follow
* a Keplerian evolution only.</p>
* @param model perturbing {@link ForceModel} to add
* @see #removeForceModels()
* @see #setMu(CalculusFieldElement)
*/
public void addForceModel(final ForceModel model) {
if (model instanceof NewtonianAttraction) {
// we want to add the central attraction force model
try {
// ensure we are notified of any mu change
model.getParametersDrivers().get(0).addObserver(new ParameterObserver() {
/** {@inheritDoc} */
@Override
public void valueChanged(final double previousValue, final ParameterDriver driver, final AbsoluteDate date) {
// mu PDriver should have only 1 span
superSetMu(field.getZero().newInstance(driver.getValue(date)));
}
/** {@inheritDoc} */
@Override
public void valueSpanMapChanged(final TimeSpanMap<Double> previousValue, final ParameterDriver driver) {
// mu PDriver should have only 1 span
superSetMu(field.getZero().newInstance(driver.getValue()));
}
});
} catch (OrekitException oe) {
// this should never happen
throw new OrekitInternalError(oe);
}
if (hasNewtonianAttraction()) {
// there is already a central attraction model, replace it
forceModels.set(forceModels.size() - 1, model);
} else {
// there are no central attraction model yet, add it at the end of the list
forceModels.add(model);
}
} else {
// we want to add a perturbing force model
if (hasNewtonianAttraction()) {
// insert the new force model before Newtonian attraction,
// which should always be the last one in the list
forceModels.add(forceModels.size() - 1, model);
} else {
// we only have perturbing force models up to now, just append at the end of the list
forceModels.add(model);
}
}
}
/** Remove all perturbing force models from the global perturbation model.
* <p>Once all perturbing forces have been removed (and as long as no new force
* model is added), the integrated orbit will follow a Keplerian evolution
* only.</p>
* @see #addForceModel(ForceModel)
*/
public void removeForceModels() {
forceModels.clear();
}
/** Get all the force models, perturbing forces and Newtonian attraction included.
* @return list of perturbing force models, with Newtonian attraction being the
* last one
* @see #addForceModel(ForceModel)
* @see #setMu(CalculusFieldElement)
* @since 9.1
*/
public List<ForceModel> getAllForceModels() {
return Collections.unmodifiableList(forceModels);
}
/** Set propagation orbit type.
* @param orbitType orbit type to use for propagation
*/
@Override
public void setOrbitType(final OrbitType orbitType) {
super.setOrbitType(orbitType);
}
/** Get propagation parameter type.
* @return orbit type used for propagation
*/
@Override
public OrbitType getOrbitType() {
return superGetOrbitType();
}
/** Get propagation parameter type.
* @return orbit type used for propagation
*/
private OrbitType superGetOrbitType() {
return super.getOrbitType();
}
/** Set position angle type.
* <p>
* The position parameter type is meaningful only if {@link
* #getOrbitType() propagation orbit type}
* support it. As an example, it is not meaningful for propagation
* in {@link OrbitType#CARTESIAN Cartesian} parameters.
* </p>
* @param positionAngleType angle type to use for propagation
*/
@Override
public void setPositionAngleType(final PositionAngleType positionAngleType) {
super.setPositionAngleType(positionAngleType);
}
/** Get propagation parameter type.
* @return angle type to use for propagation
*/
@Override
public PositionAngleType getPositionAngleType() {
return super.getPositionAngleType();
}
/** Set the initial state.
* @param initialState initial state
*/
public void setInitialState(final FieldSpacecraftState<T> initialState) {
resetInitialState(initialState);
}
/** {@inheritDoc} */
@Override
public void resetInitialState(final FieldSpacecraftState<T> state) {
super.resetInitialState(state);
if (!hasNewtonianAttraction()) {
setMu(state.getMu());
}
setStartDate(state.getDate());
}
/** {@inheritDoc} */
protected FieldStateMapper<T> createMapper(final FieldAbsoluteDate<T> referenceDate, final T mu,
final OrbitType orbitType, final PositionAngleType positionAngleType,
final AttitudeProvider attitudeProvider, final Frame frame) {
return new FieldOsculatingMapper(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
}
/** Internal mapper using directly osculating parameters. */
private class FieldOsculatingMapper extends FieldStateMapper<T> {
/** Simple constructor.
* <p>
* The position parameter type is meaningful only if {@link
* #getOrbitType() propagation orbit type}
* support it. As an example, it is not meaningful for propagation
* in {@link OrbitType#CARTESIAN Cartesian} parameters.
* </p>
* @param referenceDate reference date
* @param mu central attraction coefficient (m³/s²)
* @param orbitType orbit type to use for mapping
* @param positionAngleType angle type to use for propagation
* @param attitudeProvider attitude provider
* @param frame inertial frame
*/
FieldOsculatingMapper(final FieldAbsoluteDate<T> referenceDate, final T mu,
final OrbitType orbitType, final PositionAngleType positionAngleType,
final AttitudeProvider attitudeProvider, final Frame frame) {
super(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
}
/** {@inheritDoc} */
public FieldSpacecraftState<T> mapArrayToState(final FieldAbsoluteDate<T> date, final T[] y, final T[] yDot,
final PropagationType type) {
// the parameter type is ignored for the Numerical Propagator
final T mass = y[6];
if (mass.getReal() <= 0.0) {
throw new OrekitException(OrekitMessages.NOT_POSITIVE_SPACECRAFT_MASS, mass);
}
if (superGetOrbitType() == null) {
// propagation uses absolute position-velocity-acceleration
final FieldVector3D<T> p = new FieldVector3D<>(y[0], y[1], y[2]);
final FieldVector3D<T> v = new FieldVector3D<>(y[3], y[4], y[5]);
final FieldVector3D<T> a;
final FieldAbsolutePVCoordinates<T> absPva;
if (yDot == null) {
absPva = new FieldAbsolutePVCoordinates<>(getFrame(), new TimeStampedFieldPVCoordinates<>(date, p, v, FieldVector3D.getZero(date.getField())));
} else {
a = new FieldVector3D<>(yDot[3], yDot[4], yDot[5]);
absPva = new FieldAbsolutePVCoordinates<>(getFrame(), new TimeStampedFieldPVCoordinates<>(date, p, v, a));
}
final FieldAttitude<T> attitude = getAttitudeProvider().getAttitude(absPva, date, getFrame());
return new FieldSpacecraftState<>(absPva, attitude, mass);
} else {
// propagation uses regular orbits
final FieldOrbit<T> orbit = superGetOrbitType().mapArrayToOrbit(y, yDot, super.getPositionAngleType(), date, getMu(), getFrame());
final FieldAttitude<T> attitude = getAttitudeProvider().getAttitude(orbit, date, getFrame());
return new FieldSpacecraftState<>(orbit, attitude, mass);
}
}
/** {@inheritDoc} */
public void mapStateToArray(final FieldSpacecraftState<T> state, final T[] y, final T[] yDot) {
if (superGetOrbitType() == null) {
// propagation uses absolute position-velocity-acceleration
final FieldVector3D<T> p = state.getAbsPVA().getPosition();
final FieldVector3D<T> v = state.getAbsPVA().getVelocity();
y[0] = p.getX();
y[1] = p.getY();
y[2] = p.getZ();
y[3] = v.getX();
y[4] = v.getY();
y[5] = v.getZ();
y[6] = state.getMass();
}
else {
superGetOrbitType().mapOrbitToArray(state.getOrbit(), super.getPositionAngleType(), y, yDot);
y[6] = state.getMass();
}
}
}
/** {@inheritDoc} */
protected MainStateEquations<T> getMainStateEquations(final FieldODEIntegrator<T> integrator) {
return new Main(integrator);
}
/** Internal class for osculating parameters integration. */
private class Main implements MainStateEquations<T>, FieldTimeDerivativesEquations<T> {
/** Derivatives array. */
private final T[] yDot;
/** Current state. */
private FieldSpacecraftState<T> currentState;
/** Jacobian of the orbital parameters with respect to the Cartesian parameters. */
private T[][] jacobian;
/** Flag keeping track whether Jacobian matrix needs to be recomputed or not. */
private boolean recomputingJacobian;
/** Simple constructor.
* @param integrator numerical integrator to use for propagation.
*/
Main(final FieldODEIntegrator<T> integrator) {
this.yDot = MathArrays.buildArray(getField(), 7);
this.jacobian = MathArrays.buildArray(getField(), 6, 6);
this.recomputingJacobian = true;
for (final ForceModel forceModel : forceModels) {
forceModel.getFieldEventDetectors(getField()).forEach(detector -> setUpEventDetector(integrator, detector));
}
// default value for Jacobian is identity
for (int i = 0; i < jacobian.length; ++i) {
Arrays.fill(jacobian[i], getField().getZero());
jacobian[i][i] = getField().getOne();
}
}
/** {@inheritDoc} */
@Override
public void init(final FieldSpacecraftState<T> initialState, final FieldAbsoluteDate<T> target) {
forceModels.forEach(fm -> fm.init(initialState, target));
final int numberOfForces = forceModels.size();
final OrbitType orbitType = superGetOrbitType();
if (orbitType != null && orbitType != OrbitType.CARTESIAN && numberOfForces > 0) {
if (numberOfForces > 1) {
recomputingJacobian = true;
} else {
recomputingJacobian = !(forceModels.get(0) instanceof NewtonianAttraction);
}
} else {
recomputingJacobian = false;
}
}
/** {@inheritDoc} */
@Override
public T[] computeDerivatives(final FieldSpacecraftState<T> state) {
final T zero = state.getA().getField().getZero();
currentState = state;
Arrays.fill(yDot, zero);
if (recomputingJacobian) {
// propagation uses Jacobian matrix of orbital parameters w.r.t. Cartesian ones
currentState.getOrbit().getJacobianWrtCartesian(getPositionAngleType(), jacobian);
}
// compute the contributions of all perturbing forces,
// using the Kepler contribution at the end since
// NewtonianAttraction is always the last instance in the list
for (final ForceModel forceModel : forceModels) {
forceModel.addContribution(state, this);
}
if (superGetOrbitType() == null) {
// position derivative is velocity, and was not added above in the force models
// (it is added when orbit type is non-null because NewtonianAttraction considers it)
final FieldVector3D<T> velocity = currentState.getPVCoordinates().getVelocity();
yDot[0] = yDot[0].add(velocity.getX());
yDot[1] = yDot[1].add(velocity.getY());
yDot[2] = yDot[2].add(velocity.getZ());
}
return yDot.clone();
}
/** {@inheritDoc} */
@Override
public void addKeplerContribution(final T mu) {
if (superGetOrbitType() == null) {
// if mu is neither 0 nor NaN, we want to include Newtonian acceleration
if (mu.getReal() > 0) {
// velocity derivative is Newtonian acceleration
final FieldVector3D<T> position = currentState.getPosition();
final T r2 = position.getNormSq();
final T coeff = r2.multiply(r2.sqrt()).reciprocal().negate().multiply(mu);
yDot[3] = yDot[3].add(coeff.multiply(position.getX()));
yDot[4] = yDot[4].add(coeff.multiply(position.getY()));
yDot[5] = yDot[5].add(coeff.multiply(position.getZ()));
}
} else {
// propagation uses regular orbits
currentState.getOrbit().addKeplerContribution(getPositionAngleType(), mu, yDot);
}
}
/** {@inheritDoc} */
@Override
public void addNonKeplerianAcceleration(final FieldVector3D<T> gamma) {
for (int i = 0; i < 6; ++i) {
final T[] jRow = jacobian[i];
yDot[i] = yDot[i].add(jRow[3].linearCombination(jRow[3], gamma.getX(),
jRow[4], gamma.getY(),
jRow[5], gamma.getZ()));
}
}
/** {@inheritDoc} */
@Override
public void addMassDerivative(final T q) {
if (q.getReal() > 0) {
throw new OrekitIllegalArgumentException(OrekitMessages.POSITIVE_FLOW_RATE, q);
}
yDot[6] = yDot[6].add(q);
}
}
/** Estimate tolerance vectors for integrators.
* <p>
* The errors are estimated from partial derivatives properties of orbits,
* starting from a scalar position error specified by the user.
* Considering the energy conservation equation V = sqrt(mu (2/r - 1/a)),
* we get at constant energy (i.e. on a Keplerian trajectory):
* <pre>
* V r² |dV| = mu |dr|
* </pre>
* So we deduce a scalar velocity error consistent with the position error.
* From here, we apply orbits Jacobians matrices to get consistent errors
* on orbital parameters.
* <p>
* The tolerances are only <em>orders of magnitude</em>, and integrator tolerances
* are only local estimates, not global ones. So some care must be taken when using
* these tolerances. Setting 1mm as a position error does NOT mean the tolerances
* will guarantee a 1mm error position after several orbits integration.
* </p>
* @param dP user specified position error
* @param orbit reference orbit
* @param type propagation type for the meaning of the tolerance vectors elements
* (it may be different from {@code orbit.getType()})
* @return a two rows array, row 0 being the absolute tolerance error and row 1
* being the relative tolerance error
* @param <T> elements type
*/
public static <T extends CalculusFieldElement<T>> double[][] tolerances(final T dP, final FieldOrbit<T> orbit, final OrbitType type) {
// estimate the scalar velocity error
final FieldPVCoordinates<T> pv = orbit.getPVCoordinates();
final T r2 = pv.getPosition().getNormSq();
final T v = pv.getVelocity().getNorm();
final T dV = dP.multiply(orbit.getMu()).divide(v.multiply(r2));
return tolerances(dP, dV, orbit, type);
}
/** Estimate tolerance vectors for integrators when propagating in orbits.
* <p>
* The errors are estimated from partial derivatives properties of orbits,
* starting from scalar position and velocity errors specified by the user.
* <p>
* The tolerances are only <em>orders of magnitude</em>, and integrator tolerances
* are only local estimates, not global ones. So some care must be taken when using
* these tolerances. Setting 1mm as a position error does NOT mean the tolerances
* will guarantee a 1mm error position after several orbits integration.
* </p>
* @param <T> elements type
* @param dP user specified position error
* @param dV user specified velocity error
* @param orbit reference orbit
* @param type propagation type for the meaning of the tolerance vectors elements
* (it may be different from {@code orbit.getType()})
* @return a two rows array, row 0 being the absolute tolerance error and row 1
* being the relative tolerance error
* @since 10.3
*/
public static <T extends CalculusFieldElement<T>> double[][] tolerances(final T dP, final T dV,
final FieldOrbit<T> orbit, final OrbitType type) {
final double[] absTol = new double[7];
final double[] relTol = new double[7];
// we set the mass tolerance arbitrarily to 1.0e-6 kg, as mass evolves linearly
// with trust, this often has no influence at all on propagation
absTol[6] = 1.0e-6;
if (type == OrbitType.CARTESIAN) {
absTol[0] = dP.getReal();
absTol[1] = dP.getReal();
absTol[2] = dP.getReal();
absTol[3] = dV.getReal();
absTol[4] = dV.getReal();
absTol[5] = dV.getReal();
} else {
// convert the orbit to the desired type
final T[][] jacobian = MathArrays.buildArray(dP.getField(), 6, 6);
final FieldOrbit<T> converted = type.convertType(orbit);
converted.getJacobianWrtCartesian(PositionAngleType.TRUE, jacobian);
for (int i = 0; i < 6; ++i) {
final T[] row = jacobian[i];
absTol[i] = row[0].abs().multiply(dP).
add(row[1].abs().multiply(dP)).
add(row[2].abs().multiply(dP)).
add(row[3].abs().multiply(dV)).
add(row[4].abs().multiply(dV)).
add(row[5].abs().multiply(dV)).
getReal();
if (Double.isNaN(absTol[i])) {
throw new OrekitException(OrekitMessages.SINGULAR_JACOBIAN_FOR_ORBIT_TYPE, type);
}
}
}
Arrays.fill(relTol, dP.divide(orbit.getPosition().getNormSq().sqrt()).getReal());
return new double[][] { absTol, relTol };
}
}