FieldEcksteinHechlerPropagator.java
/* Copyright 2002-2020 CS GROUP
* Licensed to CS GROUP (CS) under one or more
* 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
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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package org.orekit.propagation.analytical;
import org.hipparchus.Field;
import org.hipparchus.RealFieldElement;
import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
import org.orekit.annotation.DefaultDataContext;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.data.DataContext;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider;
import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics;
import org.orekit.orbits.FieldCartesianOrbit;
import org.orekit.orbits.FieldCircularOrbit;
import org.orekit.orbits.FieldOrbit;
import org.orekit.orbits.OrbitType;
import org.orekit.orbits.PositionAngle;
import org.orekit.propagation.FieldSpacecraftState;
import org.orekit.propagation.PropagationType;
import org.orekit.propagation.Propagator;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.FieldTimeSpanMap;
import org.orekit.utils.TimeStampedFieldPVCoordinates;
/** This class propagates a {@link org.orekit.propagation.FieldSpacecraftState}
* using the analytical Eckstein-Hechler model.
* <p>The Eckstein-Hechler model is suited for near circular orbits
* (e < 0.1, with poor accuracy between 0.005 and 0.1) and inclination
* neither equatorial (direct or retrograde) nor critical (direct or
* retrograde).</p>
* @see FieldOrbit
* @author Guylaine Prat
*/
public class FieldEcksteinHechlerPropagator<T extends RealFieldElement<T>> extends FieldAbstractAnalyticalPropagator<T> {
/** Initial Eckstein-Hechler model. */
private FieldEHModel<T> initialModel;
/** All models. */
private transient FieldTimeSpanMap<FieldEHModel<T>, T> models;
/** Reference radius of the central body attraction model (m). */
private double referenceRadius;
/** Central attraction coefficient (m³/s²). */
private T mu;
/** Un-normalized zonal coefficients. */
private double[] ck0;
/** Build a propagator from FieldOrbit and potential provider.
* <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
*
* <p>This constructor uses the {@link DataContext#getDefault() default data context}.
*
* <p>Using this constructor, an initial osculating orbit is considered.</p>
*
* @param initialOrbit initial FieldOrbit
* @param provider for un-normalized zonal coefficients
* @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider,
* UnnormalizedSphericalHarmonicsProvider)
* @see #FieldEcksteinHechlerPropagator(FieldOrbit, UnnormalizedSphericalHarmonicsProvider,
* PropagationType)
*/
@DefaultDataContext
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final UnnormalizedSphericalHarmonicsProvider provider) {
this(initialOrbit, Propagator.getDefaultLaw(DataContext.getDefault().getFrames()),
initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider,
provider.onDate(initialOrbit.getDate().toAbsoluteDate()));
}
/**
* Private helper constructor.
* <p>Using this constructor, an initial osculating orbit is considered.</p>
* @param initialOrbit initial FieldOrbit
* @param attitude attitude provider
* @param mass spacecraft mass
* @param provider for un-normalized zonal coefficients
* @param harmonics {@code provider.onDate(initialOrbit.getDate())}
* @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider, RealFieldElement,
* UnnormalizedSphericalHarmonicsProvider, UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics, PropagationType)
*/
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final AttitudeProvider attitude,
final T mass,
final UnnormalizedSphericalHarmonicsProvider provider,
final UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics harmonics) {
this(initialOrbit, attitude, mass, provider.getAe(), initialOrbit.getA().getField().getZero().add(provider.getMu()),
harmonics.getUnnormalizedCnm(2, 0),
harmonics.getUnnormalizedCnm(3, 0),
harmonics.getUnnormalizedCnm(4, 0),
harmonics.getUnnormalizedCnm(5, 0),
harmonics.getUnnormalizedCnm(6, 0));
}
/** Build a propagator from FieldOrbit and potential.
* <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
* <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
* are related to both the normalized coefficients
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* and the J<sub>n</sub> one as follows:
* <p>
* C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* <p>
* C<sub>n,0</sub> = -J<sub>n</sub>
*
* <p>This constructor uses the {@link DataContext#getDefault() default data context}.
*
* <p>Using this constructor, an initial osculating orbit is considered.</p>
*
* @param initialOrbit initial FieldOrbit
* @param referenceRadius reference radius of the Earth for the potential model (m)
* @param mu central attraction coefficient (m³/s²)
* @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
* @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
* @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
* @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
* @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
* @see org.orekit.utils.Constants
* @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider, double,
* RealFieldElement, double, double, double, double, double)
*/
@DefaultDataContext
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final double referenceRadius, final T mu,
final double c20, final double c30, final double c40,
final double c50, final double c60) {
this(initialOrbit, Propagator.getDefaultLaw(DataContext.getDefault().getFrames()),
initialOrbit.getDate().getField().getZero().add(DEFAULT_MASS),
referenceRadius, mu, c20, c30, c40, c50, c60);
}
/** Build a propagator from FieldOrbit, mass and potential provider.
* <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
*
* <p>This constructor uses the {@link DataContext#getDefault() default data context}.
*
* <p>Using this constructor, an initial osculating orbit is considered.</p>
*
* @param initialOrbit initial FieldOrbit
* @param mass spacecraft mass
* @param provider for un-normalized zonal coefficients
* @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider,
* RealFieldElement, UnnormalizedSphericalHarmonicsProvider)
*/
@DefaultDataContext
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit, final T mass,
final UnnormalizedSphericalHarmonicsProvider provider) {
this(initialOrbit, Propagator.getDefaultLaw(DataContext.getDefault().getFrames()),
mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()));
}
/** Build a propagator from FieldOrbit, mass and potential.
* <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
* <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
* are related to both the normalized coefficients
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* and the J<sub>n</sub> one as follows:</p>
* <p>
* C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* <p>
* C<sub>n,0</sub> = -J<sub>n</sub>
*
* <p>This constructor uses the {@link DataContext#getDefault() default data context}.
*
* <p>Using this constructor, an initial osculating orbit is considered.</p>
*
* @param initialOrbit initial FieldOrbit
* @param mass spacecraft mass
* @param referenceRadius reference radius of the Earth for the potential model (m)
* @param mu central attraction coefficient (m³/s²)
* @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
* @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
* @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
* @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
* @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
* @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider,
* RealFieldElement, double, RealFieldElement, double, double, double, double, double)
*/
@DefaultDataContext
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit, final T mass,
final double referenceRadius, final T mu,
final double c20, final double c30, final double c40,
final double c50, final double c60) {
this(initialOrbit, Propagator.getDefaultLaw(DataContext.getDefault().getFrames()),
mass, referenceRadius, mu, c20, c30, c40, c50, c60);
}
/** Build a propagator from FieldOrbit, attitude provider and potential provider.
* <p>Mass is set to an unspecified non-null arbitrary value.</p>
* <p>Using this constructor, an initial osculating orbit is considered.</p>
* @param initialOrbit initial FieldOrbit
* @param attitudeProv attitude provider
* @param provider for un-normalized zonal coefficients
*/
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final AttitudeProvider attitudeProv,
final UnnormalizedSphericalHarmonicsProvider provider) {
this(initialOrbit, attitudeProv, initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()));
}
/** Build a propagator from FieldOrbit, attitude provider and potential.
* <p>Mass is set to an unspecified non-null arbitrary value.</p>
* <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
* are related to both the normalized coefficients
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* and the J<sub>n</sub> one as follows:</p>
* <p>
* C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* <p>
* C<sub>n,0</sub> = -J<sub>n</sub>
*
* <p>Using this constructor, an initial osculating orbit is considered.</p>
*
* @param initialOrbit initial FieldOrbit
* @param attitudeProv attitude provider
* @param referenceRadius reference radius of the Earth for the potential model (m)
* @param mu central attraction coefficient (m³/s²)
* @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
* @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
* @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
* @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
* @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
*/
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final AttitudeProvider attitudeProv,
final double referenceRadius, final T mu,
final double c20, final double c30, final double c40,
final double c50, final double c60) {
this(initialOrbit, attitudeProv, initialOrbit.getDate().getField().getZero().add(DEFAULT_MASS),
referenceRadius, mu, c20, c30, c40, c50, c60);
}
/** Build a propagator from FieldOrbit, attitude provider, mass and potential provider.
* <p>Using this constructor, an initial osculating orbit is considered.</p>
* @param initialOrbit initial FieldOrbit
* @param attitudeProv attitude provider
* @param mass spacecraft mass
* @param provider for un-normalized zonal coefficients
* @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider, RealFieldElement,
* UnnormalizedSphericalHarmonicsProvider, PropagationType)
*/
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final AttitudeProvider attitudeProv,
final T mass,
final UnnormalizedSphericalHarmonicsProvider provider) {
this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()));
}
/** Build a propagator from FieldOrbit, attitude provider, mass and potential.
* <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
* are related to both the normalized coefficients
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* and the J<sub>n</sub> one as follows:</p>
* <p>
* C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* <p>
* C<sub>n,0</sub> = -J<sub>n</sub>
*
* <p>Using this constructor, an initial osculating orbit is considered.</p>
*
* @param initialOrbit initial FieldOrbit
* @param attitudeProv attitude provider
* @param mass spacecraft mass
* @param referenceRadius reference radius of the Earth for the potential model (m)
* @param mu central attraction coefficient (m³/s²)
* @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
* @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
* @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
* @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
* @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
* @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider, RealFieldElement, double,
* RealFieldElement, double, double, double, double, double, PropagationType)
*/
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final AttitudeProvider attitudeProv,
final T mass,
final double referenceRadius, final T mu,
final double c20, final double c30, final double c40,
final double c50, final double c60) {
this(initialOrbit, attitudeProv, mass, referenceRadius, mu, c20, c30, c40, c50, c60, PropagationType.OSCULATING);
}
/** Build a propagator from orbit and potential provider.
* <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
*
* <p>This constructor uses the {@link DataContext#getDefault() default data context}.
*
* <p>Using this constructor, it is possible to define the initial orbit as
* a mean Eckstein-Hechler orbit or an osculating one.</p>
*
* @param initialOrbit initial orbit
* @param provider for un-normalized zonal coefficients
* @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
* @since 10.2
*/
@DefaultDataContext
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final UnnormalizedSphericalHarmonicsProvider provider,
final PropagationType initialType) {
this(initialOrbit, Propagator.getDefaultLaw(DataContext.getDefault().getFrames()),
initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider,
provider.onDate(initialOrbit.getDate().toAbsoluteDate()), initialType);
}
/** Build a propagator from orbit, attitude provider, mass and potential provider.
* <p>Using this constructor, it is possible to define the initial orbit as
* a mean Eckstein-Hechler orbit or an osculating one.</p>
* @param initialOrbit initial orbit
* @param attitudeProv attitude provider
* @param mass spacecraft mass
* @param provider for un-normalized zonal coefficients
* @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
* @since 10.2
*/
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final AttitudeProvider attitudeProv,
final T mass,
final UnnormalizedSphericalHarmonicsProvider provider,
final PropagationType initialType) {
this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()), initialType);
}
/**
* Private helper constructor.
* <p>Using this constructor, it is possible to define the initial orbit as
* a mean Eckstein-Hechler orbit or an osculating one.</p>
* @param initialOrbit initial orbit
* @param attitude attitude provider
* @param mass spacecraft mass
* @param provider for un-normalized zonal coefficients
* @param harmonics {@code provider.onDate(initialOrbit.getDate())}
* @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
* @since 10.2
*/
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final AttitudeProvider attitude,
final T mass,
final UnnormalizedSphericalHarmonicsProvider provider,
final UnnormalizedSphericalHarmonics harmonics,
final PropagationType initialType) {
this(initialOrbit, attitude, mass, provider.getAe(), initialOrbit.getA().getField().getZero().add(provider.getMu()),
harmonics.getUnnormalizedCnm(2, 0),
harmonics.getUnnormalizedCnm(3, 0),
harmonics.getUnnormalizedCnm(4, 0),
harmonics.getUnnormalizedCnm(5, 0),
harmonics.getUnnormalizedCnm(6, 0),
initialType);
}
/** Build a propagator from FieldOrbit, attitude provider, mass and potential.
* <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
* are related to both the normalized coefficients
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* and the J<sub>n</sub> one as follows:</p>
* <p>
* C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
* <span style="text-decoration: overline">C</span><sub>n,0</sub>
* <p>
* C<sub>n,0</sub> = -J<sub>n</sub>
*
* <p>Using this constructor, it is possible to define the initial orbit as
* a mean Eckstein-Hechler orbit or an osculating one.</p>
*
* @param initialOrbit initial FieldOrbit
* @param attitudeProv attitude provider
* @param mass spacecraft mass
* @param referenceRadius reference radius of the Earth for the potential model (m)
* @param mu central attraction coefficient (m³/s²)
* @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
* @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
* @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
* @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
* @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
* @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
* @since 10.2
*/
public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
final AttitudeProvider attitudeProv,
final T mass,
final double referenceRadius, final T mu,
final double c20, final double c30, final double c40,
final double c50, final double c60,
final PropagationType initialType) {
super(mass.getField(), attitudeProv);
try {
// store model coefficients
this.referenceRadius = referenceRadius;
this.mu = mu;
this.ck0 = new double[] {
0.0, 0.0, c20, c30, c40, c50, c60
};
// compute mean parameters if needed
// transform into circular adapted parameters used by the Eckstein-Hechler model
resetInitialState(new FieldSpacecraftState<>(initialOrbit,
attitudeProv.getAttitude(initialOrbit,
initialOrbit.getDate(),
initialOrbit.getFrame()),
mass),
initialType);
} catch (OrekitException oe) {
throw new OrekitException(oe);
}
}
/** {@inheritDoc}
* <p>The new initial state to consider
* must be defined with an osculating orbit.</p>
* @see #resetInitialState(FieldSpacecraftState, PropagationType)
*/
public void resetInitialState(final FieldSpacecraftState<T> state) {
resetInitialState(state, PropagationType.OSCULATING);
}
/** Reset the propagator initial state.
* @param state new initial state to consider
* @param stateType mean Eckstein-Hechler orbit or osculating orbit
* @since 10.2
*/
public void resetInitialState(final FieldSpacecraftState<T> state, final PropagationType stateType) {
super.resetInitialState(state);
final FieldCircularOrbit<T> circular = (FieldCircularOrbit<T>) OrbitType.CIRCULAR.convertType(state.getOrbit());
this.initialModel = (stateType == PropagationType.MEAN) ?
new FieldEHModel<>(circular, state.getMass(), referenceRadius, mu, ck0) :
computeMeanParameters(circular, state.getMass());
this.models = new FieldTimeSpanMap<FieldEHModel<T>, T>(initialModel, state.getA().getField());
}
/** {@inheritDoc} */
protected void resetIntermediateState(final FieldSpacecraftState<T> state, final boolean forward) {
final FieldEHModel<T> newModel = computeMeanParameters((FieldCircularOrbit<T>) OrbitType.CIRCULAR.convertType(state.getOrbit()),
state.getMass());
if (forward) {
models.addValidAfter(newModel, state.getDate());
} else {
models.addValidBefore(newModel, state.getDate());
}
stateChanged(state);
}
/** Compute mean parameters according to the Eckstein-Hechler analytical model.
* @param osculating osculating FieldOrbit
* @param mass constant mass
* @return Eckstein-Hechler mean model
*/
private FieldEHModel<T> computeMeanParameters(final FieldCircularOrbit<T> osculating, final T mass) {
// sanity check
if (osculating.getA().getReal() < referenceRadius) {
throw new OrekitException(OrekitMessages.TRAJECTORY_INSIDE_BRILLOUIN_SPHERE,
osculating.getA());
}
final Field<T> field = mass.getField();
final T one = field.getOne();
final T zero = field.getZero();
// rough initialization of the mean parameters
FieldEHModel<T> current = new FieldEHModel<>(osculating, mass, referenceRadius, mu, ck0);
// threshold for each parameter
final T epsilon = one .multiply(1.0e-13);
final T thresholdA = epsilon.multiply(current.mean.getA().abs().add(1.0));
final T thresholdE = epsilon.multiply(current.mean.getE().add(1.0));
final T thresholdAngles = epsilon.multiply(FastMath.PI);
int i = 0;
while (i++ < 100) {
// recompute the osculating parameters from the current mean parameters
final FieldUnivariateDerivative2<T>[] parameters = current.propagateParameters(current.mean.getDate());
// adapted parameters residuals
final T deltaA = osculating.getA() .subtract(parameters[0].getValue());
final T deltaEx = osculating.getCircularEx().subtract(parameters[1].getValue());
final T deltaEy = osculating.getCircularEy().subtract(parameters[2].getValue());
final T deltaI = osculating.getI() .subtract(parameters[3].getValue());
final T deltaRAAN = MathUtils.normalizeAngle(osculating.getRightAscensionOfAscendingNode().subtract(
parameters[4].getValue()),
zero);
final T deltaAlphaM = MathUtils.normalizeAngle(osculating.getAlphaM().subtract(parameters[5].getValue()), zero);
// update mean parameters
current = new FieldEHModel<>(new FieldCircularOrbit<>(current.mean.getA().add(deltaA),
current.mean.getCircularEx().add( deltaEx),
current.mean.getCircularEy().add( deltaEy),
current.mean.getI() .add( deltaI ),
current.mean.getRightAscensionOfAscendingNode().add(deltaRAAN),
current.mean.getAlphaM().add(deltaAlphaM),
PositionAngle.MEAN,
current.mean.getFrame(),
current.mean.getDate(), mu),
mass, referenceRadius, mu, ck0);
// check convergence
if ((FastMath.abs(deltaA.getReal()) < thresholdA.getReal()) &&
(FastMath.abs(deltaEx.getReal()) < thresholdE.getReal()) &&
(FastMath.abs(deltaEy.getReal()) < thresholdE.getReal()) &&
(FastMath.abs(deltaI.getReal()) < thresholdAngles.getReal()) &&
(FastMath.abs(deltaRAAN.getReal()) < thresholdAngles.getReal()) &&
(FastMath.abs(deltaAlphaM.getReal()) < thresholdAngles.getReal())) {
return current;
}
}
throw new OrekitException(OrekitMessages.UNABLE_TO_COMPUTE_ECKSTEIN_HECHLER_MEAN_PARAMETERS, i);
}
/** {@inheritDoc} */
public FieldCartesianOrbit<T> propagateOrbit(final FieldAbsoluteDate<T> date) {
// compute Cartesian parameters, taking derivatives into account
// to make sure velocity and acceleration are consistent
final FieldEHModel<T> current = models.get(date);
return new FieldCartesianOrbit<>(toCartesian(date, current.propagateParameters(date)),
current.mean.getFrame(), mu);
}
/** Local class for Eckstein-Hechler model, with fixed mean parameters. */
private static class FieldEHModel<T extends RealFieldElement<T>> {
/** Mean FieldOrbit. */
private final FieldCircularOrbit<T> mean;
/** Constant mass. */
private final T mass;
// CHECKSTYLE: stop JavadocVariable check
// preprocessed values
private final T xnotDot;
private final T rdpom;
private final T rdpomp;
private final T eps1;
private final T eps2;
private final T xim;
private final T ommD;
private final T rdl;
private final T aMD;
private final T kh;
private final T kl;
private final T ax1;
private final T ay1;
private final T as1;
private final T ac2;
private final T axy3;
private final T as3;
private final T ac4;
private final T as5;
private final T ac6;
private final T ex1;
private final T exx2;
private final T exy2;
private final T ex3;
private final T ex4;
private final T ey1;
private final T eyx2;
private final T eyy2;
private final T ey3;
private final T ey4;
private final T rx1;
private final T ry1;
private final T r2;
private final T r3;
private final T rl;
private final T iy1;
private final T ix1;
private final T i2;
private final T i3;
private final T ih;
private final T lx1;
private final T ly1;
private final T l2;
private final T l3;
private final T ll;
// CHECKSTYLE: resume JavadocVariable check
/** Create a model for specified mean FieldOrbit.
* @param mean mean FieldOrbit
* @param mass constant mass
* @param referenceRadius reference radius of the central body attraction model (m)
* @param mu central attraction coefficient (m³/s²)
* @param ck0 un-normalized zonal coefficients
*/
FieldEHModel(final FieldCircularOrbit<T> mean, final T mass,
final double referenceRadius, final T mu, final double[] ck0) {
this.mean = mean;
this.mass = mass;
final T zero = mass.getField().getZero();
final T one = mass.getField().getOne();
// preliminary processing
T q = zero.add(referenceRadius).divide(mean.getA());
T ql = q.multiply(q);
final T g2 = ql.multiply(ck0[2]);
ql = ql.multiply(q);
final T g3 = ql.multiply(ck0[3]);
ql = ql.multiply(q);
final T g4 = ql.multiply(ck0[4]);
ql = ql.multiply(q);
final T g5 = ql.multiply(ck0[5]);
ql = ql.multiply(q);
final T g6 = ql.multiply(ck0[6]);
final FieldSinCos<T> sc = FastMath.sinCos(mean.getI());
final T cosI1 = sc.cos();
final T sinI1 = sc.sin();
final T sinI2 = sinI1.multiply(sinI1);
final T sinI4 = sinI2.multiply(sinI2);
final T sinI6 = sinI2.multiply(sinI4);
if (sinI2.getReal() < 1.0e-10) {
throw new OrekitException(OrekitMessages.ALMOST_EQUATORIAL_ORBIT,
FastMath.toDegrees(mean.getI().getReal()));
}
if (FastMath.abs(sinI2.getReal() - 4.0 / 5.0) < 1.0e-3) {
throw new OrekitException(OrekitMessages.ALMOST_CRITICALLY_INCLINED_ORBIT,
FastMath.toDegrees(mean.getI().getReal()));
}
if (mean.getE().getReal() > 0.1) {
// if 0.005 < e < 0.1 no error is triggered, but accuracy is poor
throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL,
mean.getE());
}
xnotDot = mu.divide(mean.getA()).sqrt().divide(mean.getA());
rdpom = g2.multiply(-0.75).multiply(sinI2.multiply(-5.0).add(4.0));
rdpomp = g4.multiply(7.5).multiply(sinI2.multiply(-31.0 / 8.0).add(1.0).add( sinI4.multiply(49.0 / 16.0))).subtract(
g6.multiply(13.125).multiply(one.subtract(sinI2.multiply(8.0)).add(sinI4.multiply(129.0 / 8.0)).subtract(sinI6.multiply(297.0 / 32.0)) ));
q = zero.add(3.0).divide(rdpom.multiply(32.0));
eps1 = q.multiply(g4).multiply(sinI2).multiply(sinI2.multiply(-35.0).add(30.0)).subtract(
q.multiply(175.0).multiply(g6).multiply(sinI2).multiply(sinI2.multiply(-3.0).add(sinI4.multiply(2.0625)).add(1.0)));
q = sinI1.multiply(3.0).divide(rdpom.multiply(8.0));
eps2 = q.multiply(g3).multiply(sinI2.multiply(-5.0).add(4.0)).subtract(q.multiply(g5).multiply(sinI2.multiply(-35.0).add(sinI4.multiply(26.25)).add(10.0)));
xim = mean.getI();
ommD = cosI1.multiply(g2.multiply(1.50).subtract(g2.multiply(2.25).multiply(g2).multiply(sinI2.multiply(-19.0 / 6.0).add(2.5))).add(
g4.multiply(0.9375).multiply(sinI2.multiply(7.0).subtract(4.0))).add(
g6.multiply(3.28125).multiply(sinI2.multiply(-9.0).add(2.0).add(sinI4.multiply(8.25)))));
rdl = g2.multiply(-1.50).multiply(sinI2.multiply(-4.0).add(3.0)).add(1.0);
aMD = rdl.add(
g2.multiply(2.25).multiply(g2.multiply(sinI2.multiply(-263.0 / 12.0 ).add(9.0).add(sinI4.multiply(341.0 / 24.0))))).add(
g4.multiply(15.0 / 16.0).multiply(sinI2.multiply(-31.0).add(8.0).add(sinI4.multiply(24.5)))).add(
g6.multiply(105.0 / 32.0).multiply(sinI2.multiply(25.0).add(-10.0 / 3.0).subtract(sinI4.multiply(48.75)).add(sinI6.multiply(27.5))));
final T qq = g2.divide(rdl).multiply(-1.5);
final T qA = g2.multiply(0.75).multiply(g2).multiply(sinI2);
final T qB = g4.multiply(0.25).multiply(sinI2);
final T qC = g6.multiply(105.0 / 16.0).multiply(sinI2);
final T qD = g3.multiply(-0.75).multiply(sinI1);
final T qE = g5.multiply(3.75).multiply(sinI1);
kh = zero.add(0.375).divide(rdpom);
kl = kh.divide(sinI1);
ax1 = qq.multiply(sinI2.multiply(-3.5).add(2.0));
ay1 = qq.multiply(sinI2.multiply(-2.5).add(2.0));
as1 = qD.multiply(sinI2.multiply(-5.0).add(4.0)).add(
qE.multiply(sinI4.multiply(2.625).add(sinI2.multiply(-3.5)).add(1.0)));
ac2 = qq.multiply(sinI2).add(
qA.multiply(7.0).multiply(sinI2.multiply(-3.0).add(2.0))).add(
qB.multiply(sinI2.multiply(-17.5).add(15.0))).add(
qC.multiply(sinI2.multiply(3.0).subtract(1.0).subtract(sinI4.multiply(33.0 / 16.0))));
axy3 = qq.multiply(3.5).multiply(sinI2);
as3 = qD.multiply(5.0 / 3.0).multiply(sinI2).add(
qE.multiply(7.0 / 6.0).multiply(sinI2).multiply(sinI2.multiply(-1.125).add(1)));
ac4 = qA.multiply(sinI2).add(
qB.multiply(4.375).multiply(sinI2)).add(
qC.multiply(0.75).multiply(sinI4.multiply(1.1).subtract(sinI2)));
as5 = qE.multiply(21.0 / 80.0).multiply(sinI4);
ac6 = qC.multiply(-11.0 / 80.0).multiply(sinI4);
ex1 = qq.multiply(sinI2.multiply(-1.25).add(1.0));
exx2 = qq.multiply(0.5).multiply(sinI2.multiply(-5.0).add(3.0));
exy2 = qq.multiply(sinI2.multiply(-1.5).add(2.0));
ex3 = qq.multiply(7.0 / 12.0).multiply(sinI2);
ex4 = qq.multiply(17.0 / 8.0).multiply(sinI2);
ey1 = qq.multiply(sinI2.multiply(-1.75).add(1.0));
eyx2 = qq.multiply(sinI2.multiply(-3.0).add(1.0));
eyy2 = qq.multiply(sinI2.multiply(2.0).subtract(1.5));
ey3 = qq.multiply(7.0 / 12.0).multiply(sinI2);
ey4 = qq.multiply(17.0 / 8.0).multiply(sinI2);
q = cosI1.multiply(qq).negate();
rx1 = q.multiply(3.5);
ry1 = q.multiply(-2.5);
r2 = q.multiply(-0.5);
r3 = q.multiply(7.0 / 6.0);
rl = g3 .multiply( cosI1).multiply(sinI2.multiply(-15.0).add(4.0)).subtract(
g5.multiply(2.5).multiply(cosI1).multiply(sinI2.multiply(-42.0).add(4.0).add(sinI4.multiply(52.5))));
q = qq.multiply(0.5).multiply(sinI1).multiply(cosI1);
iy1 = q;
ix1 = q.negate();
i2 = q;
i3 = q.multiply(7.0 / 3.0);
ih = g3.negate().multiply(cosI1).multiply(sinI2.multiply(-5.0).add(4)).add(
g5.multiply(2.5).multiply(cosI1).multiply(sinI2.multiply(-14.0).add(4.0).add(sinI4.multiply(10.5))));
lx1 = qq.multiply(sinI2.multiply(-77.0 / 8.0).add(7.0));
ly1 = qq.multiply(sinI2.multiply(55.0 / 8.0).subtract(7.50));
l2 = qq.multiply(sinI2.multiply(1.25).subtract(0.5));
l3 = qq.multiply(sinI2.multiply(77.0 / 24.0).subtract(7.0 / 6.0));
ll = g3.multiply(sinI2.multiply(53.0).subtract(4.0).add(sinI4.multiply(-57.5))).add(
g5.multiply(2.5).multiply(sinI2.multiply(-96.0).add(4.0).add(sinI4.multiply(269.5).subtract(sinI6.multiply(183.75)))));
}
/** Extrapolate a FieldOrbit up to a specific target date.
* @param date target date for the FieldOrbit
* @return propagated parameters
*/
public FieldUnivariateDerivative2<T>[] propagateParameters(final FieldAbsoluteDate<T> date) {
final Field<T> field = date.durationFrom(mean.getDate()).getField();
final T one = field.getOne();
final T zero = field.getZero();
// Keplerian evolution
final FieldUnivariateDerivative2<T> dt = new FieldUnivariateDerivative2<>(date.durationFrom(mean.getDate()), one, zero);
final FieldUnivariateDerivative2<T> xnot = dt.multiply(xnotDot);
// secular effects
// eccentricity
final FieldUnivariateDerivative2<T> x = xnot.multiply(rdpom.add(rdpomp));
final FieldUnivariateDerivative2<T> cx = x.cos();
final FieldUnivariateDerivative2<T> sx = x.sin();
final FieldUnivariateDerivative2<T> exm = cx.multiply(mean.getCircularEx()).
add(sx.multiply(eps2.subtract(one.subtract(eps1).multiply(mean.getCircularEy()))));
final FieldUnivariateDerivative2<T> eym = sx.multiply(eps1.add(1.0).multiply(mean.getCircularEx())).
add(cx.multiply(mean.getCircularEy().subtract(eps2))).
add(eps2);
// no secular effect on inclination
// right ascension of ascending node
final FieldUnivariateDerivative2<T> omm =
new FieldUnivariateDerivative2<>(MathUtils.normalizeAngle(mean.getRightAscensionOfAscendingNode().add(ommD.multiply(xnot.getValue())),
zero.add(FastMath.PI)),
ommD.multiply(xnotDot),
zero);
// latitude argument
final FieldUnivariateDerivative2<T> xlm =
new FieldUnivariateDerivative2<>(MathUtils.normalizeAngle(mean.getAlphaM().add(aMD.multiply(xnot.getValue())),
zero.add(FastMath.PI)),
aMD.multiply(xnotDot),
zero);
// periodical terms
final FieldUnivariateDerivative2<T> cl1 = xlm.cos();
final FieldUnivariateDerivative2<T> sl1 = xlm.sin();
final FieldUnivariateDerivative2<T> cl2 = cl1.multiply(cl1).subtract(sl1.multiply(sl1));
final FieldUnivariateDerivative2<T> sl2 = cl1.multiply(sl1).add(sl1.multiply(cl1));
final FieldUnivariateDerivative2<T> cl3 = cl2.multiply(cl1).subtract(sl2.multiply(sl1));
final FieldUnivariateDerivative2<T> sl3 = cl2.multiply(sl1).add(sl2.multiply(cl1));
final FieldUnivariateDerivative2<T> cl4 = cl3.multiply(cl1).subtract(sl3.multiply(sl1));
final FieldUnivariateDerivative2<T> sl4 = cl3.multiply(sl1).add(sl3.multiply(cl1));
final FieldUnivariateDerivative2<T> cl5 = cl4.multiply(cl1).subtract(sl4.multiply(sl1));
final FieldUnivariateDerivative2<T> sl5 = cl4.multiply(sl1).add(sl4.multiply(cl1));
final FieldUnivariateDerivative2<T> cl6 = cl5.multiply(cl1).subtract(sl5.multiply(sl1));
final FieldUnivariateDerivative2<T> qh = eym.subtract(eps2).multiply(kh);
final FieldUnivariateDerivative2<T> ql = exm.multiply(kl);
final FieldUnivariateDerivative2<T> exmCl1 = exm.multiply(cl1);
final FieldUnivariateDerivative2<T> exmSl1 = exm.multiply(sl1);
final FieldUnivariateDerivative2<T> eymCl1 = eym.multiply(cl1);
final FieldUnivariateDerivative2<T> eymSl1 = eym.multiply(sl1);
final FieldUnivariateDerivative2<T> exmCl2 = exm.multiply(cl2);
final FieldUnivariateDerivative2<T> exmSl2 = exm.multiply(sl2);
final FieldUnivariateDerivative2<T> eymCl2 = eym.multiply(cl2);
final FieldUnivariateDerivative2<T> eymSl2 = eym.multiply(sl2);
final FieldUnivariateDerivative2<T> exmCl3 = exm.multiply(cl3);
final FieldUnivariateDerivative2<T> exmSl3 = exm.multiply(sl3);
final FieldUnivariateDerivative2<T> eymCl3 = eym.multiply(cl3);
final FieldUnivariateDerivative2<T> eymSl3 = eym.multiply(sl3);
final FieldUnivariateDerivative2<T> exmCl4 = exm.multiply(cl4);
final FieldUnivariateDerivative2<T> exmSl4 = exm.multiply(sl4);
final FieldUnivariateDerivative2<T> eymCl4 = eym.multiply(cl4);
final FieldUnivariateDerivative2<T> eymSl4 = eym.multiply(sl4);
// semi major axis
final FieldUnivariateDerivative2<T> rda = exmCl1.multiply(ax1).
add(eymSl1.multiply(ay1)).
add(sl1.multiply(as1)).
add(cl2.multiply(ac2)).
add(exmCl3.add(eymSl3).multiply(axy3)).
add(sl3.multiply(as3)).
add(cl4.multiply(ac4)).
add(sl5.multiply(as5)).
add(cl6.multiply(ac6));
// eccentricity
final FieldUnivariateDerivative2<T> rdex = cl1.multiply(ex1).
add(exmCl2.multiply(exx2)).
add(eymSl2.multiply(exy2)).
add(cl3.multiply(ex3)).
add(exmCl4.add(eymSl4).multiply(ex4));
final FieldUnivariateDerivative2<T> rdey = sl1.multiply(ey1).
add(exmSl2.multiply(eyx2)).
add(eymCl2.multiply(eyy2)).
add(sl3.multiply(ey3)).
add(exmSl4.subtract(eymCl4).multiply(ey4));
// ascending node
final FieldUnivariateDerivative2<T> rdom = exmSl1.multiply(rx1).
add(eymCl1.multiply(ry1)).
add(sl2.multiply(r2)).
add(eymCl3.subtract(exmSl3).multiply(r3)).
add(ql.multiply(rl));
// inclination
final FieldUnivariateDerivative2<T> rdxi = eymSl1.multiply(iy1).
add(exmCl1.multiply(ix1)).
add(cl2.multiply(i2)).
add(exmCl3.add(eymSl3).multiply(i3)).
add(qh.multiply(ih));
// latitude argument
final FieldUnivariateDerivative2<T> rdxl = exmSl1.multiply(lx1).
add(eymCl1.multiply(ly1)).
add(sl2.multiply(l2)).
add(exmSl3.subtract(eymCl3).multiply(l3)).
add(ql.multiply(ll));
// osculating parameters
final FieldUnivariateDerivative2<T>[] FTD = MathArrays.buildArray(rdxl.getField(), 6);
FTD[0] = rda.add(1.0).multiply(mean.getA());
FTD[1] = rdex.add(exm);
FTD[2] = rdey.add(eym);
FTD[3] = rdxi.add(xim);
FTD[4] = rdom.add(omm);
FTD[5] = rdxl.add(xlm);
return FTD;
}
}
/** Convert circular parameters <em>with derivatives</em> to Cartesian coordinates.
* @param date date of the parameters
* @param parameters circular parameters (a, ex, ey, i, raan, alphaM)
* @return Cartesian coordinates consistent with values and derivatives
*/
private TimeStampedFieldPVCoordinates<T> toCartesian(final FieldAbsoluteDate<T> date, final FieldUnivariateDerivative2<T>[] parameters) {
// evaluate coordinates in the FieldOrbit canonical reference frame
final FieldUnivariateDerivative2<T> cosOmega = parameters[4].cos();
final FieldUnivariateDerivative2<T> sinOmega = parameters[4].sin();
final FieldUnivariateDerivative2<T> cosI = parameters[3].cos();
final FieldUnivariateDerivative2<T> sinI = parameters[3].sin();
final FieldUnivariateDerivative2<T> alphaE = meanToEccentric(parameters[5], parameters[1], parameters[2]);
final FieldUnivariateDerivative2<T> cosAE = alphaE.cos();
final FieldUnivariateDerivative2<T> sinAE = alphaE.sin();
final FieldUnivariateDerivative2<T> ex2 = parameters[1].multiply(parameters[1]);
final FieldUnivariateDerivative2<T> ey2 = parameters[2].multiply(parameters[2]);
final FieldUnivariateDerivative2<T> exy = parameters[1].multiply(parameters[2]);
final FieldUnivariateDerivative2<T> q = ex2.add(ey2).subtract(1).negate().sqrt();
final FieldUnivariateDerivative2<T> beta = q.add(1).reciprocal();
final FieldUnivariateDerivative2<T> bx2 = beta.multiply(ex2);
final FieldUnivariateDerivative2<T> by2 = beta.multiply(ey2);
final FieldUnivariateDerivative2<T> bxy = beta.multiply(exy);
final FieldUnivariateDerivative2<T> u = bxy.multiply(sinAE).subtract(parameters[1].add(by2.subtract(1).multiply(cosAE)));
final FieldUnivariateDerivative2<T> v = bxy.multiply(cosAE).subtract(parameters[2].add(bx2.subtract(1).multiply(sinAE)));
final FieldUnivariateDerivative2<T> x = parameters[0].multiply(u);
final FieldUnivariateDerivative2<T> y = parameters[0].multiply(v);
// canonical FieldOrbit reference frame
final FieldVector3D<FieldUnivariateDerivative2<T>> p =
new FieldVector3D<>(x.multiply(cosOmega).subtract(y.multiply(cosI.multiply(sinOmega))),
x.multiply(sinOmega).add(y.multiply(cosI.multiply(cosOmega))),
y.multiply(sinI));
// dispatch derivatives
final FieldVector3D<T> p0 = new FieldVector3D<>(p.getX().getValue(),
p.getY().getValue(),
p.getZ().getValue());
final FieldVector3D<T> p1 = new FieldVector3D<>(p.getX().getFirstDerivative(),
p.getY().getFirstDerivative(),
p.getZ().getFirstDerivative());
final FieldVector3D<T> p2 = new FieldVector3D<>(p.getX().getSecondDerivative(),
p.getY().getSecondDerivative(),
p.getZ().getSecondDerivative());
return new TimeStampedFieldPVCoordinates<>(date, p0, p1, p2);
}
/** Computes the eccentric latitude argument from the mean latitude argument.
* @param alphaM = M + Ω mean latitude argument (rad)
* @param ex e cos(Ω), first component of circular eccentricity vector
* @param ey e sin(Ω), second component of circular eccentricity vector
* @return the eccentric latitude argument.
*/
private FieldUnivariateDerivative2<T> meanToEccentric(final FieldUnivariateDerivative2<T> alphaM,
final FieldUnivariateDerivative2<T> ex,
final FieldUnivariateDerivative2<T> ey) {
// Generalization of Kepler equation to circular parameters
// with alphaE = PA + E and
// alphaM = PA + M = alphaE - ex.sin(alphaE) + ey.cos(alphaE)
FieldUnivariateDerivative2<T> alphaE = alphaM;
FieldUnivariateDerivative2<T> shift = alphaM.getField().getZero();
FieldUnivariateDerivative2<T> alphaEMalphaM = alphaM.getField().getZero();
FieldUnivariateDerivative2<T> cosAlphaE = alphaE.cos();
FieldUnivariateDerivative2<T> sinAlphaE = alphaE.sin();
int iter = 0;
do {
final FieldUnivariateDerivative2<T> f2 = ex.multiply(sinAlphaE).subtract(ey.multiply(cosAlphaE));
final FieldUnivariateDerivative2<T> f1 = alphaM.getField().getOne().subtract(ex.multiply(cosAlphaE)).subtract(ey.multiply(sinAlphaE));
final FieldUnivariateDerivative2<T> f0 = alphaEMalphaM.subtract(f2);
final FieldUnivariateDerivative2<T> f12 = f1.multiply(2);
shift = f0.multiply(f12).divide(f1.multiply(f12).subtract(f0.multiply(f2)));
alphaEMalphaM = alphaEMalphaM.subtract(shift);
alphaE = alphaM.add(alphaEMalphaM);
cosAlphaE = alphaE.cos();
sinAlphaE = alphaE.sin();
} while ((++iter < 50) && (FastMath.abs(shift.getValue().getReal()) > 1.0e-12));
return alphaE;
}
/** {@inheritDoc} */
protected T getMass(final FieldAbsoluteDate<T> date) {
return models.get(date).mass;
}
/**
* Normalize an angle in a 2π wide interval around a center value.
* <p>This method has three main uses:</p>
* <ul>
* <li>normalize an angle between 0 and 2π:<br>
* {@code a = MathUtils.normalizeAngle(a, FastMath.PI);}</li>
* <li>normalize an angle between -π and +π<br>
* {@code a = MathUtils.normalizeAngle(a, 0.0);}</li>
* <li>compute the angle between two defining angular positions:<br>
* {@code angle = MathUtils.normalizeAngle(end, start) - start;}</li>
* </ul>
* <p>Note that due to numerical accuracy and since π cannot be represented
* exactly, the result interval is <em>closed</em>, it cannot be half-closed
* as would be more satisfactory in a purely mathematical view.</p>
* @param a angle to normalize
* @param center center of the desired 2π interval for the result
* @param <T> the type of the field elements
* @return a-2kπ with integer k and center-π <= a-2kπ <= center+π
* @since 1.2
* @deprecated replaced by {@link MathUtils#normalizeAngle(RealFieldElement, RealFieldElement)}
*/
@Deprecated
public static <T extends RealFieldElement<T>> T normalizeAngle(final T a, final T center) {
return a.subtract(2 * FastMath.PI * FastMath.floor((a.getReal() + FastMath.PI - center.getReal()) / (2 * FastMath.PI)));
}
}