L2TransformProvider.java
/* Copyright 2002-2019 CS Systèmes d'Information
* Licensed to CS Systèmes d'Information (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.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.orekit.frames;
import org.hipparchus.Field;
import org.hipparchus.RealFieldElement;
import org.hipparchus.analysis.RealFieldUnivariateFunction;
import org.hipparchus.analysis.UnivariateFunction;
import org.hipparchus.analysis.solvers.AllowedSolution;
import org.hipparchus.analysis.solvers.BracketingNthOrderBrentSolver;
import org.hipparchus.analysis.solvers.FieldBracketingNthOrderBrentSolver;
import org.hipparchus.analysis.solvers.UnivariateSolverUtils;
import org.hipparchus.geometry.euclidean.threed.FieldRotation;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Rotation;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.orekit.bodies.CelestialBody;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.PVCoordinates;
/** L2 Transform provider for a frame on the L2 Lagrange point of two celestial bodies.
*
* @author Luc Maisonobe
* @author Julio Hernanz
*/
class L2TransformProvider implements TransformProvider {
/** Relative accuracy on position for solver. */
private static final double RELATIVE_ACCURACY = 1e-14;
/** Absolute accuracy on position for solver (1mm). */
private static final double ABSOLUTE_ACCURACY = 1e-3;
/** Function value ccuracy for solver (set to 0 so we rely only on position for convergence). */
private static final double FUNCTION_ACCURACY = 0;
/** Maximal order for solver. */
private static final int MAX_ORDER = 5;
/** Maximal number of evaluations for solver. */
private static final int MAX_EVALUATIONS = 1000;
/** Serializable UID.*/
private static final long serialVersionUID = 20170725L;
/** Frame for results. Always defined as primaryBody's inertially oriented frame.*/
private final Frame frame;
/** Celestial body with bigger mass, m1.*/
private final CelestialBody primaryBody;
/** Celestial body with smaller mass, m2.*/
private final CelestialBody secondaryBody;
/** Simple constructor.
* @param primaryBody Primary body.
* @param secondaryBody Secondary body.
*/
L2TransformProvider(final CelestialBody primaryBody, final CelestialBody secondaryBody) {
this.primaryBody = primaryBody;
this.secondaryBody = secondaryBody;
this.frame = primaryBody.getInertiallyOrientedFrame();
}
/** {@inheritDoc} */
@Override
public Transform getTransform(final AbsoluteDate date) {
final PVCoordinates pv21 = secondaryBody.getPVCoordinates(date, frame);
final Vector3D translation = getL2(pv21.getPosition()).negate();
final Rotation rotation = new Rotation(pv21.getPosition(), pv21.getVelocity(),
Vector3D.PLUS_I, Vector3D.PLUS_J);
return new Transform(date, new Transform(date, translation), new Transform(date, rotation));
}
/** {@inheritDoc} */
@Override
public <T extends RealFieldElement<T>> FieldTransform<T> getTransform(final FieldAbsoluteDate<T> date) {
final FieldPVCoordinates<T> pv21 = secondaryBody.getPVCoordinates(date, frame);
final FieldVector3D<T> translation = getL2(pv21.getPosition()).negate();
final Field<T> field = pv21.getPosition().getX().getField();
final FieldRotation<T> rotation = new FieldRotation<>(pv21.getPosition(), pv21.getVelocity(),
FieldVector3D.getPlusI(field),
FieldVector3D.getPlusJ(field));
return new FieldTransform<T>(date,
new FieldTransform<>(date, translation),
new FieldTransform<>(date, rotation));
}
/** Compute the coordinates of the L2 point.
* @param primaryToSecondary relative position of secondary body with respect to primary body
* @return coordinates of the L2 point given in frame: primaryBody.getInertiallyOrientedFrame()
*/
private Vector3D getL2(final Vector3D primaryToSecondary) {
// mass ratio
final double massRatio = secondaryBody.getGM() / primaryBody.getGM();
// Approximate position of L2 point, valid when m2 << m1
final double bigR = primaryToSecondary.getNorm();
final double baseR = bigR * (FastMath.cbrt(massRatio / 3) + 1);
// Accurate position of L2 point, by solving the L2 equilibrium equation
final UnivariateFunction l2Equation = r -> {
final double rminusbigR = r - bigR;
final double lhs1 = 1.0 / (r * r);
final double lhs2 = massRatio / (rminusbigR * rminusbigR);
final double rhs1 = 1.0 / (bigR * bigR);
final double rhs2 = (1 + massRatio) * rminusbigR * rhs1 / bigR;
return (lhs1 + lhs2) - (rhs1 + rhs2);
};
final double[] searchInterval = UnivariateSolverUtils.bracket(l2Equation,
baseR, 0, 2 * bigR,
0.01 * bigR, 1, MAX_EVALUATIONS);
final BracketingNthOrderBrentSolver solver =
new BracketingNthOrderBrentSolver(RELATIVE_ACCURACY,
ABSOLUTE_ACCURACY,
FUNCTION_ACCURACY,
MAX_ORDER);
final double r = solver.solve(MAX_EVALUATIONS, l2Equation,
searchInterval[0], searchInterval[1],
AllowedSolution.ANY_SIDE);
// L2 point is built
return new Vector3D(r / bigR, primaryToSecondary);
}
/** Compute the coordinates of the L2 point.
* @param <T> type of the field elements
* @param primaryToSecondary relative position of secondary body with respect to primary body
* @return coordinates of the L2 point given in frame: primaryBody.getInertiallyOrientedFrame()
*/
private <T extends RealFieldElement<T>> FieldVector3D<T>
getL2(final FieldVector3D<T> primaryToSecondary) {
// mass ratio
final double massRatio = secondaryBody.getGM() / primaryBody.getGM();
// Approximate position of L2 point, valid when m2 << m1
final T bigR = primaryToSecondary.getNorm();
final T baseR = bigR.multiply(FastMath.cbrt(massRatio / 3) + 1);
// Accurate position of L2 point, by solving the L2 equilibrium equation
final RealFieldUnivariateFunction<T> l2Equation = r -> {
final T rminusbigR = r.subtract(bigR);
final T lhs1 = r.multiply(r).reciprocal();
final T lhs2 = rminusbigR.multiply(rminusbigR).reciprocal().multiply(massRatio);
final T rhs1 = bigR.multiply(bigR).reciprocal();
final T rhs2 = rminusbigR.multiply(rhs1).multiply(1 + massRatio).divide(bigR);
return lhs1.add(lhs2).subtract(rhs1.add(rhs2));
};
final T zero = primaryToSecondary.getX().getField().getZero();
final T[] searchInterval = UnivariateSolverUtils.bracket(l2Equation,
baseR, zero, bigR.multiply(2),
bigR.multiply(0.01), zero.add(1),
MAX_EVALUATIONS);
final T relativeAccuracy = zero.add(RELATIVE_ACCURACY);
final T absoluteAccuracy = zero.add(ABSOLUTE_ACCURACY);
final T functionAccuracy = zero.add(FUNCTION_ACCURACY);
final FieldBracketingNthOrderBrentSolver<T> solver =
new FieldBracketingNthOrderBrentSolver<>(relativeAccuracy,
absoluteAccuracy,
functionAccuracy,
MAX_ORDER);
final T r = solver.solve(MAX_EVALUATIONS, l2Equation,
searchInterval[0], searchInterval[1],
AllowedSolution.ANY_SIDE);
// L2 point is built
return new FieldVector3D<>(r.divide(bigR), primaryToSecondary);
}
}