FieldHansenThirdBodyLinear.java
- /* Copyright 2002-2024 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.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
- package org.orekit.propagation.semianalytical.dsst.utilities.hansen;
- import org.hipparchus.Field;
- import org.hipparchus.CalculusFieldElement;
- import org.hipparchus.analysis.polynomials.PolynomialFunction;
- import org.hipparchus.util.FastMath;
- import org.hipparchus.util.MathArrays;
- /**
- * Hansen coefficients K(t,n,s) for t=0 and n > 0.
- * <p>
- * Implements Collins 4-254 or Danielson 2.7.3-(7) for Hansen Coefficients and
- * Danielson 3.2-(3) for derivatives. The recursions are transformed into
- * composition of linear transformations to obtain the associated polynomials
- * for coefficients and their derivatives - see Petre's paper
- *
- * @author Petre Bazavan
- * @author Lucian Barbulescu
- * @author Bryan Cazabonne
- * @param <T> type of the field elements
- */
- public class FieldHansenThirdBodyLinear <T extends CalculusFieldElement<T>> {
- /** The number of coefficients that will be computed with a set of roots. */
- private static final int SLICE = 10;
- /**
- * The first vector of polynomials associated to Hansen coefficients and
- * derivatives.
- */
- private final PolynomialFunction[][] mpvec;
- /** The second vector of polynomials associated only to derivatives. */
- private final PolynomialFunction[][] mpvecDeriv;
- /** The Hansen coefficients used as roots. */
- private final T[][] hansenRoot;
- /** The derivatives of the Hansen coefficients used as roots. */
- private final T[][] hansenDerivRoot;
- /** The number of slices needed to compute the coefficients. */
- private final int numSlices;
- /** The s index. */
- private final int s;
- /** (-1)<sup>s</sup> * (2*s + 1)!! / (s+1)! */
- private double twosp1dfosp1f;
- /** (-1)<sup>s</sup> * (2*s + 1)!! / (s+2)! */
- private final double twosp1dfosp2f;
- /** (-1)<sup>s</sup> * 2 * (2*s + 1)!! / (s+2)! */
- private final double two2sp1dfosp2f;
- /** (2*s + 3). */
- private final double twosp3;
- /**
- * Constructor.
- *
- * @param nMax the maximum value of n
- * @param s the value of s
- * @param field field used by default
- */
- public FieldHansenThirdBodyLinear(final int nMax, final int s, final Field<T> field) {
- // initialise fields
- this.s = s;
- //Compute the fields that will be used to determine the initial values for the coefficients
- this.twosp1dfosp1f = (s % 2 == 0) ? 1.0 : -1.0;
- for (int i = s; i >= 1; i--) {
- this.twosp1dfosp1f *= (2.0 * i + 1.0) / (i + 1.0);
- }
- this.twosp1dfosp2f = this.twosp1dfosp1f / (s + 2.);
- this.twosp3 = 2 * s + 3;
- this.two2sp1dfosp2f = 2 * this.twosp1dfosp2f;
- // initialization of structures for stored data
- mpvec = new PolynomialFunction[nMax + 1][];
- mpvecDeriv = new PolynomialFunction[nMax + 1][];
- this.numSlices = FastMath.max(1, (nMax - s + SLICE - 2) / SLICE);
- hansenRoot = MathArrays.buildArray(field, numSlices, 2);
- hansenDerivRoot = MathArrays.buildArray(field, numSlices, 2);
- // Prepare the database of the associated polynomials
- HansenUtilities.generateThirdBodyPolynomials(s, nMax, SLICE, s,
- mpvec, mpvecDeriv);
- }
- /**
- * Compute the initial values (see Collins, 4-255, 4-256 and 4.259)
- * <p>
- * K₀<sup>s, s</sup> = (-1)<sup>s</sup> * ( (2*s+1)!! / (s+1)! )
- * </p>
- * <p>
- * K₀<sup>s+1, s</sup> = (-1)<sup>s</sup> * ( (2*s+1)!! / (s+2)!
- * ) * (2*s+3 - χ<sup>-2</sup>)
- * </p>
- * <p>
- * dK₀<sup>s+1, s</sup> / dχ = = (-1)<sup>s</sup> * 2 * (
- * (2*s+1)!! / (s+2)! ) * χ<sup>-3</sup>
- * </p>
- * @param chitm1 sqrt(1 - e²)
- * @param chitm2 sqrt(1 - e²)²
- * @param chitm3 sqrt(1 - e²)³
- */
- public void computeInitValues(final T chitm1, final T chitm2, final T chitm3) {
- final Field<T> field = chitm2.getField();
- final T zero = field.getZero();
- this.hansenRoot[0][0] = zero.newInstance(twosp1dfosp1f);
- this.hansenRoot[0][1] = (chitm2.negate().add(this.twosp3)).multiply(this.twosp1dfosp2f);
- this.hansenDerivRoot[0][0] = zero;
- this.hansenDerivRoot[0][1] = chitm3.multiply(two2sp1dfosp2f);
- for (int i = 1; i < numSlices; i++) {
- for (int j = 0; j < 2; j++) {
- // Get the required polynomials
- final PolynomialFunction[] mv = mpvec[s + (i * SLICE) + j];
- final PolynomialFunction[] sv = mpvecDeriv[s + (i * SLICE) + j];
- //Compute the root derivatives
- hansenDerivRoot[i][j] = mv[1].value(chitm1).multiply(hansenDerivRoot[i - 1][1]).
- add(mv[0].value(chitm1).multiply(hansenDerivRoot[i - 1][0])).
- add(sv[1].value(chitm1).multiply(hansenRoot[i - 1][1])).
- add(sv[0].value(chitm1).multiply(hansenRoot[i - 1][0]));
- //Compute the root Hansen coefficients
- hansenRoot[i][j] = mv[1].value(chitm1).multiply(hansenRoot[i - 1][1]).
- add(mv[0].value(chitm1).multiply(hansenRoot[i - 1][0]));
- }
- }
- }
- /**
- * Compute the value of the Hansen coefficient K₀<sup>n, s</sup>.
- *
- * @param n n value
- * @param chitm1 χ<sup>-1</sup>
- * @return the coefficient K₀<sup>n, s</sup>
- */
- public T getValue(final int n, final T chitm1) {
- //Compute the potential slice
- int sliceNo = (n - s) / SLICE;
- if (sliceNo < numSlices) {
- //Compute the index within the slice
- final int indexInSlice = (n - s) % SLICE;
- //Check if a root must be returned
- if (indexInSlice <= 1) {
- return hansenRoot[sliceNo][indexInSlice];
- }
- } else {
- //the value was a potential root for a slice, but that slice was not required
- //Decrease the slice number
- sliceNo--;
- }
- // Danielson 2.7.3-(6c)/Collins 4-242 and Petre's paper
- final PolynomialFunction[] v = mpvec[n];
- T ret = v[1].value(chitm1).multiply(hansenRoot[sliceNo][1]);
- if (hansenRoot[sliceNo][0].getReal() != 0) {
- ret = ret.add(v[0].value(chitm1).multiply(hansenRoot[sliceNo][0]));
- }
- return ret;
- }
- /**
- * Compute the value of the Hansen coefficient dK₀<sup>n, s</sup> / dΧ.
- *
- * @param n n value
- * @param chitm1 χ<sup>-1</sup>
- * @return the coefficient dK₀<sup>n, s</sup> / dΧ
- */
- public T getDerivative(final int n, final T chitm1) {
- //Compute the potential slice
- int sliceNo = (n - s) / SLICE;
- if (sliceNo < numSlices) {
- //Compute the index within the slice
- final int indexInSlice = (n - s) % SLICE;
- //Check if a root must be returned
- if (indexInSlice <= 1) {
- return hansenDerivRoot[sliceNo][indexInSlice];
- }
- } else {
- //the value was a potential root for a slice, but that slice was not required
- //Decrease the slice number
- sliceNo--;
- }
- final PolynomialFunction[] v = mpvec[n];
- T ret = v[1].value(chitm1).multiply(hansenDerivRoot[sliceNo][1]);
- if (hansenDerivRoot[sliceNo][0].getReal() != 0) {
- ret = ret.add(v[0].value(chitm1).multiply(hansenDerivRoot[sliceNo][0]));
- }
- // Danielson 2.7.3-(7c)/Collins 4-254 and Petre's paper
- final PolynomialFunction[] v1 = mpvecDeriv[n];
- ret = ret.add(v1[1].value(chitm1).multiply(hansenRoot[sliceNo][1]));
- if (hansenRoot[sliceNo][0].getReal() != 0) {
- ret = ret.add(v1[0].value(chitm1).multiply(hansenRoot[sliceNo][0]));
- }
- return ret;
- }
- }