FieldHansenThirdBodyLinear.java

  1. /* Copyright 2002-2024 CS GROUP
  2.  * Licensed to CS GROUP (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.semianalytical.dsst.utilities.hansen;

  18. import org.hipparchus.Field;
  19. import org.hipparchus.CalculusFieldElement;
  20. import org.hipparchus.analysis.polynomials.PolynomialFunction;
  21. import org.hipparchus.util.FastMath;
  22. import org.hipparchus.util.MathArrays;

  23. /**
  24.  * Hansen coefficients K(t,n,s) for t=0 and n > 0.
  25.  * <p>
  26.  * Implements Collins 4-254 or Danielson 2.7.3-(7) for Hansen Coefficients and
  27.  * Danielson 3.2-(3) for derivatives. The recursions are transformed into
  28.  * composition of linear transformations to obtain the associated polynomials
  29.  * for coefficients and their derivatives - see Petre's paper
  30.  *
  31.  * @author Petre Bazavan
  32.  * @author Lucian Barbulescu
  33.  * @author Bryan Cazabonne
  34.  * @param <T> type of the field elements
  35.  */
  36. public class FieldHansenThirdBodyLinear <T extends CalculusFieldElement<T>> {

  37.     /** The number of coefficients that will be computed with a set of roots. */
  38.     private  static final int SLICE = 10;

  39.     /**
  40.      * The first vector of polynomials associated to Hansen coefficients and
  41.      * derivatives.
  42.      */
  43.     private final PolynomialFunction[][] mpvec;

  44.     /** The second vector of polynomials associated only to derivatives. */
  45.     private final PolynomialFunction[][] mpvecDeriv;

  46.     /** The Hansen coefficients used as roots. */
  47.     private final T[][] hansenRoot;

  48.     /** The derivatives of the Hansen coefficients used as roots. */
  49.     private final T[][] hansenDerivRoot;

  50.     /** The number of slices needed to compute the coefficients. */
  51.     private final int numSlices;

  52.     /** The s index. */
  53.     private final int s;

  54.     /** (-1)<sup>s</sup> * (2*s + 1)!! / (s+1)!  */
  55.     private double twosp1dfosp1f;

  56.     /** (-1)<sup>s</sup> * (2*s + 1)!! / (s+2)!  */
  57.     private final double twosp1dfosp2f;

  58.     /** (-1)<sup>s</sup> * 2 * (2*s + 1)!! / (s+2)!  */
  59.     private final double two2sp1dfosp2f;

  60.     /** (2*s + 3). */
  61.     private final double twosp3;

  62.     /**
  63.      * Constructor.
  64.      *
  65.      * @param nMax the maximum value of n
  66.      * @param s the value of s
  67.      * @param field field used by default
  68.      */
  69.     public FieldHansenThirdBodyLinear(final int nMax, final int s, final Field<T> field) {
  70.         // initialise fields
  71.         this.s = s;

  72.         //Compute the fields that will be used to determine the initial values for the coefficients
  73.         this.twosp1dfosp1f = (s % 2 == 0) ? 1.0 : -1.0;
  74.         for (int i = s; i >= 1; i--) {
  75.             this.twosp1dfosp1f *= (2.0 * i + 1.0) / (i + 1.0);
  76.         }

  77.         this.twosp1dfosp2f = this.twosp1dfosp1f / (s + 2.);
  78.         this.twosp3 = 2 * s + 3;
  79.         this.two2sp1dfosp2f = 2 * this.twosp1dfosp2f;

  80.         // initialization of structures for stored data
  81.         mpvec = new PolynomialFunction[nMax + 1][];
  82.         mpvecDeriv = new PolynomialFunction[nMax + 1][];

  83.         this.numSlices  = FastMath.max(1, (nMax - s + SLICE - 2) / SLICE);

  84.         hansenRoot      = MathArrays.buildArray(field, numSlices, 2);
  85.         hansenDerivRoot = MathArrays.buildArray(field, numSlices, 2);

  86.         // Prepare the database of the associated polynomials
  87.         HansenUtilities.generateThirdBodyPolynomials(s, nMax, SLICE, s,
  88.                                                      mpvec, mpvecDeriv);

  89.     }

  90.     /**
  91.      * Compute the initial values (see Collins, 4-255, 4-256 and 4.259)
  92.      * <p>
  93.      * K₀<sup>s, s</sup> = (-1)<sup>s</sup> * ( (2*s+1)!! / (s+1)! )
  94.      * </p>
  95.      * <p>
  96.      * K₀<sup>s+1, s</sup> = (-1)<sup>s</sup> * ( (2*s+1)!! / (s+2)!
  97.      * ) * (2*s+3 - χ<sup>-2</sup>)
  98.      * </p>
  99.      * <p>
  100.      * dK₀<sup>s+1, s</sup> / dχ = = (-1)<sup>s</sup> * 2 * (
  101.      * (2*s+1)!! / (s+2)! ) * χ<sup>-3</sup>
  102.      * </p>
  103.      * @param chitm1 sqrt(1 - e²)
  104.      * @param chitm2 sqrt(1 - e²)²
  105.      * @param chitm3 sqrt(1 - e²)³
  106.      */
  107.     public void computeInitValues(final T chitm1, final T chitm2, final T chitm3) {
  108.         final Field<T> field = chitm2.getField();
  109.         final T zero = field.getZero();
  110.         this.hansenRoot[0][0] = zero.newInstance(twosp1dfosp1f);
  111.         this.hansenRoot[0][1] = (chitm2.negate().add(this.twosp3)).multiply(this.twosp1dfosp2f);
  112.         this.hansenDerivRoot[0][0] = zero;
  113.         this.hansenDerivRoot[0][1] = chitm3.multiply(two2sp1dfosp2f);

  114.         for (int i = 1; i < numSlices; i++) {
  115.             for (int j = 0; j < 2; j++) {
  116.                 // Get the required polynomials
  117.                 final PolynomialFunction[] mv = mpvec[s + (i * SLICE) + j];
  118.                 final PolynomialFunction[] sv = mpvecDeriv[s + (i * SLICE) + j];

  119.                 //Compute the root derivatives
  120.                 hansenDerivRoot[i][j] = mv[1].value(chitm1).multiply(hansenDerivRoot[i - 1][1]).
  121.                                     add(mv[0].value(chitm1).multiply(hansenDerivRoot[i - 1][0])).
  122.                                     add(sv[1].value(chitm1).multiply(hansenRoot[i - 1][1])).
  123.                                     add(sv[0].value(chitm1).multiply(hansenRoot[i - 1][0]));

  124.                 //Compute the root Hansen coefficients
  125.                 hansenRoot[i][j] =  mv[1].value(chitm1).multiply(hansenRoot[i - 1][1]).
  126.                                 add(mv[0].value(chitm1).multiply(hansenRoot[i - 1][0]));
  127.             }
  128.         }
  129.     }

  130.     /**
  131.      * Compute the value of the Hansen coefficient K₀<sup>n, s</sup>.
  132.      *
  133.      * @param n n value
  134.      * @param chitm1 χ<sup>-1</sup>
  135.      * @return the coefficient K₀<sup>n, s</sup>
  136.      */
  137.     public T getValue(final int n, final T chitm1) {
  138.         //Compute the potential slice
  139.         int sliceNo = (n - s) / SLICE;
  140.         if (sliceNo < numSlices) {
  141.             //Compute the index within the slice
  142.             final int indexInSlice = (n - s) % SLICE;

  143.             //Check if a root must be returned
  144.             if (indexInSlice <= 1) {
  145.                 return hansenRoot[sliceNo][indexInSlice];
  146.             }
  147.         } else {
  148.             //the value was a potential root for a slice, but that slice was not required
  149.             //Decrease the slice number
  150.             sliceNo--;
  151.         }

  152.         // Danielson 2.7.3-(6c)/Collins 4-242 and Petre's paper
  153.         final PolynomialFunction[] v = mpvec[n];
  154.         T ret = v[1].value(chitm1).multiply(hansenRoot[sliceNo][1]);
  155.         if (hansenRoot[sliceNo][0].getReal() != 0) {
  156.             ret = ret.add(v[0].value(chitm1).multiply(hansenRoot[sliceNo][0]));
  157.         }

  158.         return ret;

  159.     }

  160.     /**
  161.      * Compute the value of the Hansen coefficient dK₀<sup>n, s</sup> / d&Chi;.
  162.      *
  163.      * @param n n value
  164.      * @param chitm1 χ<sup>-1</sup>
  165.      * @return the coefficient dK₀<sup>n, s</sup> / d&Chi;
  166.      */
  167.     public T getDerivative(final int n, final T chitm1) {
  168.         //Compute the potential slice
  169.         int sliceNo = (n - s) / SLICE;
  170.         if (sliceNo < numSlices) {
  171.             //Compute the index within the slice
  172.             final int indexInSlice = (n - s) % SLICE;

  173.             //Check if a root must be returned
  174.             if (indexInSlice <= 1) {
  175.                 return hansenDerivRoot[sliceNo][indexInSlice];
  176.             }
  177.         } else {
  178.             //the value was a potential root for a slice, but that slice was not required
  179.             //Decrease the slice number
  180.             sliceNo--;
  181.         }

  182.         final PolynomialFunction[] v = mpvec[n];
  183.         T ret = v[1].value(chitm1).multiply(hansenDerivRoot[sliceNo][1]);
  184.         if (hansenDerivRoot[sliceNo][0].getReal() != 0) {
  185.             ret = ret.add(v[0].value(chitm1).multiply(hansenDerivRoot[sliceNo][0]));
  186.         }

  187.         // Danielson 2.7.3-(7c)/Collins 4-254 and Petre's paper
  188.         final PolynomialFunction[] v1 = mpvecDeriv[n];
  189.         ret = ret.add(v1[1].value(chitm1).multiply(hansenRoot[sliceNo][1]));
  190.         if (hansenRoot[sliceNo][0].getReal() != 0) {
  191.             ret = ret.add(v1[0].value(chitm1).multiply(hansenRoot[sliceNo][0]));
  192.         }
  193.         return ret;

  194.     }

  195. }