HansenThirdBodyLinear.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;

  19. import org.hipparchus.analysis.polynomials.PolynomialFunction;
  20. import org.hipparchus.util.FastMath;

  22. /**
  23.  * Hansen coefficients K(t,n,s) for t=0 and n > 0.
  24.  * <p>
  25.  * Implements Collins 4-254 or Danielson 2.7.3-(7) for Hansen Coefficients and
  26.  * Danielson 3.2-(3) for derivatives. The recursions are transformed into
  27.  * composition of linear transformations to obtain the associated polynomials
  28.  * for coefficients and their derivatives - see Petre's paper
  29.  *
  30.  * @author Petre Bazavan
  31.  * @author Lucian Barbulescu
  32.  */
  33. public class HansenThirdBodyLinear {

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

  38.     /**
  39.      * The first vector of polynomials associated to Hansen coefficients and
  40.      * derivatives.
  41.      */
  42.     private final PolynomialFunction[][] mpvec;

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

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

  50.     /** The derivatives of the Hansen coefficients used as roots. */
  51.     private final double[][] hansenDerivRoot;

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

  56.     /** The s index. */
  57.     private final int s;

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

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

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

  68.     /** (2*s + 3). */
  69.     private final double twosp3;

  71.     /**
  72.      * Constructor.
  73.      *
  74.      * @param nMax the maximum value of n
  75.      * @param s the value of s
  76.      */
  77.     public HansenThirdBodyLinear(final int nMax, final int s) {

  79.         // initialise fields
  80.         this.s = s;

  82.         //Compute the fields that will be used to determine the initial values for the coefficients
  83.         this.twosp1dfosp1f = (s % 2 == 0) ? 1.0 : -1.0;
  84.         for (int i = s; i >= 1; i--) {
  85.             this.twosp1dfosp1f *= (2.0 * i + 1.0) / (i + 1.0);
  86.         }

  88.         this.twosp1dfosp2f = this.twosp1dfosp1f / (s + 2.);
  89.         this.twosp3 = 2 * s + 3;
  90.         this.two2sp1dfosp2f = 2 * this.twosp1dfosp2f;

  92.         // initialization of structures for stored data
  93.         mpvec = new PolynomialFunction[nMax + 1][];
  94.         mpvecDeriv = new PolynomialFunction[nMax + 1][];

  96.         this.numSlices  = FastMath.max(1, (nMax - s + SLICE - 2) / SLICE);
  97.         hansenRoot      = new double[numSlices][2];
  98.         hansenDerivRoot = new double[numSlices][2];

  100.         // Prepare the database of the associated polynomials
  101.         HansenUtilities.generateThirdBodyPolynomials(s, nMax, SLICE, s,
  102.                                                      mpvec, mpvecDeriv);

  104.     }

  106.     /**
  107.      * Compute the initial values (see Collins, 4-255, 4-256 and 4.259)
  108.      * <p>
  109.      * K₀<sup>s, s</sup> = (-1)<sup>s</sup> * ( (2*s+1)!! / (s+1)! )
  110.      * </p>
  111.      * <p>
  112.      * K₀<sup>s+1, s</sup> = (-1)<sup>s</sup> * ( (2*s+1)!! / (s+2)!
  113.      * ) * (2*s+3 - χ<sup>-2</sup>)
  114.      * </p>
  115.      * <p>
  116.      * dK₀<sup>s+1, s</sup> / dχ = = (-1)<sup>s</sup> * 2 * (
  117.      * (2*s+1)!! / (s+2)! ) * χ<sup>-3</sup>
  118.      * </p>
  119.      * @param chitm1 sqrt(1 - e²)
  120.      * @param chitm2 sqrt(1 - e²)²
  121.      * @param chitm3 sqrt(1 - e²)³
  122.      */
  123.     public void computeInitValues(final double chitm1, final double chitm2, final double chitm3) {
  124.         this.hansenRoot[0][0] = this.twosp1dfosp1f;
  125.         this.hansenRoot[0][1] = this.twosp1dfosp2f * (this.twosp3 - chitm2);
  126.         this.hansenDerivRoot[0][0] = 0;
  127.         this.hansenDerivRoot[0][1] = this.two2sp1dfosp2f * chitm3;

  129.         for (int i = 1; i < numSlices; i++) {
  130.             for (int j = 0; j < 2; j++) {
  131.                 // Get the required polynomials
  132.                 final PolynomialFunction[] mv = mpvec[s + (i * SLICE) + j];
  133.                 final PolynomialFunction[] sv = mpvecDeriv[s + (i * SLICE) + j];

  135.                 //Compute the root derivatives
  136.                 hansenDerivRoot[i][j] = mv[1].value(chitm1) * hansenDerivRoot[i - 1][1] +
  137.                                         mv[0].value(chitm1) * hansenDerivRoot[i - 1][0] +
  138.                                         sv[1].value(chitm1) * hansenRoot[i - 1][1] +
  139.                                         sv[0].value(chitm1) * hansenRoot[i - 1][0];

  141.                 //Compute the root Hansen coefficients
  142.                 hansenRoot[i][j] =  mv[1].value(chitm1) * hansenRoot[i - 1][1] +
  143.                                     mv[0].value(chitm1) * hansenRoot[i - 1][0];
  144.             }
  145.         }
  146.     }

  148.     /**
  149.      * Compute the value of the Hansen coefficient K₀<sup>n, s</sup>.
  150.      *
  151.      * @param n n value
  152.      * @param chitm1 χ<sup>-1</sup>
  153.      * @return the coefficient K₀<sup>n, s</sup>
  154.      */
  155.     public double getValue(final int n, final double chitm1) {
  156.         //Compute the potential slice
  157.         int sliceNo = (n - s) / SLICE;
  158.         if (sliceNo < numSlices) {
  159.             //Compute the index within the slice
  160.             final int indexInSlice = (n - s) % SLICE;

  162.             //Check if a root must be returned
  163.             if (indexInSlice <= 1) {
  164.                 return hansenRoot[sliceNo][indexInSlice];
  165.             }
  166.         } else {
  167.             //the value was a potential root for a slice, but that slice was not required
  168.             //Decrease the slice number
  169.             sliceNo--;
  170.         }

  172.         // Danielson 2.7.3-(6c)/Collins 4-242 and Petre's paper
  173.         final PolynomialFunction[] v = mpvec[n];
  174.         double ret = v[1].value(chitm1) * hansenRoot[sliceNo][1];
  175.         if (hansenRoot[sliceNo][0] != 0) {
  176.             ret += v[0].value(chitm1) * hansenRoot[sliceNo][0];
  177.         }

  179.         return ret;

  181.     }

  183.     /**
  184.      * Compute the value of the Hansen coefficient dK₀<sup>n, s</sup> / d&Chi;.
  185.      *
  186.      * @param n n value
  187.      * @param chitm1 χ<sup>-1</sup>
  188.      * @return the coefficient dK₀<sup>n, s</sup> / d&Chi;
  189.      */
  190.     public double getDerivative(final int n, final double chitm1) {
  191.         //Compute the potential slice
  192.         int sliceNo = (n - s) / SLICE;
  193.         if (sliceNo < numSlices) {
  194.             //Compute the index within the slice
  195.             final int indexInSlice = (n - s) % SLICE;

  197.             //Check if a root must be returned
  198.             if (indexInSlice <= 1) {
  199.                 return hansenDerivRoot[sliceNo][indexInSlice];
  200.             }
  201.         } else {
  202.             //the value was a potential root for a slice, but that slice was not required
  203.             //Decrease the slice number
  204.             sliceNo--;
  205.         }

  207.         final PolynomialFunction[] v = mpvec[n];
  208.         double ret = v[1].value(chitm1) * hansenDerivRoot[sliceNo][1];
  209.         if (hansenDerivRoot[sliceNo][0] != 0) {
  210.             ret += v[0].value(chitm1) * hansenDerivRoot[sliceNo][0];
  211.         }

  213.         // Danielson 2.7.3-(7c)/Collins 4-254 and Petre's paper
  214.         final PolynomialFunction[] v1 = mpvecDeriv[n];
  215.         ret += v1[1].value(chitm1) * hansenRoot[sliceNo][1];
  216.         if (hansenRoot[sliceNo][0] != 0) {
  217.             ret += v1[0].value(chitm1) * hansenRoot[sliceNo][0];
  218.         }
  219.         return ret;

  221.     }

  223. }
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