1 /* Copyright 2002-2025 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
19 import org.hipparchus.Field;
20 import org.hipparchus.CalculusFieldElement;
21 import org.hipparchus.analysis.polynomials.PolynomialFunction;
22 import org.hipparchus.util.FastMath;
23 import org.hipparchus.util.MathArrays;
24
25 /**
26 * Hansen coefficients K(t,n,s) for t=0 and n > 0.
27 * <p>
28 * Implements Collins 4-254 or Danielson 2.7.3-(7) for Hansen Coefficients and
29 * Danielson 3.2-(3) for derivatives. The recursions are transformed into
30 * composition of linear transformations to obtain the associated polynomials
31 * for coefficients and their derivatives - see Petre's paper
32 *
33 * @author Petre Bazavan
34 * @author Lucian Barbulescu
35 * @author Bryan Cazabonne
36 * @param <T> type of the field elements
37 */
38 public class FieldHansenThirdBodyLinear <T extends CalculusFieldElement<T>> {
39
40 /** The number of coefficients that will be computed with a set of roots. */
41 private static final int SLICE = 10;
42
43 /**
44 * The first vector of polynomials associated to Hansen coefficients and
45 * derivatives.
46 */
47 private final PolynomialFunction[][] mpvec;
48
49 /** The second vector of polynomials associated only to derivatives. */
50 private final PolynomialFunction[][] mpvecDeriv;
51
52 /** The Hansen coefficients used as roots. */
53 private final T[][] hansenRoot;
54
55 /** The derivatives of the Hansen coefficients used as roots. */
56 private final T[][] hansenDerivRoot;
57
58 /** The number of slices needed to compute the coefficients. */
59 private final int numSlices;
60
61 /** The s index. */
62 private final int s;
63
64 /** (-1)<sup>s</sup> * (2*s + 1)!! / (s+1)! */
65 private double twosp1dfosp1f;
66
67 /** (-1)<sup>s</sup> * (2*s + 1)!! / (s+2)! */
68 private final double twosp1dfosp2f;
69
70 /** (-1)<sup>s</sup> * 2 * (2*s + 1)!! / (s+2)! */
71 private final double two2sp1dfosp2f;
72
73 /** (2*s + 3). */
74 private final double twosp3;
75
76 /**
77 * Constructor.
78 *
79 * @param nMax the maximum value of n
80 * @param s the value of s
81 * @param field field used by default
82 */
83 public FieldHansenThirdBodyLinear(final int nMax, final int s, final Field<T> field) {
84 // initialise fields
85 this.s = s;
86
87 //Compute the fields that will be used to determine the initial values for the coefficients
88 this.twosp1dfosp1f = (s % 2 == 0) ? 1.0 : -1.0;
89 for (int i = s; i >= 1; i--) {
90 this.twosp1dfosp1f *= (2.0 * i + 1.0) / (i + 1.0);
91 }
92
93 this.twosp1dfosp2f = this.twosp1dfosp1f / (s + 2.);
94 this.twosp3 = 2 * s + 3;
95 this.two2sp1dfosp2f = 2 * this.twosp1dfosp2f;
96
97 // initialization of structures for stored data
98 mpvec = new PolynomialFunction[nMax + 1][];
99 mpvecDeriv = new PolynomialFunction[nMax + 1][];
100
101 this.numSlices = FastMath.max(1, (nMax - s + SLICE - 2) / SLICE);
102
103 hansenRoot = MathArrays.buildArray(field, numSlices, 2);
104 hansenDerivRoot = MathArrays.buildArray(field, numSlices, 2);
105
106 // Prepare the database of the associated polynomials
107 HansenUtilities.generateThirdBodyPolynomials(s, nMax, SLICE, s,
108 mpvec, mpvecDeriv);
109
110 }
111
112 /**
113 * Compute the initial values (see Collins, 4-255, 4-256 and 4.259)
114 * <p>
115 * K₀<sup>s, s</sup> = (-1)<sup>s</sup> * ( (2*s+1)!! / (s+1)! )
116 * </p>
117 * <p>
118 * K₀<sup>s+1, s</sup> = (-1)<sup>s</sup> * ( (2*s+1)!! / (s+2)!
119 * ) * (2*s+3 - χ<sup>-2</sup>)
120 * </p>
121 * <p>
122 * dK₀<sup>s+1, s</sup> / dχ = = (-1)<sup>s</sup> * 2 * (
123 * (2*s+1)!! / (s+2)! ) * χ<sup>-3</sup>
124 * </p>
125 * @param chitm1 sqrt(1 - e²)
126 * @param chitm2 sqrt(1 - e²)²
127 * @param chitm3 sqrt(1 - e²)³
128 */
129 public void computeInitValues(final T chitm1, final T chitm2, final T chitm3) {
130 final Field<T> field = chitm2.getField();
131 final T zero = field.getZero();
132 this.hansenRoot[0][0] = zero.newInstance(twosp1dfosp1f);
133 this.hansenRoot[0][1] = (chitm2.negate().add(this.twosp3)).multiply(this.twosp1dfosp2f);
134 this.hansenDerivRoot[0][0] = zero;
135 this.hansenDerivRoot[0][1] = chitm3.multiply(two2sp1dfosp2f);
136
137 for (int i = 1; i < numSlices; i++) {
138 for (int j = 0; j < 2; j++) {
139 // Get the required polynomials
140 final PolynomialFunction[] mv = mpvec[s + (i * SLICE) + j];
141 final PolynomialFunction[] sv = mpvecDeriv[s + (i * SLICE) + j];
142
143 //Compute the root derivatives
144 hansenDerivRoot[i][j] = mv[1].value(chitm1).multiply(hansenDerivRoot[i - 1][1]).
145 add(mv[0].value(chitm1).multiply(hansenDerivRoot[i - 1][0])).
146 add(sv[1].value(chitm1).multiply(hansenRoot[i - 1][1])).
147 add(sv[0].value(chitm1).multiply(hansenRoot[i - 1][0]));
148
149 //Compute the root Hansen coefficients
150 hansenRoot[i][j] = mv[1].value(chitm1).multiply(hansenRoot[i - 1][1]).
151 add(mv[0].value(chitm1).multiply(hansenRoot[i - 1][0]));
152 }
153 }
154 }
155
156 /**
157 * Compute the value of the Hansen coefficient K₀<sup>n, s</sup>.
158 *
159 * @param n n value
160 * @param chitm1 χ<sup>-1</sup>
161 * @return the coefficient K₀<sup>n, s</sup>
162 */
163 public T getValue(final int n, final T chitm1) {
164 //Compute the potential slice
165 int sliceNo = (n - s) / SLICE;
166 if (sliceNo < numSlices) {
167 //Compute the index within the slice
168 final int indexInSlice = (n - s) % SLICE;
169
170 //Check if a root must be returned
171 if (indexInSlice <= 1) {
172 return hansenRoot[sliceNo][indexInSlice];
173 }
174 } else {
175 //the value was a potential root for a slice, but that slice was not required
176 //Decrease the slice number
177 sliceNo--;
178 }
179
180 // Danielson 2.7.3-(6c)/Collins 4-242 and Petre's paper
181 final PolynomialFunction[] v = mpvec[n];
182 T ret = v[1].value(chitm1).multiply(hansenRoot[sliceNo][1]);
183 if (hansenRoot[sliceNo][0].getReal() != 0) {
184 ret = ret.add(v[0].value(chitm1).multiply(hansenRoot[sliceNo][0]));
185 }
186
187 return ret;
188
189 }
190
191 /**
192 * Compute the value of the Hansen coefficient dK₀<sup>n, s</sup> / dΧ.
193 *
194 * @param n n value
195 * @param chitm1 χ<sup>-1</sup>
196 * @return the coefficient dK₀<sup>n, s</sup> / dΧ
197 */
198 public T getDerivative(final int n, final T chitm1) {
199 //Compute the potential slice
200 int sliceNo = (n - s) / SLICE;
201 if (sliceNo < numSlices) {
202 //Compute the index within the slice
203 final int indexInSlice = (n - s) % SLICE;
204
205 //Check if a root must be returned
206 if (indexInSlice <= 1) {
207 return hansenDerivRoot[sliceNo][indexInSlice];
208 }
209 } else {
210 //the value was a potential root for a slice, but that slice was not required
211 //Decrease the slice number
212 sliceNo--;
213 }
214
215 final PolynomialFunction[] v = mpvec[n];
216 T ret = v[1].value(chitm1).multiply(hansenDerivRoot[sliceNo][1]);
217 if (hansenDerivRoot[sliceNo][0].getReal() != 0) {
218 ret = ret.add(v[0].value(chitm1).multiply(hansenDerivRoot[sliceNo][0]));
219 }
220
221 // Danielson 2.7.3-(7c)/Collins 4-254 and Petre's paper
222 final PolynomialFunction[] v1 = mpvecDeriv[n];
223 ret = ret.add(v1[1].value(chitm1).multiply(hansenRoot[sliceNo][1]));
224 if (hansenRoot[sliceNo][0].getReal() != 0) {
225 ret = ret.add(v1[0].value(chitm1).multiply(hansenRoot[sliceNo][0]));
226 }
227 return ret;
228
229 }
230
231 }