HansenThirdBodyLinear.java
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package org.orekit.propagation.semianalytical.dsst.utilities.hansen;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.util.FastMath;
/**
* 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
*/
public class HansenThirdBodyLinear {
/** 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 PolynomialFunction[][] mpvec;
/** The second vector of polynomials associated only to derivatives. */
private PolynomialFunction[][] mpvecDeriv;
/** The Hansen coefficients used as roots. */
private double[][] hansenRoot;
/** The derivatives of the Hansen coefficients used as roots. */
private double[][] hansenDerivRoot;
/** The number of slices needed to compute the coefficients. */
private int numSlices;
/** The maximum order of n indexes. */
private int nMax;
/** The index of the initial condition, Petre's paper. */
private int N0;
/** The s index. */
private int s;
/** (-1)<sup>s</sup> * (2*s + 1)!! / (s+1)! */
private double twosp1dfosp1f;
/** (-1)<sup>s</sup> * (2*s + 1)!! / (s+2)! */
private double twosp1dfosp2f;
/** (-1)<sup>s</sup> * 2 * (2*s + 1)!! / (s+2)! */
private double two2sp1dfosp2f;
/** (2*s + 3). */
private double twosp3;
/**
* Constructor.
*
* @param nMax the maximum value of n
* @param s the value of s
*/
public HansenThirdBodyLinear(final int nMax, final int s) {
// initialise fields
this.nMax = nMax;
N0 = s;
this.s = s;
// initialization of structures for stored data
mpvec = new PolynomialFunction[this.nMax + 1][];
mpvecDeriv = new PolynomialFunction[this.nMax + 1][];
//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[this.nMax + 1][];
mpvecDeriv = new PolynomialFunction[this.nMax + 1][];
this.numSlices = (int) FastMath.ceil(((double) nMax - s - 1) / SLICE);
hansenRoot = new double[numSlices][2];
hansenDerivRoot = new double[numSlices][2];
// Prepare the database of the associated polynomials
generatePolynomials();
}
/**
* Compute polynomial coefficient a.
*
* <p>
* It is used to generate the coefficient for K₀<sup>n-1, s</sup> when computing K₀<sup>n, s</sup>
* and the coefficient for dK₀<sup>n-1, s</sup> / dΧ when computing dK₀<sup>n, s</sup> / dΧ
* </p>
*
* <p>
* See Danielson 2.7.3-(7c) and Collins 4-254 and 4-257
* </p>
*
* @param n n value
* @return the polynomial
*/
private PolynomialFunction a(final int n) {
// from recurrence Danielson 2.7.3-(7c), Collins 4-254
final double r1 = 2 * n + 1;
final double r2 = n + 1;
return new PolynomialFunction(new double[] {
r1 / r2
});
}
/**
* Compute polynomial coefficient b.
*
* <p>
* It is used to generate the coefficient for K₀<sup>n-2, s</sup> when computing K₀<sup>n, s</sup>
* and the coefficient for dK₀<sup>n-2, s</sup> / dΧ when computing dK₀<sup>n, s</sup> / dΧ
* </p>
*
* <p>
* See Danielson 2.7.3-(7c) and Collins 4-254 and 4-257
* </p>
*
* @param n n value
* @return the polynomial
*/
private PolynomialFunction b(final int n) {
// from recurrence Danielson 2.7.3-(7c), Collins 4-254
final double r1 = (n + s) * (n - s);
final double r2 = n * (n + 1);
return new PolynomialFunction(new double[] {
0.0, 0.0, -r1 / r2
});
}
/**
* Compute polynomial coefficient d.
*
* <p>
* It is used to generate the coefficient for K₀<sup>n-2, s</sup> when computing dK₀<sup>n, s</sup> / dΧ
* </p>
*
* <p>
* See Danielson 2.7.3-(7c) and Collins 4-254 and 4-257
* </p>
*
* @param n n value
* @return the polynomial
*/
private PolynomialFunction d(final int n) {
// from Danielson 3.2-(3b)
final double r1 = 2 * (n + s) * (n - s);
final double r2 = n * (n + 1);
return new PolynomialFunction(new double[] {
0.0, 0.0, 0.0, r1 / r2
});
}
/**
* Generate the polynomials needed in the linear transformation.
*
* <p>
* See Petre's paper
* </p>
*/
private void generatePolynomials() {
int sliceCounter = 0;
// Initialization of the matrices for linear transformations
// The final configuration of these matrices are obtained by composition
// of linear transformations
// the matrix A for the polynomials associated
// to Hansen coefficients, Petre's pater
PolynomialFunctionMatrix A = HansenUtilities.buildIdentityMatrix2();
// the matrix D for the polynomials associated
// to derivatives, Petre's paper
final PolynomialFunctionMatrix B = HansenUtilities.buildZeroMatrix2();
PolynomialFunctionMatrix D = HansenUtilities.buildZeroMatrix2();
PolynomialFunctionMatrix E = HansenUtilities.buildIdentityMatrix2();
// The matrix that contains the coefficients at each step
final PolynomialFunctionMatrix a = HansenUtilities.buildZeroMatrix2();
a.setElem(0, 1, HansenUtilities.ONE);
// The generation process
for (int i = N0 + 2; i <= nMax; i++) {
// Collins 4-254 or Danielson 2.7.3-(7)
// Petre's paper
// The matrix of the current linear transformation is actualized
a.setMatrixLine(1, new PolynomialFunction[] {
b(i), a(i)
});
// composition of the linear transformations to calculate
// the polynomials associated to Hansen coefficients
A = A.multiply(a);
// store the polynomials associated to Hansen coefficients
this.mpvec[i] = A.getMatrixLine(1);
// composition of the linear transformations to calculate
// the polynomials associated to derivatives
// Danielson 3.2-(3b) and Petre's paper
D = D.multiply(a);
if (sliceCounter % SLICE != 0) {
a.setMatrixLine(1, new PolynomialFunction[] {
b(i - 1), a(i - 1)
});
E = E.multiply(a);
}
B.setElem(1, 0, d(i));
// F = E.prod(B);
D = D.add(E.multiply(B));
// store the polynomials associated to the derivatives
this.mpvecDeriv[i] = D.getMatrixLine(1);
if (++sliceCounter % SLICE == 0) {
// Re-Initialization of the matrices for linear transformations
// The final configuration of these matrices are obtained by composition
// of linear transformations
A = HansenUtilities.buildIdentityMatrix2();
D = HansenUtilities.buildZeroMatrix2();
E = HansenUtilities.buildIdentityMatrix2();
}
}
}
/**
* 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 double chitm1, final double chitm2, final double chitm3) {
this.hansenRoot[0][0] = this.twosp1dfosp1f;
this.hansenRoot[0][1] = this.twosp1dfosp2f * (this.twosp3 - chitm2);
this.hansenDerivRoot[0][0] = 0;
this.hansenDerivRoot[0][1] = this.two2sp1dfosp2f * chitm3;
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) * hansenDerivRoot[i - 1][1] +
mv[0].value(chitm1) * hansenDerivRoot[i - 1][0] +
sv[1].value(chitm1) * hansenRoot[i - 1][1] +
sv[0].value(chitm1) * hansenRoot[i - 1][0];
//Compute the root Hansen coefficients
hansenRoot[i][j] = mv[1].value(chitm1) * hansenRoot[i - 1][1] +
mv[0].value(chitm1) * 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 double getValue(final int n, final double 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];
double ret = v[1].value(chitm1) * hansenRoot[sliceNo][1];
if (hansenRoot[sliceNo][0] != 0) {
ret += v[0].value(chitm1) * 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 double getDerivative(final int n, final double 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];
double ret = v[1].value(chitm1) * hansenDerivRoot[sliceNo][1];
if (hansenDerivRoot[sliceNo][0] != 0) {
ret += v[0].value(chitm1) * hansenDerivRoot[sliceNo][0];
}
// Danielson 2.7.3-(7c)/Collins 4-254 and Petre's paper
final PolynomialFunction[] v1 = mpvecDeriv[n];
ret += v1[1].value(chitm1) * hansenRoot[sliceNo][1];
if (hansenRoot[sliceNo][0] != 0) {
ret += v1[0].value(chitm1) * hansenRoot[sliceNo][0];
}
return ret;
}
}