/**
* Simple constructor.
*
* <p>The {@code applyBefore} parameter is mainly used when the differential effect is associated
* with a maneuver. In this case, the parameter must be set to {@code false}.
*
* @param orbit0 original orbit at reference date
* @param orbit1 shifted orbit at reference date
* @param applyBefore if true, effect is applied both before and after reference date, if false it
* is only applied after reference date
* @param gravityField gravity field to use
* @exception OrekitException if gravity field does not contain J2 coefficient
*/
public J2DifferentialEffect(
final Orbit orbit0,
final Orbit orbit1,
final boolean applyBefore,
final UnnormalizedSphericalHarmonicsProvider gravityField)
throws OrekitException {
this(
orbit0,
orbit1,
applyBefore,
gravityField.getAe(),
gravityField.getMu(),
-gravityField.onDate(orbit0.getDate()).getUnnormalizedCnm(2, 0));
}
/**
* Simple constructor.
*
* <p>The {@code applyBefore} parameter is mainly used when the differential effect is associated
* with a maneuver. In this case, the parameter must be set to {@code false}.
*
* @param original original state at reference date
* @param directEffect direct effect changing the orbit
* @param applyBefore if true, effect is applied both before and after reference date, if false it
* is only applied after reference date
* @param gravityField gravity field to use
* @exception OrekitException if gravity field does not contain J2 coefficient
*/
public J2DifferentialEffect(
final SpacecraftState original,
final AdapterPropagator.DifferentialEffect directEffect,
final boolean applyBefore,
final UnnormalizedSphericalHarmonicsProvider gravityField)
throws OrekitException {
this(
original,
directEffect,
applyBefore,
gravityField.getAe(),
gravityField.getMu(),
-gravityField.onDate(original.getDate()).getUnnormalizedCnm(2, 0));
}
/**
* Single constructor.
*
* @param centralBodyFrame rotating body frame
* @param centralBodyRotationRate central body rotation rate (rad/s)
* @param provider provider for spherical harmonics
* @param mDailiesOnly if true only M-dailies tesseral harmonics are taken into account for short
* periodics
*/
TesseralContribution(
final Frame centralBodyFrame,
final double centralBodyRotationRate,
final UnnormalizedSphericalHarmonicsProvider provider,
final boolean mDailiesOnly) {
// Central body rotating frame
this.bodyFrame = centralBodyFrame;
// Save the rotation rate
this.centralBodyRotationRate = centralBodyRotationRate;
// Central body rotation period in seconds
this.bodyPeriod = MathUtils.TWO_PI / centralBodyRotationRate;
// Provider for spherical harmonics
this.provider = provider;
this.maxDegree = provider.getMaxDegree();
this.maxOrder = provider.getMaxOrder();
// set the maximum degree order for short periodics
this.maxDegreeTesseralSP = FastMath.min(maxDegree, MAX_DEGREE_TESSERAL_SP);
this.maxDegreeMdailyTesseralSP = FastMath.min(maxDegree, MAX_DEGREE_MDAILY_TESSERAL_SP);
this.maxOrderTesseralSP = FastMath.min(maxOrder, MAX_ORDER_TESSERAL_SP);
this.maxOrderMdailyTesseralSP = FastMath.min(maxOrder, MAX_ORDER_MDAILY_TESSERAL_SP);
// set the maximum value for eccentricity power
this.maxEccPowTesseralSP = MAX_ECCPOWER_SP;
this.maxEccPowMdailyTesseralSP = FastMath.min(maxDegreeMdailyTesseralSP - 2, MAX_ECCPOWER_SP);
this.jMax = FastMath.min(MAXJ, maxDegreeTesseralSP + maxEccPowTesseralSP);
// m-daylies only
this.mDailiesOnly = mDailiesOnly;
// Initialize default values
this.resOrders = new ArrayList<Integer>();
this.nonResOrders = new TreeMap<Integer, List<Integer>>();
this.maxEccPow = 0;
this.maxHansen = 0;
// Factorials computation
final int maxFact = 2 * maxDegree + 1;
this.fact = new double[maxFact];
fact[0] = 1;
for (int i = 1; i < maxFact; i++) {
fact[i] = i * fact[i - 1];
}
}
/**
* Compute the n-SUM for potential derivatives components.
*
* @param date current date
* @param j resonant index <i>j</i>
* @param m resonant order <i>m</i>
* @param s d'Alembert characteristic <i>s</i>
* @param maxN maximum possible value for <i>n</i> index
* @param roaPow powers of R/a up to degree <i>n</i>
* @param ghMSJ G<sup>j</sup><sub>m,s</sub> and H<sup>j</sup><sub>m,s</sub> polynomials
* @param gammaMNS Γ<sup>m</sup><sub>n,s</sub>(γ) function
* @return Components of U<sub>n</sub> derivatives for fixed j, m, s
* @throws OrekitException if some error occurred
*/
private double[][] computeNSum(
final AbsoluteDate date,
final int j,
final int m,
final int s,
final int maxN,
final double[] roaPow,
final GHmsjPolynomials ghMSJ,
final GammaMnsFunction gammaMNS)
throws OrekitException {
// spherical harmonics
final UnnormalizedSphericalHarmonics harmonics = provider.onDate(date);
// Potential derivatives components
double dUdaCos = 0.;
double dUdaSin = 0.;
double dUdhCos = 0.;
double dUdhSin = 0.;
double dUdkCos = 0.;
double dUdkSin = 0.;
double dUdlCos = 0.;
double dUdlSin = 0.;
double dUdAlCos = 0.;
double dUdAlSin = 0.;
double dUdBeCos = 0.;
double dUdBeSin = 0.;
double dUdGaCos = 0.;
double dUdGaSin = 0.;
// I^m
final int Im = I > 0 ? 1 : (m % 2 == 0 ? 1 : -1);
// jacobi v, w, indices from 2.7.1-(15)
final int v = FastMath.abs(m - s);
final int w = FastMath.abs(m + s);
// Initialise lower degree nmin = (Max(2, m, |s|)) for summation over n
final int nmin = FastMath.max(FastMath.max(2, m), FastMath.abs(s));
// Get the corresponding Hansen object
final int sIndex = maxDegree + (j < 0 ? -s : s);
final int jIndex = FastMath.abs(j);
final HansenTesseralLinear hans = this.hansenObjects[sIndex][jIndex];
// n-SUM from nmin to N
for (int n = nmin; n <= maxN; n++) {
// If (n - s) is odd, the contribution is null because of Vmns
if ((n - s) % 2 == 0) {
// Vmns coefficient
final double fns = fact[n + FastMath.abs(s)];
final double vMNS = CoefficientsFactory.getVmns(m, n, s, fns, fact[n - m]);
// Inclination function Gamma and derivative
final double gaMNS = gammaMNS.getValue(m, n, s);
final double dGaMNS = gammaMNS.getDerivative(m, n, s);
// Hansen kernel value and derivative
final double kJNS = hans.getValue(-n - 1, chi);
final double dkJNS = hans.getDerivative(-n - 1, chi);
// Gjms, Hjms polynomials and derivatives
final double gMSJ = ghMSJ.getGmsj(m, s, j);
final double hMSJ = ghMSJ.getHmsj(m, s, j);
final double dGdh = ghMSJ.getdGmsdh(m, s, j);
final double dGdk = ghMSJ.getdGmsdk(m, s, j);
final double dGdA = ghMSJ.getdGmsdAlpha(m, s, j);
final double dGdB = ghMSJ.getdGmsdBeta(m, s, j);
final double dHdh = ghMSJ.getdHmsdh(m, s, j);
final double dHdk = ghMSJ.getdHmsdk(m, s, j);
final double dHdA = ghMSJ.getdHmsdAlpha(m, s, j);
final double dHdB = ghMSJ.getdHmsdBeta(m, s, j);
// Jacobi l-index from 2.7.1-(15)
final int l = FastMath.min(n - m, n - FastMath.abs(s));
// Jacobi polynomial and derivative
final DerivativeStructure jacobi =
JacobiPolynomials.getValue(l, v, w, new DerivativeStructure(1, 1, 0, gamma));
// Geopotential coefficients
final double cnm = harmonics.getUnnormalizedCnm(n, m);
final double snm = harmonics.getUnnormalizedSnm(n, m);
// Common factors from expansion of equations 3.3-4
final double cf_0 = roaPow[n] * Im * vMNS;
final double cf_1 = cf_0 * gaMNS * jacobi.getValue();
final double cf_2 = cf_1 * kJNS;
final double gcPhs = gMSJ * cnm + hMSJ * snm;
final double gsMhc = gMSJ * snm - hMSJ * cnm;
final double dKgcPhsx2 = 2. * dkJNS * gcPhs;
final double dKgsMhcx2 = 2. * dkJNS * gsMhc;
final double dUdaCoef = (n + 1) * cf_2;
final double dUdlCoef = j * cf_2;
final double dUdGaCoef =
cf_0 * kJNS * (jacobi.getValue() * dGaMNS + gaMNS * jacobi.getPartialDerivative(1));
// dU / da components
dUdaCos += dUdaCoef * gcPhs;
dUdaSin += dUdaCoef * gsMhc;
// dU / dh components
dUdhCos += cf_1 * (kJNS * (cnm * dGdh + snm * dHdh) + h * dKgcPhsx2);
dUdhSin += cf_1 * (kJNS * (snm * dGdh - cnm * dHdh) + h * dKgsMhcx2);
// dU / dk components
dUdkCos += cf_1 * (kJNS * (cnm * dGdk + snm * dHdk) + k * dKgcPhsx2);
dUdkSin += cf_1 * (kJNS * (snm * dGdk - cnm * dHdk) + k * dKgsMhcx2);
// dU / dLambda components
dUdlCos += dUdlCoef * gsMhc;
dUdlSin += -dUdlCoef * gcPhs;
// dU / alpha components
dUdAlCos += cf_2 * (dGdA * cnm + dHdA * snm);
dUdAlSin += cf_2 * (dGdA * snm - dHdA * cnm);
// dU / dBeta components
dUdBeCos += cf_2 * (dGdB * cnm + dHdB * snm);
dUdBeSin += cf_2 * (dGdB * snm - dHdB * cnm);
// dU / dGamma components
dUdGaCos += dUdGaCoef * gcPhs;
dUdGaSin += dUdGaCoef * gsMhc;
}
}
return new double[][] {
{dUdaCos, dUdaSin},
{dUdhCos, dUdhSin},
{dUdkCos, dUdkSin},
{dUdlCos, dUdlSin},
{dUdAlCos, dUdAlSin},
{dUdBeCos, dUdBeSin},
{dUdGaCos, dUdGaSin}
};
}
/** {@inheritDoc} */
@Override
public double[] getShortPeriodicVariations(final AbsoluteDate date, final double[] meanElements)
throws OrekitException {
// Initialise the short periodic variations
final double[] shortPeriodicVariation = new double[] {0., 0., 0., 0., 0., 0.};
// Compute only if there is at least one non-resonant tesseral or
// only the m-daily tesseral should be taken into account
if (!nonResOrders.isEmpty() || mDailiesOnly) {
// Build an Orbit object from the mean elements
final Orbit meanOrbit =
OrbitType.EQUINOCTIAL.mapArrayToOrbit(
meanElements, PositionAngle.MEAN, date, provider.getMu(), this.frame);
// Build an auxiliary object
final AuxiliaryElements aux = new AuxiliaryElements(meanOrbit, I);
// Central body rotation angle from equation 2.7.1-(3)(4).
final Transform t = bodyFrame.getTransformTo(aux.getFrame(), aux.getDate());
final Vector3D xB = t.transformVector(Vector3D.PLUS_I);
final Vector3D yB = t.transformVector(Vector3D.PLUS_J);
final double currentTheta =
FastMath.atan2(
-f.dotProduct(yB) + I * g.dotProduct(xB), f.dotProduct(xB) + I * g.dotProduct(yB));
// Add the m-daily contribution
for (int m = 1; m <= maxOrderMdailyTesseralSP; m++) {
// Phase angle
final double jlMmt = -m * currentTheta;
final double sinPhi = FastMath.sin(jlMmt);
final double cosPhi = FastMath.cos(jlMmt);
// compute contribution for each element
for (int i = 0; i < 6; i++) {
shortPeriodicVariation[i] +=
tesseralSPCoefs.getCijm(i, 0, m, date) * cosPhi
+ tesseralSPCoefs.getSijm(i, 0, m, date) * sinPhi;
}
}
// loop through all non-resonant (j,m) pairs
for (final Map.Entry<Integer, List<Integer>> entry : nonResOrders.entrySet()) {
final int m = entry.getKey();
final List<Integer> listJ = entry.getValue();
for (int j : listJ) {
// Phase angle
final double jlMmt = j * meanElements[5] - m * currentTheta;
final double sinPhi = FastMath.sin(jlMmt);
final double cosPhi = FastMath.cos(jlMmt);
// compute contribution for each element
for (int i = 0; i < 6; i++) {
shortPeriodicVariation[i] +=
tesseralSPCoefs.getCijm(i, j, m, date) * cosPhi
+ tesseralSPCoefs.getSijm(i, j, m, date) * sinPhi;
}
}
}
}
return shortPeriodicVariation;
}
/** {@inheritDoc} */
@Override
public void initializeStep(final AuxiliaryElements aux) throws OrekitException {
// Equinoctial elements
a = aux.getSma();
k = aux.getK();
h = aux.getH();
q = aux.getQ();
p = aux.getP();
lm = aux.getLM();
// Eccentricity
ecc = aux.getEcc();
e2 = ecc * ecc;
// Retrograde factor
I = aux.getRetrogradeFactor();
// Equinoctial frame vectors
f = aux.getVectorF();
g = aux.getVectorG();
// Central body rotation angle from equation 2.7.1-(3)(4).
final Transform t = bodyFrame.getTransformTo(aux.getFrame(), aux.getDate());
final Vector3D xB = t.transformVector(Vector3D.PLUS_I);
final Vector3D yB = t.transformVector(Vector3D.PLUS_J);
theta =
FastMath.atan2(
-f.dotProduct(yB) + I * g.dotProduct(xB), f.dotProduct(xB) + I * g.dotProduct(yB));
// Direction cosines
alpha = aux.getAlpha();
beta = aux.getBeta();
gamma = aux.getGamma();
// Equinoctial coefficients
// A = sqrt(μ * a)
final double A = aux.getA();
// B = sqrt(1 - h² - k²)
final double B = aux.getB();
// C = 1 + p² + q²
final double C = aux.getC();
// Common factors from equinoctial coefficients
// 2 * a / A
ax2oA = 2. * a / A;
// B / A
BoA = B / A;
// 1 / AB
ooAB = 1. / (A * B);
// C / 2AB
Co2AB = C * ooAB / 2.;
// B / (A * (1 + B))
BoABpo = BoA / (1. + B);
// &mu / a
moa = provider.getMu() / a;
// R / a
roa = provider.getAe() / a;
// Χ = 1 / B
chi = 1. / B;
chi2 = chi * chi;
// mean motion n
meanMotion = aux.getMeanMotion();
}