/**
* Compute the <a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top"> natural
* logarithm</a> of this complex number. Implements the formula:
*
* <pre>
* <code>
* log(a + bi) = ln(|a + bi|) + arg(a + bi)i
* </code>
* </pre>
*
* where ln on the right hand side is {@link java.lang.Math#log}, {@code |a + bi|} is the modulus,
* {@link Complex#abs}, and {@code arg(a + bi) = }{@link java.lang.Math#atan2}(b, a). <br>
* Returns {@link Complex#NaN} if either real or imaginary part of the input argument is {@code
* NaN}. <br>
* Infinite (or critical) values in real or imaginary parts of the input may result in infinite or
* NaN values returned in parts of the result.
*
* <pre>
* Examples:
* <code>
* log(1 ± INFINITY i) = INFINITY ± (π/2)i
* log(INFINITY + i) = INFINITY + 0i
* log(-INFINITY + i) = INFINITY + πi
* log(INFINITY ± INFINITY i) = INFINITY ± (π/4)i
* log(-INFINITY ± INFINITY i) = INFINITY ± (3π/4)i
* log(0 + 0i) = -INFINITY + 0i
* </code>
* </pre>
*
* @return the value <code>ln this</code>, the natural logarithm of {@code this}.
* @since 1.2
*/
public Complex log() {
if (isNaN) {
return NaN;
}
return createComplex(FastMath.log(abs()), FastMath.atan2(imaginary, real));
}
@Override
public IComplexNumber log() {
IComplexNumber result = dup();
float real = (float) result.realComponent();
float imaginary = (float) result.imaginaryComponent();
double modulus = FastMath.sqrt(real * real + imaginary * imaginary);
double arg = FastMath.atan2(imaginary, real);
return result.set(FastMath.log(modulus), arg);
}
/** {@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();
}
/**
* Compute the argument of this complex number. The argument is the angle phi between the positive
* real axis and the point representing this number in the complex plane. The value returned is
* between -PI (not inclusive) and PI (inclusive), with negative values returned for numbers with
* negative imaginary parts. <br>
* If either real or imaginary part (or both) is NaN, NaN is returned. Infinite parts are handled
* as {@code Math.atan2} handles them, essentially treating finite parts as zero in the presence
* of an infinite coordinate and returning a multiple of pi/4 depending on the signs of the
* infinite parts. See the javadoc for {@code Math.atan2} for full details.
*
* @return the argument of {@code this}.
*/
public double getArgument() {
return FastMath.atan2(getImaginary(), getReal());
}