DeepSDP4.java
/* Copyright 2002-2023 CS GROUP
* Licensed to CS GROUP (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.orekit.propagation.analytical.tle;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathUtils;
import org.hipparchus.util.SinCos;
import org.orekit.annotation.DefaultDataContext;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.data.DataContext;
import org.orekit.frames.Frame;
import org.orekit.time.DateTimeComponents;
import org.orekit.utils.Constants;
/** This class contains the methods that compute deep space perturbation terms.
* <p>
* The user should not bother in this class since it is handled internaly by the
* {@link TLEPropagator}.
* </p>
* <p>This implementation is largely inspired from the paper and source code <a
* href="https://www.celestrak.com/publications/AIAA/2006-6753/">Revisiting Spacetrack
* Report #3</a> and is fully compliant with its results and tests cases.</p>
* @author Felix R. Hoots, Ronald L. Roehrich, December 1980 (original fortran)
* @author David A. Vallado, Paul Crawford, Richard Hujsak, T.S. Kelso (C++ translation and improvements)
* @author Fabien Maussion (java translation)
*/
public class DeepSDP4 extends SDP4 {
// CHECKSTYLE: stop JavadocVariable check
/** Integration step (seconds). */
private static final double SECULAR_INTEGRATION_STEP = 720.0;
/** Intermediate values. */
private double thgr;
private double xnq;
private double omegaq;
private double zcosil;
private double zsinil;
private double zsinhl;
private double zcoshl;
private double zmol;
private double zcosgl;
private double zsingl;
private double zmos;
private double savtsn;
private double ee2;
private double e3;
private double xi2;
private double xi3;
private double xl2;
private double xl3;
private double xl4;
private double xgh2;
private double xgh3;
private double xgh4;
private double xh2;
private double xh3;
private double d2201;
private double d2211;
private double d3210;
private double d3222;
private double d4410;
private double d4422;
private double d5220;
private double d5232;
private double d5421;
private double d5433;
private double xlamo;
private double sse;
private double ssi;
private double ssl;
private double ssh;
private double ssg;
private double se2;
private double si2;
private double sl2;
private double sgh2;
private double sh2;
private double se3;
private double si3;
private double sl3;
private double sgh3;
private double sh3;
private double sl4;
private double sgh4;
private double del1;
private double del2;
private double del3;
private double xfact;
private double xli;
private double xni;
private double atime;
private double pe;
private double pinc;
private double pl;
private double pgh;
private double ph;
private double[] derivs;
// CHECKSTYLE: resume JavadocVariable check
/** Flag for resonant orbits. */
private boolean resonant;
/** Flag for synchronous orbits. */
private boolean synchronous;
/** Flag for compliance with Dundee modifications. */
private boolean isDundeeCompliant = true;
/** Constructor for a unique initial TLE.
*
* <p>This constructor uses the {@link DataContext#getDefault() default data context}.
*
* @param initialTLE the TLE to propagate.
* @param attitudeProvider provider for attitude computation
* @param mass spacecraft mass (kg)
* @see #DeepSDP4(TLE, AttitudeProvider, double, Frame)
*/
@DefaultDataContext
public DeepSDP4(final TLE initialTLE, final AttitudeProvider attitudeProvider,
final double mass) {
this(initialTLE, attitudeProvider, mass,
DataContext.getDefault().getFrames().getTEME());
}
/** Constructor for a unique initial TLE.
* @param initialTLE the TLE to propagate.
* @param attitudeProvider provider for attitude computation
* @param mass spacecraft mass (kg)
* @param teme the TEME frame to use for propagation.
* @since 10.1
*/
public DeepSDP4(final TLE initialTLE,
final AttitudeProvider attitudeProvider,
final double mass,
final Frame teme) {
super(initialTLE, attitudeProvider, mass, teme);
}
/** Computes luni - solar terms from initial coordinates and epoch.
*/
protected void luniSolarTermsComputation() {
final SinCos scg = FastMath.sinCos(tle.getPerigeeArgument());
final double sing = scg.sin();
final double cosg = scg.cos();
final SinCos scq = FastMath.sinCos(tle.getRaan());
final double sinq = scq.sin();
final double cosq = scq.cos();
final double aqnv = 1.0 / a0dp;
// Compute julian days since 1900
final double daysSince1900 = (tle.getDate()
.getComponents(utc)
.offsetFrom(DateTimeComponents.JULIAN_EPOCH)) /
Constants.JULIAN_DAY - 2415020;
double cc = TLEConstants.C1SS;
double ze = TLEConstants.ZES;
double zn = TLEConstants.ZNS;
double zsinh = sinq;
double zcosh = cosq;
thgr = thetaG(tle.getDate());
xnq = xn0dp;
omegaq = tle.getPerigeeArgument();
final double xnodce = 4.5236020 - 9.2422029e-4 * daysSince1900;
final SinCos scTem = FastMath.sinCos(xnodce);
final double stem = scTem.sin();
final double ctem = scTem.cos();
final double c_minus_gam = 0.228027132 * daysSince1900 - 1.1151842;
final double gam = 5.8351514 + 0.0019443680 * daysSince1900;
zcosil = 0.91375164 - 0.03568096 * ctem;
zsinil = FastMath.sqrt(1.0 - zcosil * zcosil);
zsinhl = 0.089683511 * stem / zsinil;
zcoshl = FastMath.sqrt(1.0 - zsinhl * zsinhl);
zmol = MathUtils.normalizeAngle(c_minus_gam, FastMath.PI);
double zx = 0.39785416 * stem / zsinil;
final double zy = zcoshl * ctem + 0.91744867 * zsinhl * stem;
zx = FastMath.atan2( zx, zy) + gam - xnodce;
final SinCos scZx = FastMath.sinCos(zx);
zcosgl = scZx.cos();
zsingl = scZx.sin();
zmos = MathUtils.normalizeAngle(6.2565837 + 0.017201977 * daysSince1900, FastMath.PI);
// Do solar terms
savtsn = 1e20;
double zcosi = 0.91744867;
double zsini = 0.39785416;
double zsing = -0.98088458;
double zcosg = 0.1945905;
double se = 0;
double sgh = 0;
double sh = 0;
double si = 0;
double sl = 0;
// There was previously some convoluted logic here, but it boils
// down to this: we compute the solar terms, then the lunar terms.
// On a second pass, we recompute the solar terms, taking advantage
// of the improved data that resulted from computing lunar terms.
for (int iteration = 0; iteration < 2; ++iteration) {
final double a1 = zcosg * zcosh + zsing * zcosi * zsinh;
final double a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
final double a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
final double a8 = zsing * zsini;
final double a9 = zsing * zsinh + zcosg * zcosi * zcosh;
final double a10 = zcosg * zsini;
final double a2 = cosi0 * a7 + sini0 * a8;
final double a4 = cosi0 * a9 + sini0 * a10;
final double a5 = -sini0 * a7 + cosi0 * a8;
final double a6 = -sini0 * a9 + cosi0 * a10;
final double x1 = a1 * cosg + a2 * sing;
final double x2 = a3 * cosg + a4 * sing;
final double x3 = -a1 * sing + a2 * cosg;
final double x4 = -a3 * sing + a4 * cosg;
final double x5 = a5 * sing;
final double x6 = a6 * sing;
final double x7 = a5 * cosg;
final double x8 = a6 * cosg;
final double z31 = 12 * x1 * x1 - 3 * x3 * x3;
final double z32 = 24 * x1 * x2 - 6 * x3 * x4;
final double z33 = 12 * x2 * x2 - 3 * x4 * x4;
final double z11 = -6 * a1 * a5 + e0sq * (-24 * x1 * x7 - 6 * x3 * x5);
final double z12 = -6 * (a1 * a6 + a3 * a5) +
e0sq * (-24 * (x2 * x7 + x1 * x8) - 6 * (x3 * x6 + x4 * x5));
final double z13 = -6 * a3 * a6 + e0sq * (-24 * x2 * x8 - 6 * x4 * x6);
final double z21 = 6 * a2 * a5 + e0sq * (24 * x1 * x5 - 6 * x3 * x7);
final double z22 = 6 * (a4 * a5 + a2 * a6) +
e0sq * (24 * (x2 * x5 + x1 * x6) - 6 * (x4 * x7 + x3 * x8));
final double z23 = 6 * a4 * a6 + e0sq * (24 * x2 * x6 - 6 * x4 * x8);
final double s3 = cc / xnq;
final double s2 = -0.5 * s3 / beta0;
final double s4 = s3 * beta0;
final double s1 = -15 * tle.getE() * s4;
final double s5 = x1 * x3 + x2 * x4;
final double s6 = x2 * x3 + x1 * x4;
final double s7 = x2 * x4 - x1 * x3;
double z1 = 3 * (a1 * a1 + a2 * a2) + z31 * e0sq;
double z2 = 6 * (a1 * a3 + a2 * a4) + z32 * e0sq;
double z3 = 3 * (a3 * a3 + a4 * a4) + z33 * e0sq;
z1 = z1 + z1 + beta02 * z31;
z2 = z2 + z2 + beta02 * z32;
z3 = z3 + z3 + beta02 * z33;
se = s1 * zn * s5;
si = s2 * zn * (z11 + z13);
sl = -zn * s3 * (z1 + z3 - 14 - 6 * e0sq);
sgh = s4 * zn * (z31 + z33 - 6);
if (tle.getI() < (FastMath.PI / 60.0)) {
// inclination smaller than 3 degrees
sh = 0;
} else {
sh = -zn * s2 * (z21 + z23);
}
ee2 = 2 * s1 * s6;
e3 = 2 * s1 * s7;
xi2 = 2 * s2 * z12;
xi3 = 2 * s2 * (z13 - z11);
xl2 = -2 * s3 * z2;
xl3 = -2 * s3 * (z3 - z1);
xl4 = -2 * s3 * (-21 - 9 * e0sq) * ze;
xgh2 = 2 * s4 * z32;
xgh3 = 2 * s4 * (z33 - z31);
xgh4 = -18 * s4 * ze;
xh2 = -2 * s2 * z22;
xh3 = -2 * s2 * (z23 - z21);
if (iteration == 0) { // we compute lunar terms only on the first pass:
sse = se;
ssi = si;
ssl = sl;
ssh = (tle.getI() < (FastMath.PI / 60.0)) ? 0 : sh / sini0;
ssg = sgh - cosi0 * ssh;
se2 = ee2;
si2 = xi2;
sl2 = xl2;
sgh2 = xgh2;
sh2 = xh2;
se3 = e3;
si3 = xi3;
sl3 = xl3;
sgh3 = xgh3;
sh3 = xh3;
sl4 = xl4;
sgh4 = xgh4;
zcosg = zcosgl;
zsing = zsingl;
zcosi = zcosil;
zsini = zsinil;
zcosh = zcoshl * cosq + zsinhl * sinq;
zsinh = sinq * zcoshl - cosq * zsinhl;
zn = TLEConstants.ZNL;
cc = TLEConstants.C1L;
ze = TLEConstants.ZEL;
}
} // end of solar - lunar - solar terms computation
sse += se;
ssi += si;
ssl += sl;
ssg += sgh - ((tle.getI() < (FastMath.PI / 60.0)) ? 0 : (cosi0 / sini0 * sh));
ssh += (tle.getI() < (FastMath.PI / 60.0)) ? 0 : sh / sini0;
// Start the resonant-synchronous tests and initialization
double bfact = 0;
// if mean motion is 1.893053 to 2.117652 revs/day, and eccentricity >= 0.5,
// start of the 12-hour orbit, e > 0.5 section
if (xnq >= 0.00826 && xnq <= 0.00924 && tle.getE() >= 0.5) {
final double g201 = -0.306 - (tle.getE() - 0.64) * 0.440;
final double eoc = tle.getE() * e0sq;
final double sini2 = sini0 * sini0;
final double f220 = 0.75 * (1 + 2 * cosi0 + theta2);
final double f221 = 1.5 * sini2;
final double f321 = 1.875 * sini0 * (1 - 2 * cosi0 - 3 * theta2);
final double f322 = -1.875 * sini0 * (1 + 2 * cosi0 - 3 * theta2);
final double f441 = 35 * sini2 * f220;
final double f442 = 39.3750 * sini2 * sini2;
final double f522 = 9.84375 * sini0 * (sini2 * (1 - 2 * cosi0 - 5 * theta2) +
0.33333333 * (-2 + 4 * cosi0 + 6 * theta2));
final double f523 = sini0 * (4.92187512 * sini2 * (-2 - 4 * cosi0 + 10 * theta2) +
6.56250012 * (1 + 2 * cosi0 - 3 * theta2));
final double f542 = 29.53125 * sini0 * (2 - 8 * cosi0 + theta2 * (-12 + 8 * cosi0 + 10 * theta2));
final double f543 = 29.53125 * sini0 * (-2 - 8 * cosi0 + theta2 * (12 + 8 * cosi0 - 10 * theta2));
final double g211;
final double g310;
final double g322;
final double g410;
final double g422;
final double g520;
resonant = true; // it is resonant...
synchronous = false; // but it's not synchronous
// Geopotential resonance initialization for 12 hour orbits :
if (tle.getE() <= 0.65) {
g211 = 3.616 - 13.247 * tle.getE() + 16.290 * e0sq;
g310 = -19.302 + 117.390 * tle.getE() - 228.419 * e0sq + 156.591 * eoc;
g322 = -18.9068 + 109.7927 * tle.getE() - 214.6334 * e0sq + 146.5816 * eoc;
g410 = -41.122 + 242.694 * tle.getE() - 471.094 * e0sq + 313.953 * eoc;
g422 = -146.407 + 841.880 * tle.getE() - 1629.014 * e0sq + 1083.435 * eoc;
g520 = -532.114 + 3017.977 * tle.getE() - 5740.032 * e0sq + 3708.276 * eoc;
} else {
g211 = -72.099 + 331.819 * tle.getE() - 508.738 * e0sq + 266.724 * eoc;
g310 = -346.844 + 1582.851 * tle.getE() - 2415.925 * e0sq + 1246.113 * eoc;
g322 = -342.585 + 1554.908 * tle.getE() - 2366.899 * e0sq + 1215.972 * eoc;
g410 = -1052.797 + 4758.686 * tle.getE() - 7193.992 * e0sq + 3651.957 * eoc;
g422 = -3581.69 + 16178.11 * tle.getE() - 24462.77 * e0sq + 12422.52 * eoc;
if (tle.getE() <= 0.715) {
g520 = 1464.74 - 4664.75 * tle.getE() + 3763.64 * e0sq;
} else {
g520 = -5149.66 + 29936.92 * tle.getE() - 54087.36 * e0sq + 31324.56 * eoc;
}
}
final double g533;
final double g521;
final double g532;
if (tle.getE() < 0.7) {
g533 = -919.2277 + 4988.61 * tle.getE() - 9064.77 * e0sq + 5542.21 * eoc;
g521 = -822.71072 + 4568.6173 * tle.getE() - 8491.4146 * e0sq + 5337.524 * eoc;
g532 = -853.666 + 4690.25 * tle.getE() - 8624.77 * e0sq + 5341.4 * eoc;
} else {
g533 = -37995.78 + 161616.52 * tle.getE() - 229838.2 * e0sq + 109377.94 * eoc;
g521 = -51752.104 + 218913.95 * tle.getE() - 309468.16 * e0sq + 146349.42 * eoc;
g532 = -40023.88 + 170470.89 * tle.getE() - 242699.48 * e0sq + 115605.82 * eoc;
}
double temp1 = 3 * xnq * xnq * aqnv * aqnv;
double temp = temp1 * TLEConstants.ROOT22;
d2201 = temp * f220 * g201;
d2211 = temp * f221 * g211;
temp1 *= aqnv;
temp = temp1 * TLEConstants.ROOT32;
d3210 = temp * f321 * g310;
d3222 = temp * f322 * g322;
temp1 *= aqnv;
temp = 2 * temp1 * TLEConstants.ROOT44;
d4410 = temp * f441 * g410;
d4422 = temp * f442 * g422;
temp1 *= aqnv;
temp = temp1 * TLEConstants.ROOT52;
d5220 = temp * f522 * g520;
d5232 = temp * f523 * g532;
temp = 2 * temp1 * TLEConstants.ROOT54;
d5421 = temp * f542 * g521;
d5433 = temp * f543 * g533;
xlamo = tle.getMeanAnomaly() + tle.getRaan() + tle.getRaan() - thgr - thgr;
bfact = xmdot + xnodot + xnodot - TLEConstants.THDT - TLEConstants.THDT;
bfact += ssl + ssh + ssh;
} else if (xnq < 0.0052359877 && xnq > 0.0034906585) {
// if mean motion is .8 to 1.2 revs/day : (geosynch)
final double cosio_plus_1 = 1.0 + cosi0;
final double g200 = 1 + e0sq * (-2.5 + 0.8125 * e0sq);
final double g300 = 1 + e0sq * (-6 + 6.60937 * e0sq);
final double f311 = 0.9375 * sini0 * sini0 * (1 + 3 * cosi0) - 0.75 * cosio_plus_1;
final double g310 = 1 + 2 * e0sq;
final double f220 = 0.75 * cosio_plus_1 * cosio_plus_1;
final double f330 = 2.5 * f220 * cosio_plus_1;
resonant = true;
synchronous = true;
// Synchronous resonance terms initialization
del1 = 3 * xnq * xnq * aqnv * aqnv;
del2 = 2 * del1 * f220 * g200 * TLEConstants.Q22;
del3 = 3 * del1 * f330 * g300 * TLEConstants.Q33 * aqnv;
del1 = del1 * f311 * g310 * TLEConstants.Q31 * aqnv;
xlamo = tle.getMeanAnomaly() + tle.getRaan() + tle.getPerigeeArgument() - thgr;
bfact = xmdot + omgdot + xnodot - TLEConstants.THDT;
bfact = bfact + ssl + ssg + ssh;
} else {
// it's neither a high-e 12-hours orbit nor a geosynchronous:
resonant = false;
synchronous = false;
}
if (resonant) {
xfact = bfact - xnq;
// Initialize integrator
xli = xlamo;
xni = xnq;
atime = 0;
}
derivs = new double[2];
}
/** Computes secular terms from current coordinates and epoch.
* @param t offset from initial epoch (minutes)
*/
protected void deepSecularEffects(final double t) {
xll += ssl * t;
omgadf += ssg * t;
xnode += ssh * t;
em = tle.getE() + sse * t;
xinc = tle.getI() + ssi * t;
if (resonant) {
// If we're closer to t = 0 than to the currently-stored data
// from the previous call to this function, then we're
// better off "restarting", going back to the initial data.
// The Dundee code rigs things up to _always_ take 720-minute
// steps from epoch to end time, except for the final step.
// Easiest way to arrange similar behavior in this code is
// just to always do a restart, if we're in Dundee-compliant
// mode.
if (FastMath.abs(t) < FastMath.abs(t - atime) || isDundeeCompliant) {
// Epoch restart
atime = 0;
xni = xnq;
xli = xlamo;
}
boolean lastIntegrationStep = false;
// if |step|>|step max| then do one step at step max
while (!lastIntegrationStep) {
double delt = t - atime;
if (delt > SECULAR_INTEGRATION_STEP) {
delt = SECULAR_INTEGRATION_STEP;
} else if (delt < -SECULAR_INTEGRATION_STEP) {
delt = -SECULAR_INTEGRATION_STEP;
} else {
lastIntegrationStep = true;
}
computeSecularDerivs();
final double xldot = xni + xfact;
double xlpow = 1.;
xli += delt * xldot;
xni += delt * derivs[0];
double delt_factor = delt;
xlpow *= xldot;
derivs[1] *= xlpow;
delt_factor *= delt / 2;
xli += delt_factor * derivs[0];
xni += delt_factor * derivs[1];
atime += delt;
}
xn = xni;
final double temp = -xnode + thgr + t * TLEConstants.THDT;
xll = xli + temp + (synchronous ? -omgadf : temp);
}
}
/** Computes periodic terms from current coordinates and epoch.
* @param t offset from initial epoch (min)
*/
protected void deepPeriodicEffects(final double t) {
// If the time didn't change by more than 30 minutes,
// there's no good reason to recompute the perturbations;
// they don't change enough over so short a time span.
// However, the Dundee code _always_ recomputes, so if
// we're attempting to replicate its results, we've gotta
// recompute everything, too.
if (FastMath.abs(savtsn - t) >= 30.0 || isDundeeCompliant) {
savtsn = t;
// Update solar perturbations for time T
double zm = zmos + TLEConstants.ZNS * t;
double zf = zm + 2 * TLEConstants.ZES * FastMath.sin(zm);
SinCos sczf = FastMath.sinCos(zf);
double sinzf = sczf.sin();
double f2 = 0.5 * sinzf * sinzf - 0.25;
double f3 = -0.5 * sinzf * sczf.cos();
final double ses = se2 * f2 + se3 * f3;
final double sis = si2 * f2 + si3 * f3;
final double sls = sl2 * f2 + sl3 * f3 + sl4 * sinzf;
final double sghs = sgh2 * f2 + sgh3 * f3 + sgh4 * sinzf;
final double shs = sh2 * f2 + sh3 * f3;
// Update lunar perturbations for time T
zm = zmol + TLEConstants.ZNL * t;
zf = zm + 2 * TLEConstants.ZEL * FastMath.sin(zm);
sczf = FastMath.sinCos(zf);
sinzf = sczf.sin();
f2 = 0.5 * sinzf * sinzf - 0.25;
f3 = -0.5 * sinzf * sczf.cos();
final double sel = ee2 * f2 + e3 * f3;
final double sil = xi2 * f2 + xi3 * f3;
final double sll = xl2 * f2 + xl3 * f3 + xl4 * sinzf;
final double sghl = xgh2 * f2 + xgh3 * f3 + xgh4 * sinzf;
final double sh1 = xh2 * f2 + xh3 * f3;
// Sum the solar and lunar contributions
pe = ses + sel;
pinc = sis + sil;
pl = sls + sll;
pgh = sghs + sghl;
ph = shs + sh1;
}
xinc += pinc;
final SinCos scis = FastMath.sinCos(xinc);
final double sinis = scis.sin();
final double cosis = scis.cos();
/* Add solar/lunar perturbation correction to eccentricity: */
em += pe;
xll += pl;
omgadf += pgh;
xinc = MathUtils.normalizeAngle(xinc, 0);
if (FastMath.abs(xinc) >= 0.2) {
// Apply periodics directly
final double temp_val = ph / sinis;
omgadf -= cosis * temp_val;
xnode += temp_val;
} else {
// Apply periodics with Lyddane modification
final SinCos scok = FastMath.sinCos(xnode);
final double sinok = scok.sin();
final double cosok = scok.cos();
final double alfdp = ph * cosok + (pinc * cosis + sinis) * sinok;
final double betdp = -ph * sinok + (pinc * cosis + sinis) * cosok;
final double delta_xnode = MathUtils.normalizeAngle(FastMath.atan2(alfdp, betdp) - xnode, 0);
final double dls = -xnode * sinis * pinc;
omgadf += dls - cosis * delta_xnode;
xnode += delta_xnode;
}
}
/** Computes internal secular derivs. */
private void computeSecularDerivs() {
final SinCos sc_li = FastMath.sinCos(xli);
final double sin_li = sc_li.sin();
final double cos_li = sc_li.cos();
final double sin_2li = 2. * sin_li * cos_li;
final double cos_2li = 2. * cos_li * cos_li - 1.;
// Dot terms calculated :
if (synchronous) {
final double sin_3li = sin_2li * cos_li + cos_2li * sin_li;
final double cos_3li = cos_2li * cos_li - sin_2li * sin_li;
final double term1a = del1 * (sin_li * TLEConstants.C_FASX2 - cos_li * TLEConstants.S_FASX2);
final double term2a = del2 * (sin_2li * TLEConstants.C_2FASX4 - cos_2li * TLEConstants.S_2FASX4);
final double term3a = del3 * (sin_3li * TLEConstants.C_3FASX6 - cos_3li * TLEConstants.S_3FASX6);
final double term1b = del1 * (cos_li * TLEConstants.C_FASX2 + sin_li * TLEConstants.S_FASX2);
final double term2b = 2.0 * del2 * (cos_2li * TLEConstants.C_2FASX4 + sin_2li * TLEConstants.S_2FASX4);
final double term3b = 3.0 * del3 * (cos_3li * TLEConstants.C_3FASX6 + sin_3li * TLEConstants.S_3FASX6);
derivs[0] = term1a + term2a + term3a;
derivs[1] = term1b + term2b + term3b;
} else {
// orbit is a 12-hour resonant one
final double xomi = omegaq + omgdot * atime;
final SinCos sc_omi = FastMath.sinCos(xomi);
final double sin_omi = sc_omi.sin();
final double cos_omi = sc_omi.cos();
final double sin_li_m_omi = sin_li * cos_omi - sin_omi * cos_li;
final double sin_li_p_omi = sin_li * cos_omi + sin_omi * cos_li;
final double cos_li_m_omi = cos_li * cos_omi + sin_omi * sin_li;
final double cos_li_p_omi = cos_li * cos_omi - sin_omi * sin_li;
final double sin_2omi = 2. * sin_omi * cos_omi;
final double cos_2omi = 2. * cos_omi * cos_omi - 1.;
final double sin_2li_m_omi = sin_2li * cos_omi - sin_omi * cos_2li;
final double sin_2li_p_omi = sin_2li * cos_omi + sin_omi * cos_2li;
final double cos_2li_m_omi = cos_2li * cos_omi + sin_omi * sin_2li;
final double cos_2li_p_omi = cos_2li * cos_omi - sin_omi * sin_2li;
final double sin_2li_p_2omi = sin_2li * cos_2omi + sin_2omi * cos_2li;
final double cos_2li_p_2omi = cos_2li * cos_2omi - sin_2omi * sin_2li;
final double sin_2omi_p_li = sin_li * cos_2omi + sin_2omi * cos_li;
final double cos_2omi_p_li = cos_li * cos_2omi - sin_2omi * sin_li;
final double term1a = d2201 * (sin_2omi_p_li * TLEConstants.C_G22 - cos_2omi_p_li * TLEConstants.S_G22) +
d2211 * (sin_li * TLEConstants.C_G22 - cos_li * TLEConstants.S_G22) +
d3210 * (sin_li_p_omi * TLEConstants.C_G32 - cos_li_p_omi * TLEConstants.S_G32) +
d3222 * (sin_li_m_omi * TLEConstants.C_G32 - cos_li_m_omi * TLEConstants.S_G32) +
d5220 * (sin_li_p_omi * TLEConstants.C_G52 - cos_li_p_omi * TLEConstants.S_G52) +
d5232 * (sin_li_m_omi * TLEConstants.C_G52 - cos_li_m_omi * TLEConstants.S_G52);
final double term2a = d4410 * (sin_2li_p_2omi * TLEConstants.C_G44 - cos_2li_p_2omi * TLEConstants.S_G44) +
d4422 * (sin_2li * TLEConstants.C_G44 - cos_2li * TLEConstants.S_G44) +
d5421 * (sin_2li_p_omi * TLEConstants.C_G54 - cos_2li_p_omi * TLEConstants.S_G54) +
d5433 * (sin_2li_m_omi * TLEConstants.C_G54 - cos_2li_m_omi * TLEConstants.S_G54);
final double term1b = d2201 * (cos_2omi_p_li * TLEConstants.C_G22 + sin_2omi_p_li * TLEConstants.S_G22) +
d2211 * (cos_li * TLEConstants.C_G22 + sin_li * TLEConstants.S_G22) +
d3210 * (cos_li_p_omi * TLEConstants.C_G32 + sin_li_p_omi * TLEConstants.S_G32) +
d3222 * (cos_li_m_omi * TLEConstants.C_G32 + sin_li_m_omi * TLEConstants.S_G32) +
d5220 * (cos_li_p_omi * TLEConstants.C_G52 + sin_li_p_omi * TLEConstants.S_G52) +
d5232 * (cos_li_m_omi * TLEConstants.C_G52 + sin_li_m_omi * TLEConstants.S_G52);
final double term2b = 2.0 * (d4410 * (cos_2li_p_2omi * TLEConstants.C_G44 + sin_2li_p_2omi * TLEConstants.S_G44) +
d4422 * (cos_2li * TLEConstants.C_G44 + sin_2li * TLEConstants.S_G44) +
d5421 * (cos_2li_p_omi * TLEConstants.C_G54 + sin_2li_p_omi * TLEConstants.S_G54) +
d5433 * (cos_2li_m_omi * TLEConstants.C_G54 + sin_2li_m_omi * TLEConstants.S_G54));
derivs[0] = term1a + term2a;
derivs[1] = term1b + term2b;
}
}
}