DeepSDP4.java
- /* Copyright 2002-2017 CS Systèmes d'Information
- * Licensed to CS Systèmes d'Information (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.orekit.attitudes.AttitudeProvider;
- import org.orekit.errors.OrekitException;
- import org.orekit.time.AbsoluteDate;
- import org.orekit.time.TimeScalesFactory;
- 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="http://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
- // Internal constants
- private static final double ZNS = 1.19459E-5;
- private static final double ZES = 0.01675;
- private static final double ZNL = 1.5835218E-4;
- private static final double ZEL = 0.05490;
- private static final double THDT = 4.3752691E-3;
- private static final double C1SS = 2.9864797E-6;
- private static final double C1L = 4.7968065E-7;
- private static final double ROOT22 = 1.7891679E-6;
- private static final double ROOT32 = 3.7393792E-7;
- private static final double ROOT44 = 7.3636953E-9;
- private static final double ROOT52 = 1.1428639E-7;
- private static final double ROOT54 = 2.1765803E-9;
- private static final double Q22 = 1.7891679E-6;
- private static final double Q31 = 2.1460748E-6;
- private static final double Q33 = 2.2123015E-7;
- private static final double C_FASX2 = 0.99139134268488593;
- private static final double S_FASX2 = 0.13093206501640101;
- private static final double C_2FASX4 = 0.87051638752972937;
- private static final double S_2FASX4 = -0.49213943048915526;
- private static final double C_3FASX6 = 0.43258117585763334;
- private static final double S_3FASX6 = 0.90159499016666422;
- private static final double C_G22 = 0.87051638752972937;
- private static final double S_G22 = -0.49213943048915526;
- private static final double C_G32 = 0.57972190187001149;
- private static final double S_G32 = 0.81481440616389245;
- private static final double C_G44 = -0.22866241528815548;
- private static final double S_G44 = 0.97350577801807991;
- private static final double C_G52 = 0.49684831179884198;
- private static final double S_G52 = 0.86783740128127729;
- private static final double C_G54 = -0.29695209575316894;
- private static final double S_G54 = -0.95489237761529999;
- /** 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.
- * @param initialTLE the TLE to propagate.
- * @param attitudeProvider provider for attitude computation
- * @param mass spacecraft mass (kg)
- * @exception OrekitException if some specific error occurs
- */
- public DeepSDP4(final TLE initialTLE, final AttitudeProvider attitudeProvider,
- final double mass) throws OrekitException {
- super(initialTLE, attitudeProvider, mass);
- }
- /** Computes luni - solar terms from initial coordinates and epoch.
- * @exception OrekitException when UTC time steps can't be read
- */
- protected void luniSolarTermsComputation() throws OrekitException {
- final double sing = FastMath.sin(tle.getPerigeeArgument());
- final double cosg = FastMath.cos(tle.getPerigeeArgument());
- final double sinq = FastMath.sin(tle.getRaan());
- final double cosq = FastMath.cos(tle.getRaan());
- final double aqnv = 1.0 / a0dp;
- // Compute julian days since 1900
- final double daysSince1900 =
- (tle.getDate().durationFrom(AbsoluteDate.JULIAN_EPOCH) +
- tle.getDate().timeScalesOffset(TimeScalesFactory.getUTC(), TimeScalesFactory.getTT())) / Constants.JULIAN_DAY - 2415020;
- double cc = C1SS;
- double ze = ZES;
- double zn = 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 double stem = FastMath.sin(xnodce);
- final double ctem = FastMath.cos(xnodce);
- 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;
- zcosgl = FastMath.cos( zx);
- zsingl = FastMath.sin( zx);
- 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 = ZNL;
- cc = C1L;
- ze = 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 * ROOT22;
- d2201 = temp * f220 * g201;
- d2211 = temp * f221 * g211;
- temp1 *= aqnv;
- temp = temp1 * ROOT32;
- d3210 = temp * f321 * g310;
- d3222 = temp * f322 * g322;
- temp1 *= aqnv;
- temp = 2 * temp1 * ROOT44;
- d4410 = temp * f441 * g410;
- d4422 = temp * f442 * g422;
- temp1 *= aqnv;
- temp = temp1 * ROOT52;
- d5220 = temp * f522 * g520;
- d5232 = temp * f523 * g532;
- temp = 2 * temp1 * ROOT54;
- d5421 = temp * f542 * g521;
- d5433 = temp * f543 * g533;
- xlamo = tle.getMeanAnomaly() + tle.getRaan() + tle.getRaan() - thgr - thgr;
- bfact = xmdot + xnodot + xnodot - THDT - 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 * Q22;
- del3 = 3 * del1 * f330 * g300 * Q33 * aqnv;
- del1 = del1 * f311 * g310 * Q31 * aqnv;
- xlamo = tle.getMeanAnomaly() + tle.getRaan() + tle.getPerigeeArgument() - thgr;
- bfact = xmdot + omgdot + xnodot - 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 * 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 + ZNS * t;
- double zf = zm + 2 * ZES * FastMath.sin(zm);
- double sinzf = FastMath.sin(zf);
- double f2 = 0.5 * sinzf * sinzf - 0.25;
- double f3 = -0.5 * sinzf * FastMath.cos(zf);
- 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 + ZNL * t;
- zf = zm + 2 * ZEL * FastMath.sin(zm);
- sinzf = FastMath.sin(zf);
- f2 = 0.5 * sinzf * sinzf - 0.25;
- f3 = -0.5 * sinzf * FastMath.cos(zf);
- 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 double sinis = FastMath.sin( xinc);
- final double cosis = FastMath.cos( xinc);
- /* 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 double sinok = FastMath.sin(xnode);
- final double cosok = FastMath.cos(xnode);
- 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 double sin_li = FastMath.sin(xli);
- final double cos_li = FastMath.cos(xli);
- 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 * C_FASX2 - cos_li * S_FASX2);
- final double term2a = del2 * (sin_2li * C_2FASX4 - cos_2li * S_2FASX4);
- final double term3a = del3 * (sin_3li * C_3FASX6 - cos_3li * S_3FASX6);
- final double term1b = del1 * (cos_li * C_FASX2 + sin_li * S_FASX2);
- final double term2b = 2.0 * del2 * (cos_2li * C_2FASX4 + sin_2li * S_2FASX4);
- final double term3b = 3.0 * del3 * (cos_3li * C_3FASX6 + sin_3li * 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 double sin_omi = FastMath.sin(xomi);
- final double cos_omi = FastMath.cos(xomi);
- 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 * C_G22 - cos_2omi_p_li * S_G22) +
- d2211 * (sin_li * C_G22 - cos_li * S_G22) +
- d3210 * (sin_li_p_omi * C_G32 - cos_li_p_omi * S_G32) +
- d3222 * (sin_li_m_omi * C_G32 - cos_li_m_omi * S_G32) +
- d5220 * (sin_li_p_omi * C_G52 - cos_li_p_omi * S_G52) +
- d5232 * (sin_li_m_omi * C_G52 - cos_li_m_omi * S_G52);
- final double term2a = d4410 * (sin_2li_p_2omi * C_G44 - cos_2li_p_2omi * S_G44) +
- d4422 * (sin_2li * C_G44 - cos_2li * S_G44) +
- d5421 * (sin_2li_p_omi * C_G54 - cos_2li_p_omi * S_G54) +
- d5433 * (sin_2li_m_omi * C_G54 - cos_2li_m_omi * S_G54);
- final double term1b = d2201 * (cos_2omi_p_li * C_G22 + sin_2omi_p_li * S_G22) +
- d2211 * (cos_li * C_G22 + sin_li * S_G22) +
- d3210 * (cos_li_p_omi * C_G32 + sin_li_p_omi * S_G32) +
- d3222 * (cos_li_m_omi * C_G32 + sin_li_m_omi * S_G32) +
- d5220 * (cos_li_p_omi * C_G52 + sin_li_p_omi * S_G52) +
- d5232 * (cos_li_m_omi * C_G52 + sin_li_m_omi * S_G52);
- final double term2b = 2.0 * (d4410 * (cos_2li_p_2omi * C_G44 + sin_2li_p_2omi * S_G44) +
- d4422 * (cos_2li * C_G44 + sin_2li * S_G44) +
- d5421 * (cos_2li_p_omi * C_G54 + sin_2li_p_omi * S_G54) +
- d5433 * (cos_2li_m_omi * C_G54 + sin_2li_m_omi * S_G54));
- derivs[0] = term1a + term2a;
- derivs[1] = term1b + term2b;
- }
- }
- }