Java tutorial
/* Copyright 2002-2010 CS Communication & Systmes * Licensed to CS Communication & Systmes (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.tle; import org.apache.commons.math.util.MathUtils; 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) * @version $Revision:1665 $ $Date:2008-06-11 12:12:59 +0200 (mer., 11 juin 2008) $ */ class DeepSDP4 extends SDP4 { /** Serializable UID. */ private static final long serialVersionUID = 7155645502511295218L; // 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; /** Integration order. */ private static final int SECULAR_INTEGRATION_ORDER = 2; /** 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. * @exception OrekitException if some specific error occurs */ protected DeepSDP4(final TLE initialTLE) throws OrekitException { super(initialTLE); } /** 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 = Math.sin(tle.getPerigeeArgument()); final double cosg = Math.cos(tle.getPerigeeArgument()); final double sinq = Math.sin(tle.getRaan()); final double cosq = Math.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 = Math.sin(xnodce); final double ctem = Math.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 = Math.sqrt(1.0 - zcosil * zcosil); zsinhl = 0.089683511 * stem / zsinil; zcoshl = Math.sqrt(1.0 - zsinhl * zsinhl); zmol = MathUtils.normalizeAngle(c_minus_gam, Math.PI); double zx = 0.39785416 * stem / zsinil; final double zy = zcoshl * ctem + 0.91744867 * zsinhl * stem; zx = Math.atan2(zx, zy) + gam - xnodce; zcosgl = Math.cos(zx); zsingl = Math.sin(zx); zmos = MathUtils.normalizeAngle(6.2565837 + 0.017201977 * daysSince1900, Math.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() < (Math.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 = 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 - cosi0 / sini0 * sh; ssh += 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)); double g211; double g310; double g322; double g410; double g422; 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; } } double g533; double g521; 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[SECULAR_INTEGRATION_ORDER]; } /** 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 (Math.abs(t) < Math.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; for (int j = 2; j <= SECULAR_INTEGRATION_ORDER; ++j) { xlpow *= xldot; derivs[j - 1] *= xlpow; delt_factor *= delt / (double) j; xli += delt_factor * derivs[j - 2]; xni += delt_factor * derivs[j - 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 ((Math.abs(savtsn - t) >= 30.0) || isDundeeCompliant) { savtsn = t; // Update solar perturbations for time T double zm = zmos + ZNS * t; double zf = zm + 2 * ZES * Math.sin(zm); double sinzf = Math.sin(zf); double f2 = 0.5 * sinzf * sinzf - 0.25; double f3 = -0.5 * sinzf * Math.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 * Math.sin(zm); sinzf = Math.sin(zf); f2 = 0.5 * sinzf * sinzf - 0.25; f3 = -0.5 * sinzf * Math.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 = Math.sin(xinc); final double cosis = Math.cos(xinc); /* Add solar/lunar perturbation correction to eccentricity: */ em += pe; xll += pl; omgadf += pgh; xinc = MathUtils.normalizeAngle(xinc, 0); if (Math.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 = Math.sin(xnode); final double cosok = Math.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(Math.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 = Math.sin(xli); final double cos_li = Math.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; double term1a = del1 * (sin_li * C_FASX2 - cos_li * S_FASX2); double term2a = del2 * (sin_2li * C_2FASX4 - cos_2li * S_2FASX4); double term3a = del3 * (sin_3li * C_3FASX6 - cos_3li * S_3FASX6); double term1b = del1 * (cos_li * C_FASX2 + sin_li * S_FASX2); double term2b = 2.0 * del2 * (cos_2li * C_2FASX4 + sin_2li * S_2FASX4); double term3b = 3.0 * del3 * (cos_3li * C_3FASX6 + sin_3li * S_3FASX6); for (int j = 0; j < SECULAR_INTEGRATION_ORDER; j += 2) { derivs[j] = term1a + term2a + term3a; derivs[j + 1] = term1b + term2b + term3b; if ((i + 2) < SECULAR_INTEGRATION_ORDER) { term1a = -term1a; term2a *= -4.0; term3a *= -9.0; term1b = -term1b; term2b *= -4.0; term3b *= -9.0; } } } else { // orbit is a 12-hour resonant one final double xomi = omegaq + omgdot * atime; final double sin_omi = Math.sin(xomi); final double cos_omi = Math.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; 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); 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); 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); 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)); for (int j = 0; j < SECULAR_INTEGRATION_ORDER; j += 2) { derivs[j] = term1a + term2a; derivs[j + 1] = term1b + term2b; if ((j + 2) < SECULAR_INTEGRATION_ORDER) { term1a = -term1a; term2a *= -4.0; term1b = -term1b; term2b *= -4.0; } } } } }