DeepSDP4.java

  1. /* Copyright 2002-2020 CS Group
  2.  * Licensed to CS Group (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.propagation.analytical.tle;

  19. import org.hipparchus.util.FastMath;
  20. import org.hipparchus.util.MathUtils;
  21. import org.orekit.annotation.DefaultDataContext;
  22. import org.orekit.attitudes.AttitudeProvider;
  23. import org.orekit.data.DataContext;
  24. import org.orekit.frames.Frame;
  25. import org.orekit.time.DateTimeComponents;
  26. import org.orekit.utils.Constants;


  29. /** This class contains the methods that compute deep space perturbation terms.
  30.  * <p>
  31.  * The user should not bother in this class since it is handled internaly by the
  32.  * {@link TLEPropagator}.
  33.  * </p>
  34.  * <p>This implementation is largely inspired from the paper and source code <a
  35.  * href="https://www.celestrak.com/publications/AIAA/2006-6753/">Revisiting Spacetrack
  36.  * Report #3</a> and is fully compliant with its results and tests cases.</p>
  37.  * @author Felix R. Hoots, Ronald L. Roehrich, December 1980 (original fortran)
  38.  * @author David A. Vallado, Paul Crawford, Richard Hujsak, T.S. Kelso (C++ translation and improvements)
  39.  * @author Fabien Maussion (java translation)
  40.  */
  41. public class DeepSDP4 extends SDP4 {

  43.     // CHECKSTYLE: stop JavadocVariable check

  45.     // Internal constants
  46.     private static final double ZNS      = 1.19459E-5;
  47.     private static final double ZES      = 0.01675;
  48.     private static final double ZNL      = 1.5835218E-4;
  49.     private static final double ZEL      = 0.05490;
  50.     private static final double THDT     = 4.3752691E-3;
  51.     private static final double C1SS     =  2.9864797E-6;
  52.     private static final double C1L      = 4.7968065E-7;

  54.     private static final double ROOT22   = 1.7891679E-6;
  55.     private static final double ROOT32   = 3.7393792E-7;
  56.     private static final double ROOT44   = 7.3636953E-9;
  57.     private static final double ROOT52   = 1.1428639E-7;
  58.     private static final double ROOT54   = 2.1765803E-9;

  60.     private static final double Q22      =  1.7891679E-6;
  61.     private static final double Q31      =  2.1460748E-6;
  62.     private static final double Q33      =  2.2123015E-7;

  64.     private static final double C_FASX2  =  0.99139134268488593;
  65.     private static final double S_FASX2  =  0.13093206501640101;
  66.     private static final double C_2FASX4 =  0.87051638752972937;
  67.     private static final double S_2FASX4 = -0.49213943048915526;
  68.     private static final double C_3FASX6 =  0.43258117585763334;
  69.     private static final double S_3FASX6 =  0.90159499016666422;

  71.     private static final double C_G22    =  0.87051638752972937;
  72.     private static final double S_G22    = -0.49213943048915526;
  73.     private static final double C_G32    =  0.57972190187001149;
  74.     private static final double S_G32    =  0.81481440616389245;
  75.     private static final double C_G44    = -0.22866241528815548;
  76.     private static final double S_G44    =  0.97350577801807991;
  77.     private static final double C_G52    =  0.49684831179884198;
  78.     private static final double S_G52    =  0.86783740128127729;
  79.     private static final double C_G54    = -0.29695209575316894;
  80.     private static final double S_G54    = -0.95489237761529999;

  82.     /** Integration step (seconds). */
  83.     private static final double SECULAR_INTEGRATION_STEP  = 720.0;

  85.     /** Intermediate values. */
  86.     private double thgr;
  87.     private double xnq;
  88.     private double omegaq;
  89.     private double zcosil;
  90.     private double zsinil;
  91.     private double zsinhl;
  92.     private double zcoshl;
  93.     private double zmol;
  94.     private double zcosgl;
  95.     private double zsingl;
  96.     private double zmos;
  97.     private double savtsn;

  99.     private double ee2;
  100.     private double e3;
  101.     private double xi2;
  102.     private double xi3;
  103.     private double xl2;
  104.     private double xl3;
  105.     private double xl4;
  106.     private double xgh2;
  107.     private double xgh3;
  108.     private double xgh4;
  109.     private double xh2;
  110.     private double xh3;

  112.     private double d2201;
  113.     private double d2211;
  114.     private double d3210;
  115.     private double d3222;
  116.     private double d4410;
  117.     private double d4422;
  118.     private double d5220;
  119.     private double d5232;
  120.     private double d5421;
  121.     private double d5433;
  122.     private double xlamo;

  124.     private double sse;
  125.     private double ssi;
  126.     private double ssl;
  127.     private double ssh;
  128.     private double ssg;
  129.     private double se2;
  130.     private double si2;
  131.     private double sl2;
  132.     private double sgh2;
  133.     private double sh2;
  134.     private double se3;
  135.     private double si3;
  136.     private double sl3;
  137.     private double sgh3;
  138.     private double sh3;
  139.     private double sl4;
  140.     private double sgh4;

  142.     private double del1;
  143.     private double del2;
  144.     private double del3;
  145.     private double xfact;
  146.     private double xli;
  147.     private double xni;
  148.     private double atime;

  150.     private double pe;
  151.     private double pinc;
  152.     private double pl;
  153.     private double pgh;
  154.     private double ph;

  156.     private double[] derivs;

  158.     // CHECKSTYLE: resume JavadocVariable check

  160.     /** Flag for resonant orbits. */
  161.     private boolean resonant;

  163.     /** Flag for synchronous orbits. */
  164.     private boolean synchronous;

  166.     /** Flag for compliance with Dundee modifications. */
  167.     private boolean isDundeeCompliant = true;

  169.     /** Constructor for a unique initial TLE.
  170.      *
  171.      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
  172.      *
  173.      * @param initialTLE the TLE to propagate.
  174.      * @param attitudeProvider provider for attitude computation
  175.      * @param mass spacecraft mass (kg)
  176.      * @see #DeepSDP4(TLE, AttitudeProvider, double, Frame)
  177.      */
  178.     @DefaultDataContext
  179.     public DeepSDP4(final TLE initialTLE, final AttitudeProvider attitudeProvider,
  180.                     final double mass) {
  181.         this(initialTLE, attitudeProvider, mass,
  182.                 DataContext.getDefault().getFrames().getTEME());
  183.     }

  185.     /** Constructor for a unique initial TLE.
  186.      * @param initialTLE the TLE to propagate.
  187.      * @param attitudeProvider provider for attitude computation
  188.      * @param mass spacecraft mass (kg)
  189.      * @param teme the TEME frame to use for propagation.
  190.      * @since 10.1
  191.      */
  192.     public DeepSDP4(final TLE initialTLE,
  193.                     final AttitudeProvider attitudeProvider,
  194.                     final double mass,
  195.                     final Frame teme) {
  196.         super(initialTLE, attitudeProvider, mass, teme);
  197.     }

  199.     /** Computes luni - solar terms from initial coordinates and epoch.
  200.      */
  201.     protected void luniSolarTermsComputation() {

  203.         final double sing = FastMath.sin(tle.getPerigeeArgument());
  204.         final double cosg = FastMath.cos(tle.getPerigeeArgument());

  206.         final double sinq = FastMath.sin(tle.getRaan());
  207.         final double cosq = FastMath.cos(tle.getRaan());
  208.         final double aqnv = 1.0 / a0dp;

  210.         // Compute julian days since 1900
  211.         final double daysSince1900 = (tle.getDate()
  212.                 .getComponents(utc)
  213.                 .offsetFrom(DateTimeComponents.JULIAN_EPOCH)) /
  214.                 Constants.JULIAN_DAY - 2415020;

  216.         double cc = C1SS;
  217.         double ze = ZES;
  218.         double zn = ZNS;
  219.         double zsinh = sinq;
  220.         double zcosh = cosq;

  222.         thgr = thetaG(tle.getDate());
  223.         xnq = xn0dp;
  224.         omegaq = tle.getPerigeeArgument();

  226.         final double xnodce = 4.5236020 - 9.2422029e-4 * daysSince1900;
  227.         final double stem = FastMath.sin(xnodce);
  228.         final double ctem = FastMath.cos(xnodce);
  229.         final double c_minus_gam = 0.228027132 * daysSince1900 - 1.1151842;
  230.         final double gam = 5.8351514 + 0.0019443680 * daysSince1900;

  232.         zcosil = 0.91375164 - 0.03568096 * ctem;
  233.         zsinil = FastMath.sqrt(1.0 - zcosil * zcosil);
  234.         zsinhl = 0.089683511 * stem / zsinil;
  235.         zcoshl = FastMath.sqrt(1.0 - zsinhl * zsinhl);
  236.         zmol = MathUtils.normalizeAngle(c_minus_gam, FastMath.PI);

  238.         double zx = 0.39785416 * stem / zsinil;
  239.         final double zy = zcoshl * ctem + 0.91744867 * zsinhl * stem;
  240.         zx = FastMath.atan2( zx, zy) + gam - xnodce;
  241.         zcosgl = FastMath.cos( zx);
  242.         zsingl = FastMath.sin( zx);
  243.         zmos = MathUtils.normalizeAngle(6.2565837 + 0.017201977 * daysSince1900, FastMath.PI);

  245.         // Do solar terms
  246.         savtsn = 1e20;

  248.         double zcosi =  0.91744867;
  249.         double zsini =  0.39785416;
  250.         double zsing = -0.98088458;
  251.         double zcosg =  0.1945905;

  253.         double se = 0;
  254.         double sgh = 0;
  255.         double sh = 0;
  256.         double si = 0;
  257.         double sl = 0;

  259.         // There was previously some convoluted logic here, but it boils
  260.         // down to this:  we compute the solar terms,  then the lunar terms.
  261.         // On a second pass,  we recompute the solar terms, taking advantage
  262.         // of the improved data that resulted from computing lunar terms.
  263.         for (int iteration = 0; iteration < 2; ++iteration) {
  264.             final double a1 = zcosg * zcosh + zsing * zcosi * zsinh;
  265.             final double a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
  266.             final double a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
  267.             final double a8 = zsing * zsini;
  268.             final double a9 = zsing * zsinh + zcosg * zcosi * zcosh;
  269.             final double a10 = zcosg * zsini;
  270.             final double a2 = cosi0 * a7 + sini0 * a8;
  271.             final double a4 = cosi0 * a9 + sini0 * a10;
  272.             final double a5 = -sini0 * a7 + cosi0 * a8;
  273.             final double a6 = -sini0 * a9 + cosi0 * a10;
  274.             final double x1 = a1 * cosg + a2 * sing;
  275.             final double x2 = a3 * cosg + a4 * sing;
  276.             final double x3 = -a1 * sing + a2 * cosg;
  277.             final double x4 = -a3 * sing + a4 * cosg;
  278.             final double x5 = a5 * sing;
  279.             final double x6 = a6 * sing;
  280.             final double x7 = a5 * cosg;
  281.             final double x8 = a6 * cosg;
  282.             final double z31 = 12 * x1 * x1 - 3 * x3 * x3;
  283.             final double z32 = 24 * x1 * x2 - 6 * x3 * x4;
  284.             final double z33 = 12 * x2 * x2 - 3 * x4 * x4;
  285.             final double z11 = -6 * a1 * a5 + e0sq * (-24 * x1 * x7 - 6 * x3 * x5);
  286.             final double z12 = -6 * (a1 * a6 + a3 * a5) +
  287.                                e0sq * (-24 * (x2 * x7 + x1 * x8) - 6 * (x3 * x6 + x4 * x5));
  288.             final double z13 = -6 * a3 * a6 + e0sq * (-24 * x2 * x8 - 6 * x4 * x6);
  289.             final double z21 = 6 * a2 * a5 + e0sq * (24 * x1 * x5 - 6 * x3 * x7);
  290.             final double z22 = 6 * (a4 * a5 + a2 * a6) +
  291.                                e0sq * (24 * (x2 * x5 + x1 * x6) - 6 * (x4 * x7 + x3 * x8));
  292.             final double z23 = 6 * a4 * a6 + e0sq * (24 * x2 * x6 - 6 * x4 * x8);
  293.             final double s3 = cc / xnq;
  294.             final double s2 = -0.5 * s3 / beta0;
  295.             final double s4 = s3 * beta0;
  296.             final double s1 = -15 * tle.getE() * s4;
  297.             final double s5 = x1 * x3 + x2 * x4;
  298.             final double s6 = x2 * x3 + x1 * x4;
  299.             final double s7 = x2 * x4 - x1 * x3;
  300.             double z1 = 3 * (a1 * a1 + a2 * a2) + z31 * e0sq;
  301.             double z2 = 6 * (a1 * a3 + a2 * a4) + z32 * e0sq;
  302.             double z3 = 3 * (a3 * a3 + a4 * a4) + z33 * e0sq;

  304.             z1 = z1 + z1 + beta02 * z31;
  305.             z2 = z2 + z2 + beta02 * z32;
  306.             z3 = z3 + z3 + beta02 * z33;
  307.             se = s1 * zn * s5;
  308.             si = s2 * zn * (z11 + z13);
  309.             sl = -zn * s3 * (z1 + z3 - 14 - 6 * e0sq);
  310.             sgh = s4 * zn * (z31 + z33 - 6);
  311.             if (tle.getI() < (FastMath.PI / 60.0)) {
  312.                 // inclination smaller than 3 degrees
  313.                 sh = 0;
  314.             } else {
  315.                 sh = -zn * s2 * (z21 + z23);
  316.             }
  317.             ee2  =  2 * s1 * s6;
  318.             e3   =  2 * s1 * s7;
  319.             xi2  =  2 * s2 * z12;
  320.             xi3  =  2 * s2 * (z13 - z11);
  321.             xl2  = -2 * s3 * z2;
  322.             xl3  = -2 * s3 * (z3 - z1);
  323.             xl4  = -2 * s3 * (-21 - 9 * e0sq) * ze;
  324.             xgh2 =  2 * s4 * z32;
  325.             xgh3 =  2 * s4 * (z33 - z31);
  326.             xgh4 = -18 * s4 * ze;
  327.             xh2  = -2 * s2 * z22;
  328.             xh3  = -2 * s2 * (z23 - z21);

  330.             if (iteration == 0) { // we compute lunar terms only on the first pass:
  331.                 sse = se;
  332.                 ssi = si;
  333.                 ssl = sl;
  334.                 ssh = (tle.getI() < (FastMath.PI / 60.0)) ? 0 : sh / sini0;
  335.                 ssg = sgh - cosi0 * ssh;
  336.                 se2 = ee2;
  337.                 si2 = xi2;
  338.                 sl2 = xl2;
  339.                 sgh2 = xgh2;
  340.                 sh2 = xh2;
  341.                 se3 = e3;
  342.                 si3 = xi3;
  343.                 sl3 = xl3;
  344.                 sgh3 = xgh3;
  345.                 sh3 = xh3;
  346.                 sl4 = xl4;
  347.                 sgh4 = xgh4;
  348.                 zcosg = zcosgl;
  349.                 zsing = zsingl;
  350.                 zcosi = zcosil;
  351.                 zsini = zsinil;
  352.                 zcosh = zcoshl * cosq + zsinhl * sinq;
  353.                 zsinh = sinq * zcoshl - cosq * zsinhl;
  354.                 zn = ZNL;
  355.                 cc = C1L;
  356.                 ze = ZEL;
  357.             }
  358.         } // end of solar - lunar - solar terms computation

  360.         sse += se;
  361.         ssi += si;
  362.         ssl += sl;
  363.         ssg += sgh - ((tle.getI() < (FastMath.PI / 60.0)) ? 0 : (cosi0 / sini0 * sh));
  364.         ssh += (tle.getI() < (FastMath.PI / 60.0)) ? 0 : sh / sini0;



  368.         //        Start the resonant-synchronous tests and initialization

  370.         double bfact = 0;

  372.         // if mean motion is 1.893053 to 2.117652 revs/day, and eccentricity >= 0.5,
  373.         // start of the 12-hour orbit, e > 0.5 section
  374.         if ((xnq >= 0.00826) && (xnq <= 0.00924) && (tle.getE() >= 0.5)) {

  376.             final double g201 = -0.306 - (tle.getE() - 0.64) * 0.440;
  377.             final double eoc = tle.getE() * e0sq;
  378.             final double sini2 = sini0 * sini0;
  379.             final double f220 = 0.75 * (1 + 2 * cosi0 + theta2);
  380.             final double f221 = 1.5 * sini2;
  381.             final double f321 =  1.875 * sini0 * (1 - 2 * cosi0 - 3 * theta2);
  382.             final double f322 = -1.875 * sini0 * (1 + 2 * cosi0 - 3 * theta2);
  383.             final double f441 = 35 * sini2 * f220;
  384.             final double f442 = 39.3750 * sini2 * sini2;
  385.             final double f522 = 9.84375 * sini0 * (sini2 * (1 - 2 * cosi0 - 5 * theta2) +
  386.                                                    0.33333333 * (-2 + 4 * cosi0 + 6 * theta2));
  387.             final double f523 = sini0 * (4.92187512 * sini2 * (-2 - 4 * cosi0 + 10 * theta2) +
  388.                                          6.56250012 * (1 + 2 * cosi0 - 3 * theta2));
  389.             final double f542 = 29.53125 * sini0 * (2 - 8 * cosi0 + theta2 * (-12 + 8 * cosi0 + 10 * theta2));
  390.             final double f543 = 29.53125 * sini0 * (-2 - 8 * cosi0 + theta2 * (12 + 8 * cosi0 - 10 * theta2));
  391.             final double g211;
  392.             final double g310;
  393.             final double g322;
  394.             final double g410;
  395.             final double g422;
  396.             final double g520;

  398.             resonant = true;       // it is resonant...
  399.             synchronous = false;     // but it's not synchronous

  401.             // Geopotential resonance initialization for 12 hour orbits :
  402.             if (tle.getE() <= 0.65) {
  403.                 g211 =    3.616  -   13.247  * tle.getE() +   16.290  * e0sq;
  404.                 g310 =  -19.302  +  117.390  * tle.getE() -  228.419  * e0sq +  156.591  * eoc;
  405.                 g322 =  -18.9068 +  109.7927 * tle.getE() -  214.6334 * e0sq +  146.5816 * eoc;
  406.                 g410 =  -41.122  +  242.694  * tle.getE() -  471.094  * e0sq +  313.953  * eoc;
  407.                 g422 = -146.407  +  841.880  * tle.getE() - 1629.014  * e0sq + 1083.435  * eoc;
  408.                 g520 = -532.114  + 3017.977  * tle.getE() - 5740.032  * e0sq + 3708.276  * eoc;
  409.             } else  {
  410.                 g211 =   -72.099 +   331.819 * tle.getE() -   508.738 * e0sq +   266.724 * eoc;
  411.                 g310 =  -346.844 +  1582.851 * tle.getE() -  2415.925 * e0sq +  1246.113 * eoc;
  412.                 g322 =  -342.585 +  1554.908 * tle.getE() -  2366.899 * e0sq +  1215.972 * eoc;
  413.                 g410 = -1052.797 +  4758.686 * tle.getE() -  7193.992 * e0sq +  3651.957 * eoc;
  414.                 g422 = -3581.69  + 16178.11  * tle.getE() - 24462.77  * e0sq + 12422.52  * eoc;
  415.                 if (tle.getE() <= 0.715) {
  416.                     g520 = 1464.74 - 4664.75 * tle.getE() + 3763.64 * e0sq;
  417.                 } else {
  418.                     g520 = -5149.66 + 29936.92 * tle.getE() - 54087.36 * e0sq + 31324.56 * eoc;
  419.                 }
  420.             }

  422.             final double g533;
  423.             final double g521;
  424.             final double g532;
  425.             if (tle.getE() < 0.7) {
  426.                 g533 = -919.2277  + 4988.61   * tle.getE() - 9064.77   * e0sq + 5542.21  * eoc;
  427.                 g521 = -822.71072 + 4568.6173 * tle.getE() - 8491.4146 * e0sq + 5337.524 * eoc;
  428.                 g532 = -853.666   + 4690.25   * tle.getE() - 8624.77   * e0sq + 5341.4   * eoc;
  429.             } else {
  430.                 g533 = -37995.78  + 161616.52 * tle.getE() - 229838.2  * e0sq + 109377.94 * eoc;
  431.                 g521 = -51752.104 + 218913.95 * tle.getE() - 309468.16 * e0sq + 146349.42 * eoc;
  432.                 g532 = -40023.88  + 170470.89 * tle.getE() - 242699.48 * e0sq + 115605.82 * eoc;
  433.             }

  435.             double temp1 = 3 * xnq * xnq * aqnv * aqnv;
  436.             double temp = temp1 * ROOT22;
  437.             d2201 = temp * f220 * g201;
  438.             d2211 = temp * f221 * g211;
  439.             temp1 *= aqnv;
  440.             temp = temp1 * ROOT32;
  441.             d3210 = temp * f321 * g310;
  442.             d3222 = temp * f322 * g322;
  443.             temp1 *= aqnv;
  444.             temp = 2 * temp1 * ROOT44;
  445.             d4410 = temp * f441 * g410;
  446.             d4422 = temp * f442 * g422;
  447.             temp1 *= aqnv;
  448.             temp = temp1 * ROOT52;
  449.             d5220 = temp * f522 * g520;
  450.             d5232 = temp * f523 * g532;
  451.             temp = 2 * temp1 * ROOT54;
  452.             d5421 = temp * f542 * g521;
  453.             d5433 = temp * f543 * g533;
  454.             xlamo = tle.getMeanAnomaly() + tle.getRaan() + tle.getRaan() - thgr - thgr;
  455.             bfact = xmdot + xnodot + xnodot - THDT - THDT;
  456.             bfact += ssl + ssh + ssh;
  457.         } else if ((xnq < 0.0052359877) && (xnq > 0.0034906585)) {
  458.             // if mean motion is .8 to 1.2 revs/day : (geosynch)

  460.             final double cosio_plus_1 = 1.0 + cosi0;
  461.             final double g200 = 1 + e0sq * (-2.5 + 0.8125  * e0sq);
  462.             final double g300 = 1 + e0sq * (-6   + 6.60937 * e0sq);
  463.             final double f311 = 0.9375 * sini0 * sini0 * (1 + 3 * cosi0) - 0.75 * cosio_plus_1;
  464.             final double g310 = 1 + 2 * e0sq;
  465.             final double f220 = 0.75 * cosio_plus_1 * cosio_plus_1;
  466.             final double f330 = 2.5 * f220 * cosio_plus_1;

  468.             resonant = true;
  469.             synchronous = true;

  471.             // Synchronous resonance terms initialization
  472.             del1 = 3 * xnq * xnq * aqnv * aqnv;
  473.             del2 = 2 * del1 * f220 * g200 * Q22;
  474.             del3 = 3 * del1 * f330 * g300 * Q33 * aqnv;
  475.             del1 = del1 * f311 * g310 * Q31 * aqnv;
  476.             xlamo = tle.getMeanAnomaly() + tle.getRaan() + tle.getPerigeeArgument() - thgr;
  477.             bfact = xmdot + omgdot + xnodot - THDT;
  478.             bfact = bfact + ssl + ssg + ssh;
  479.         } else {
  480.             // it's neither a high-e 12-hours orbit nor a geosynchronous:
  481.             resonant = false;
  482.             synchronous = false;
  483.         }

  485.         if (resonant) {
  486.             xfact = bfact - xnq;

  488.             // Initialize integrator
  489.             xli   = xlamo;
  490.             xni   = xnq;
  491.             atime = 0;
  492.         }
  493.         derivs = new double[2];
  494.     }

  496.     /** Computes secular terms from current coordinates and epoch.
  497.      * @param t offset from initial epoch (minutes)
  498.      */
  499.     protected void deepSecularEffects(final double t)  {

  501.         xll    += ssl * t;
  502.         omgadf += ssg * t;
  503.         xnode  += ssh * t;
  504.         em      = tle.getE() + sse * t;
  505.         xinc    = tle.getI() + ssi * t;

  507.         if (resonant) {
  508.             // If we're closer to t = 0 than to the currently-stored data
  509.             // from the previous call to this function,  then we're
  510.             // better off "restarting",  going back to the initial data.
  511.             // The Dundee code rigs things up to _always_ take 720-minute
  512.             // steps from epoch to end time,  except for the final step.
  513.             // Easiest way to arrange similar behavior in this code is
  514.             // just to always do a restart,  if we're in Dundee-compliant
  515.             // mode.
  516.             if (FastMath.abs(t) < FastMath.abs(t - atime) || isDundeeCompliant)  {
  517.                 // Epoch restart
  518.                 atime = 0;
  519.                 xni = xnq;
  520.                 xli = xlamo;
  521.             }
  522.             boolean lastIntegrationStep = false;
  523.             // if |step|>|step max| then do one step at step max
  524.             while (!lastIntegrationStep) {
  525.                 double delt = t - atime;
  526.                 if (delt > SECULAR_INTEGRATION_STEP) {
  527.                     delt = SECULAR_INTEGRATION_STEP;
  528.                 } else if (delt < -SECULAR_INTEGRATION_STEP) {
  529.                     delt = -SECULAR_INTEGRATION_STEP;
  530.                 } else {
  531.                     lastIntegrationStep = true;
  532.                 }

  534.                 computeSecularDerivs();

  536.                 final double xldot = xni + xfact;

  538.                 double xlpow = 1.;
  539.                 xli += delt * xldot;
  540.                 xni += delt * derivs[0];
  541.                 double delt_factor = delt;
  542.                 xlpow *= xldot;
  543.                 derivs[1] *= xlpow;
  544.                 delt_factor *= delt / 2;
  545.                 xli += delt_factor * derivs[0];
  546.                 xni += delt_factor * derivs[1];
  547.                 atime += delt;
  548.             }
  549.             xn = xni;
  550.             final double temp = -xnode + thgr + t * THDT;
  551.             xll = xli + temp + (synchronous ? -omgadf : temp);
  552.         }
  553.     }

  555.     /** Computes periodic terms from current coordinates and epoch.
  556.      * @param t offset from initial epoch (min)
  557.      */
  558.     protected void deepPeriodicEffects(final double t)  {

  560.         // If the time didn't change by more than 30 minutes,
  561.         // there's no good reason to recompute the perturbations;
  562.         // they don't change enough over so short a time span.
  563.         // However,  the Dundee code _always_ recomputes,  so if
  564.         // we're attempting to replicate its results,  we've gotta
  565.         // recompute everything,  too.
  566.         if ((FastMath.abs(savtsn - t) >= 30.0) || isDundeeCompliant)  {

  568.             savtsn = t;

  570.             // Update solar perturbations for time T
  571.             double zm = zmos + ZNS * t;
  572.             double zf = zm + 2 * ZES * FastMath.sin(zm);
  573.             double sinzf = FastMath.sin(zf);
  574.             double f2 = 0.5 * sinzf * sinzf - 0.25;
  575.             double f3 = -0.5 * sinzf * FastMath.cos(zf);
  576.             final double ses = se2 * f2 + se3 * f3;
  577.             final double sis = si2 * f2 + si3 * f3;
  578.             final double sls = sl2 * f2 + sl3 * f3 + sl4 * sinzf;
  579.             final double sghs = sgh2 * f2 + sgh3 * f3 + sgh4 * sinzf;
  580.             final double shs = sh2 * f2 + sh3 * f3;

  582.             // Update lunar perturbations for time T
  583.             zm = zmol + ZNL * t;
  584.             zf = zm + 2 * ZEL * FastMath.sin(zm);
  585.             sinzf = FastMath.sin(zf);
  586.             f2 =  0.5 * sinzf * sinzf - 0.25;
  587.             f3 = -0.5 * sinzf * FastMath.cos(zf);
  588.             final double sel = ee2 * f2 + e3 * f3;
  589.             final double sil = xi2 * f2 + xi3 * f3;
  590.             final double sll = xl2 * f2 + xl3 * f3 + xl4 * sinzf;
  591.             final double sghl = xgh2 * f2 + xgh3 * f3 + xgh4 * sinzf;
  592.             final double sh1 = xh2 * f2 + xh3 * f3;

  594.             // Sum the solar and lunar contributions
  595.             pe   = ses  + sel;
  596.             pinc = sis  + sil;
  597.             pl   = sls  + sll;
  598.             pgh  = sghs + sghl;
  599.             ph   = shs  + sh1;
  600.         }

  602.         xinc += pinc;

  604.         final double sinis = FastMath.sin( xinc);
  605.         final double cosis = FastMath.cos( xinc);

  607.         /* Add solar/lunar perturbation correction to eccentricity: */
  608.         em     += pe;
  609.         xll    += pl;
  610.         omgadf += pgh;
  611.         xinc    = MathUtils.normalizeAngle(xinc, 0);

  613.         if (FastMath.abs(xinc) >= 0.2) {
  614.             // Apply periodics directly
  615.             final double temp_val = ph / sinis;
  616.             omgadf -= cosis * temp_val;
  617.             xnode += temp_val;
  618.         } else {
  619.             // Apply periodics with Lyddane modification
  620.             final double sinok = FastMath.sin(xnode);
  621.             final double cosok = FastMath.cos(xnode);
  622.             final double alfdp =  ph * cosok + (pinc * cosis + sinis) * sinok;
  623.             final double betdp = -ph * sinok + (pinc * cosis + sinis) * cosok;
  624.             final double delta_xnode = MathUtils.normalizeAngle(FastMath.atan2(alfdp, betdp) - xnode, 0);
  625.             final double dls = -xnode * sinis * pinc;
  626.             omgadf += dls - cosis * delta_xnode;
  627.             xnode  += delta_xnode;
  628.         }
  629.     }

  631.     /** Computes internal secular derivs. */
  632.     private void computeSecularDerivs() {

  634.         final double sin_li = FastMath.sin(xli);
  635.         final double cos_li = FastMath.cos(xli);
  636.         final double sin_2li = 2. * sin_li * cos_li;
  637.         final double cos_2li = 2. * cos_li * cos_li - 1.;

  639.         // Dot terms calculated :
  640.         if (synchronous)  {
  641.             final double sin_3li = sin_2li * cos_li + cos_2li * sin_li;
  642.             final double cos_3li = cos_2li * cos_li - sin_2li * sin_li;
  643.             final double term1a = del1 * (sin_li  * C_FASX2  - cos_li  * S_FASX2);
  644.             final double term2a = del2 * (sin_2li * C_2FASX4 - cos_2li * S_2FASX4);
  645.             final double term3a = del3 * (sin_3li * C_3FASX6 - cos_3li * S_3FASX6);
  646.             final double term1b = del1 * (cos_li  * C_FASX2  + sin_li  * S_FASX2);
  647.             final double term2b = 2.0 * del2 * (cos_2li * C_2FASX4 + sin_2li * S_2FASX4);
  648.             final double term3b = 3.0 * del3 * (cos_3li * C_3FASX6 + sin_3li * S_3FASX6);
  649.             derivs[0] = term1a + term2a + term3a;
  650.             derivs[1] = term1b + term2b + term3b;
  651.         } else {
  652.             // orbit is a 12-hour resonant one
  653.             final double xomi = omegaq + omgdot * atime;
  654.             final double sin_omi = FastMath.sin(xomi);
  655.             final double cos_omi = FastMath.cos(xomi);
  656.             final double sin_li_m_omi = sin_li * cos_omi - sin_omi * cos_li;
  657.             final double sin_li_p_omi = sin_li * cos_omi + sin_omi * cos_li;
  658.             final double cos_li_m_omi = cos_li * cos_omi + sin_omi * sin_li;
  659.             final double cos_li_p_omi = cos_li * cos_omi - sin_omi * sin_li;
  660.             final double sin_2omi = 2. * sin_omi * cos_omi;
  661.             final double cos_2omi = 2. * cos_omi * cos_omi - 1.;
  662.             final double sin_2li_m_omi = sin_2li * cos_omi - sin_omi * cos_2li;
  663.             final double sin_2li_p_omi = sin_2li * cos_omi + sin_omi * cos_2li;
  664.             final double cos_2li_m_omi = cos_2li * cos_omi + sin_omi * sin_2li;
  665.             final double cos_2li_p_omi = cos_2li * cos_omi - sin_omi * sin_2li;
  666.             final double sin_2li_p_2omi = sin_2li * cos_2omi + sin_2omi * cos_2li;
  667.             final double cos_2li_p_2omi = cos_2li * cos_2omi - sin_2omi * sin_2li;
  668.             final double sin_2omi_p_li = sin_li * cos_2omi + sin_2omi * cos_li;
  669.             final double cos_2omi_p_li = cos_li * cos_2omi - sin_2omi * sin_li;
  670.             final double term1a = d2201 * (sin_2omi_p_li * C_G22 - cos_2omi_p_li * S_G22) +
  671.                                   d2211 * (sin_li * C_G22 - cos_li * S_G22) +
  672.                                   d3210 * (sin_li_p_omi * C_G32 - cos_li_p_omi * S_G32) +
  673.                                   d3222 * (sin_li_m_omi * C_G32 - cos_li_m_omi * S_G32) +
  674.                                   d5220 * (sin_li_p_omi * C_G52 - cos_li_p_omi * S_G52) +
  675.                                   d5232 * (sin_li_m_omi * C_G52 - cos_li_m_omi * S_G52);
  676.             final double term2a = d4410 * (sin_2li_p_2omi * C_G44 - cos_2li_p_2omi * S_G44) +
  677.                                   d4422 * (sin_2li * C_G44 - cos_2li * S_G44) +
  678.                                   d5421 * (sin_2li_p_omi * C_G54 - cos_2li_p_omi * S_G54) +
  679.                                   d5433 * (sin_2li_m_omi * C_G54 - cos_2li_m_omi * S_G54);
  680.             final double term1b = d2201 * (cos_2omi_p_li * C_G22 + sin_2omi_p_li * S_G22) +
  681.                                   d2211 * (cos_li * C_G22 + sin_li * S_G22) +
  682.                                   d3210 * (cos_li_p_omi * C_G32 + sin_li_p_omi * S_G32) +
  683.                                   d3222 * (cos_li_m_omi * C_G32 + sin_li_m_omi * S_G32) +
  684.                                   d5220 * (cos_li_p_omi * C_G52 + sin_li_p_omi * S_G52) +
  685.                                   d5232 * (cos_li_m_omi * C_G52 + sin_li_m_omi * S_G52);
  686.             final double term2b = 2.0 * (d4410 * (cos_2li_p_2omi * C_G44 + sin_2li_p_2omi * S_G44) +
  687.                                          d4422 * (cos_2li * C_G44 + sin_2li * S_G44) +
  688.                                          d5421 * (cos_2li_p_omi * C_G54 + sin_2li_p_omi * S_G54) +
  689.                                          d5433 * (cos_2li_m_omi * C_G54 + sin_2li_m_omi * S_G54));

  691.             derivs[0] = term1a + term2a;
  692.             derivs[1] = term1b + term2b;

  694.         }
  695.     }

  697. }
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