| 1 |
//
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| 2 |
// cNoradSDP4.cpp
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| 3 |
//
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// NORAD SDP4 implementation. See historical note in cNoradBase.cpp
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// Copyright (c) 2003 Michael F. Henry
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//
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// mfh 12/07/2003
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//
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#include "stdafx.h"
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#include "cNoradSDP4.h"
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#include "cTle.h"
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#include "coord.h"
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#include "cOrbit.h"
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#include "cVector.h"
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const double zns = 1.19459E-5; const double c1ss = 2.9864797E-6;
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const double zes = 0.01675; const double znl = 1.5835218E-4;
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const double c1l = 4.7968065E-7; const double zel = 0.05490;
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const double zcosis = 0.91744867; const double zsinis = 0.39785416;
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const double zsings = -0.98088458; const double zcosgs = 0.1945905;
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const double q22 = 1.7891679E-6; const double q31 = 2.1460748E-6;
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const double q33 = 2.2123015E-7; const double g22 = 5.7686396;
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const double g32 = 0.95240898; const double g44 = 1.8014998;
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const double g52 = 1.0508330; const double g54 = 4.4108898;
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const double root22 = 1.7891679E-6; const double root32 = 3.7393792E-7;
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const double root44 = 7.3636953E-9; const double root52 = 1.1428639E-7;
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const double root54 = 2.1765803E-9; const double thdt = 4.3752691E-3;
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//////////////////////////////////////////////////////////////////////////////
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cNoradSDP4::cNoradSDP4(const cOrbit &orbit) :
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cNoradBase(orbit)
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{
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m_sing = sin(m_Orbit.ArgPerigee());
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m_cosg = cos(m_Orbit.ArgPerigee());
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dp_savtsn = 0.0;
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dp_zmos = 0.0;
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dp_se2 = 0.0;
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dp_se3 = 0.0;
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dp_si2 = 0.0;
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dp_si3 = 0.0;
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dp_sl2 = 0.0;
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dp_sl3 = 0.0;
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dp_sl4 = 0.0;
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dp_sghs = 0.0;
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dp_sgh2 = 0.0;
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dp_sgh3 = 0.0;
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dp_sgh4 = 0.0;
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dp_sh2 = 0.0;
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dp_sh3 = 0.0;
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dp_zmol = 0.0;
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dp_ee2 = 0.0;
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dp_e3 = 0.0;
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dp_xi2 = 0.0;
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dp_xi3 = 0.0;
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dp_xl2 = 0.0;
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dp_xl3 = 0.0;
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dp_xl4 = 0.0;
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dp_xgh2 = 0.0;
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dp_xgh3 = 0.0;
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dp_xgh4 = 0.0;
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dp_xh2 = 0.0;
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dp_xh3 = 0.0;
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dp_xqncl = 0.0;
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dp_thgr = 0.0;
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dp_omegaq = 0.0;
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dp_sse = 0.0;
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dp_ssi = 0.0;
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dp_ssl = 0.0;
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dp_ssh = 0.0;
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dp_ssg = 0.0;
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dp_d2201 = 0.0;
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dp_d2211 = 0.0;
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dp_d3210 = 0.0;
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dp_d3222 = 0.0;
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dp_d4410 = 0.0;
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dp_d4422 = 0.0;
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dp_d5220 = 0.0;
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dp_d5232 = 0.0;
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dp_d5421 = 0.0;
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dp_d5433 = 0.0;
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dp_xlamo = 0.0;
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dp_del1 = 0.0;
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dp_del2 = 0.0;
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dp_del3 = 0.0;
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dp_fasx2 = 0.0;
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dp_fasx4 = 0.0;
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dp_fasx6 = 0.0;
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dp_xfact = 0.0;
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dp_xli = 0.0;
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dp_xni = 0.0;
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dp_atime = 0.0;
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dp_stepp = 0.0;
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dp_stepn = 0.0;
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dp_step2 = 0.0;
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dp_iresfl = false;
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dp_isynfl = false;
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}
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cNoradSDP4::~cNoradSDP4(void)
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{
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}
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//////////////////////////////////////////////////////////////////////////////
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bool cNoradSDP4::DeepInit(double *eosq, double *sinio, double *cosio,
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double *betao, double *aodp, double *theta2,
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double *sing, double *cosg, double *betao2,
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double *xmdot, double *omgdot, double *xnodott)
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{
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eqsq = *eosq;
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siniq = *sinio;
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cosiq = *cosio;
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rteqsq = *betao;
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ao = *aodp;
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cosq2 = *theta2;
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sinomo = *sing;
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cosomo = *cosg;
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bsq = *betao2;
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xlldot = *xmdot;
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omgdt = *omgdot;
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xnodot = *xnodott;
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// Deep space initialization
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cJulian jd = m_Orbit.Epoch();
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dp_thgr = jd.toGMST();
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double eq = m_Orbit.Eccentricity();
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double aqnv = 1.0 / ao;
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dp_xqncl = m_Orbit.Inclination();
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double xmao = m_Orbit.mnAnomaly();
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double xpidot = omgdt + xnodot;
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double sinq = sin(m_Orbit.RAAN());
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double cosq = cos(m_Orbit.RAAN());
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dp_omegaq = m_Orbit.ArgPerigee();
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// Initialize lunar solar terms
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double day = jd.FromJan1_12h_1900();
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if (day != dpi_day)
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{
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dpi_day = day;
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dpi_xnodce = 4.5236020 - 9.2422029E-4 * day;
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dpi_stem = sin(dpi_xnodce);
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dpi_ctem = cos(dpi_xnodce);
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dpi_zcosil = 0.91375164 - 0.03568096 * dpi_ctem;
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dpi_zsinil = sqrt(1.0 - dpi_zcosil * dpi_zcosil);
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dpi_zsinhl = 0.089683511 *dpi_stem / dpi_zsinil;
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dpi_zcoshl = sqrt(1.0 - dpi_zsinhl * dpi_zsinhl);
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dpi_c = 4.7199672 + 0.22997150 * day;
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dpi_gam = 5.8351514 + 0.0019443680 * day;
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dp_zmol = Fmod2p(dpi_c - dpi_gam);
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dpi_zx = 0.39785416 * dpi_stem / dpi_zsinil;
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dpi_zy = dpi_zcoshl * dpi_ctem + 0.91744867 * dpi_zsinhl * dpi_stem;
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dpi_zx = AcTan(dpi_zx,dpi_zy) + dpi_gam - dpi_xnodce;
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dpi_zcosgl = cos(dpi_zx);
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dpi_zsingl = sin(dpi_zx);
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dp_zmos = 6.2565837 + 0.017201977 * day;
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dp_zmos = Fmod2p(dp_zmos);
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}
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dp_savtsn = 1.0e20;
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double zcosg = zcosgs;
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double zsing = zsings;
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double zcosi = zcosis;
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double zsini = zsinis;
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double zcosh = cosq;
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double zsinh = sinq;
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double cc = c1ss;
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double zn = zns;
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double ze = zes;
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double zmo = dp_zmos;
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double xnoi = 1.0 / m_xnodp;
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double a1; double a3; double a7; double a8; double a9; double a10;
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double a2; double a4; double a5; double a6; double x1; double x2;
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double x3; double x4; double x5; double x6; double x7; double x8;
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double z31; double z32; double z33; double z1; double z2; double z3;
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double z11; double z12; double z13; double z21; double z22; double z23;
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double s3; double s2; double s4; double s1; double s5; double s6;
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double s7;
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double se = 0.0; double si = 0.0; double sl = 0.0;
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double sgh = 0.0; double sh = 0.0;
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// Apply the solar and lunar terms on the first pass, then re-apply the
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// solar terms again on the second pass.
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for (int pass = 1; pass <= 2; pass++)
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{
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// Do solar terms
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a1 = zcosg * zcosh + zsing * zcosi * zsinh;
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a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
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a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
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a8 = zsing * zsini;
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a9 = zsing * zsinh + zcosg * zcosi * zcosh;
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a10 = zcosg * zsini;
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a2 = cosiq * a7 + siniq * a8;
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a4 = cosiq * a9 + siniq * a10;
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a5 = -siniq * a7 + cosiq * a8;
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a6 = -siniq * a9 + cosiq * a10;
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x1 = a1 * cosomo + a2 * sinomo;
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x2 = a3 * cosomo + a4 * sinomo;
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x3 = -a1 * sinomo + a2 * cosomo;
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x4 = -a3 * sinomo + a4 * cosomo;
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x5 = a5 * sinomo;
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| 213 |
x6 = a6 * sinomo;
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x7 = a5 * cosomo;
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| 215 |
x8 = a6 * cosomo;
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| 216 |
z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3;
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| 217 |
z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4;
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| 218 |
z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4;
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| 219 |
z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * eqsq;
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| 220 |
z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * eqsq;
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| 221 |
z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * eqsq;
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| 222 |
z11 = -6.0 * a1 * a5 + eqsq*(-24.0 * x1 * x7 - 6.0 * x3 * x5);
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| 223 |
z12 = -6.0 * (a1 * a6 + a3 * a5) +
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| 224 |
eqsq * (-24.0 * (x2 * x7 + x1 * x8) - 6.0 * (x3 * x6 + x4 * x5));
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| 225 |
z13 = -6.0 * a3 * a6 + eqsq * (-24.0 * x2 * x8 - 6.0 * x4 * x6);
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| 226 |
z21 = 6.0 * a2 * a5 + eqsq * (24.0 * x1 * x5 - 6.0 * x3 * x7);
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| 227 |
z22 = 6.0*(a4 * a5 + a2 * a6) +
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| 228 |
eqsq * (24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8));
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| 229 |
z23 = 6.0 * a4 * a6 + eqsq*(24.0 * x2 * x6 - 6.0 * x4 * x8);
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| 230 |
z1 = z1 + z1 + bsq * z31;
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| 231 |
z2 = z2 + z2 + bsq * z32;
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| 232 |
z3 = z3 + z3 + bsq * z33;
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| 233 |
s3 = cc * xnoi;
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| 234 |
s2 = -0.5 * s3/rteqsq;
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| 235 |
s4 = s3 * rteqsq;
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| 236 |
s1 = -15.0 * eq * s4;
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| 237 |
s5 = x1 * x3 + x2 * x4;
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| 238 |
s6 = x2 * x3 + x1 * x4;
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| 239 |
s7 = x2 * x4 - x1 * x3;
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| 240 |
se = s1 * zn * s5;
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| 241 |
si = s2 * zn * (z11 + z13);
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| 242 |
sl = -zn * s3 * (z1 + z3 - 14.0 - 6.0 * eqsq);
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| 243 |
sgh = s4 * zn * (z31 + z33 - 6.0);
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| 244 |
sh = -zn * s2 * (z21 + z23);
|
| 245 |
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| 246 |
if (dp_xqncl < 5.2359877E-2)
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| 247 |
sh = 0.0;
|
| 248 |
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| 249 |
dp_ee2 = 2.0 * s1 * s6;
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| 250 |
dp_e3 = 2.0 * s1 * s7;
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| 251 |
dp_xi2 = 2.0 * s2 * z12;
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| 252 |
dp_xi3 = 2.0 * s2 * (z13 - z11);
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| 253 |
dp_xl2 = -2.0 * s3 * z2;
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| 254 |
dp_xl3 = -2.0 * s3 * (z3 - z1);
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| 255 |
dp_xl4 = -2.0 * s3 * (-21.0 - 9.0 * eqsq) * ze;
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| 256 |
dp_xgh2 = 2.0 * s4 * z32;
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| 257 |
dp_xgh3 = 2.0 * s4 * (z33 - z31);
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| 258 |
dp_xgh4 = -18.0 * s4 * ze;
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| 259 |
dp_xh2 = -2.0 * s2 * z22;
|
| 260 |
dp_xh3 = -2.0 * s2 * (z23 - z21);
|
| 261 |
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| 262 |
if (pass == 1)
|
| 263 |
{
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| 264 |
// Do lunar terms
|
| 265 |
dp_sse = se;
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| 266 |
dp_ssi = si;
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| 267 |
dp_ssl = sl;
|
| 268 |
dp_ssh = sh / siniq;
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| 269 |
dp_ssg = sgh - cosiq * dp_ssh;
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| 270 |
dp_se2 = dp_ee2;
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| 271 |
dp_si2 = dp_xi2;
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| 272 |
dp_sl2 = dp_xl2;
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| 273 |
dp_sgh2 = dp_xgh2;
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| 274 |
dp_sh2 = dp_xh2;
|
| 275 |
dp_se3 = dp_e3;
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| 276 |
dp_si3 = dp_xi3;
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| 277 |
dp_sl3 = dp_xl3;
|
| 278 |
dp_sgh3 = dp_xgh3;
|
| 279 |
dp_sh3 = dp_xh3;
|
| 280 |
dp_sl4 = dp_xl4;
|
| 281 |
dp_sgh4 = dp_xgh4;
|
| 282 |
zcosg = dpi_zcosgl;
|
| 283 |
zsing = dpi_zsingl;
|
| 284 |
zcosi = dpi_zcosil;
|
| 285 |
zsini = dpi_zsinil;
|
| 286 |
zcosh = dpi_zcoshl * cosq + dpi_zsinhl * sinq;
|
| 287 |
zsinh = sinq * dpi_zcoshl - cosq * dpi_zsinhl;
|
| 288 |
zn = znl;
|
| 289 |
cc = c1l;
|
| 290 |
ze = zel;
|
| 291 |
zmo = dp_zmol;
|
| 292 |
}
|
| 293 |
}
|
| 294 |
|
| 295 |
dp_sse = dp_sse + se;
|
| 296 |
dp_ssi = dp_ssi + si;
|
| 297 |
dp_ssl = dp_ssl + sl;
|
| 298 |
dp_ssg = dp_ssg + sgh - cosiq / siniq * sh;
|
| 299 |
dp_ssh = dp_ssh + sh / siniq;
|
| 300 |
|
| 301 |
// Geopotential resonance initialization for 12 hour orbits
|
| 302 |
dp_iresfl = false;
|
| 303 |
dp_isynfl = false;
|
| 304 |
|
| 305 |
bool bInitOnExit = true;
|
| 306 |
double g310;
|
| 307 |
double f220;
|
| 308 |
double bfact = 0.0;
|
| 309 |
|
| 310 |
if ((m_xnodp >= 0.0052359877) || (m_xnodp <= 0.0034906585))
|
| 311 |
{
|
| 312 |
if ((m_xnodp < 8.26E-3) || (m_xnodp > 9.24E-3) || (eq < 0.5))
|
| 313 |
{
|
| 314 |
bInitOnExit = false;
|
| 315 |
}
|
| 316 |
else
|
| 317 |
{
|
| 318 |
dp_iresfl = true;
|
| 319 |
|
| 320 |
double eoc = eq * eqsq;
|
| 321 |
double g201 = -0.306 - (eq - 0.64) * 0.440;
|
| 322 |
|
| 323 |
double g211; double g322;
|
| 324 |
double g410; double g422;
|
| 325 |
double g520;
|
| 326 |
|
| 327 |
if (eq <= 0.65)
|
| 328 |
{
|
| 329 |
g211 = 3.616 - 13.247 * eq + 16.290 * eqsq;
|
| 330 |
g310 = -19.302 + 117.390 * eq - 228.419 * eqsq + 156.591 * eoc;
|
| 331 |
g322 = -18.9068 + 109.7927 * eq - 214.6334 * eqsq + 146.5816 * eoc;
|
| 332 |
g410 = -41.122 + 242.694 * eq - 471.094 * eqsq + 313.953 * eoc;
|
| 333 |
g422 = -146.407 + 841.880 * eq - 1629.014 * eqsq + 1083.435 * eoc;
|
| 334 |
g520 = -532.114 + 3017.977 * eq - 5740.0 * eqsq + 3708.276 * eoc;
|
| 335 |
}
|
| 336 |
else
|
| 337 |
{
|
| 338 |
g211 = -72.099 + 331.819 * eq - 508.738 * eqsq + 266.724 * eoc;
|
| 339 |
g310 = -346.844 + 1582.851 * eq - 2415.925 * eqsq + 1246.113 * eoc;
|
| 340 |
g322 = -342.585 + 1554.908 * eq - 2366.899 * eqsq + 1215.972 * eoc;
|
| 341 |
g410 = -1052.797 + 4758.686 * eq - 7193.992 * eqsq + 3651.957 * eoc;
|
| 342 |
g422 = -3581.69 + 16178.11 * eq - 24462.77 * eqsq + 12422.52 * eoc;
|
| 343 |
|
| 344 |
if (eq <= 0.715)
|
| 345 |
g520 = 1464.74 - 4664.75 * eq + 3763.64 * eqsq;
|
| 346 |
else
|
| 347 |
g520 = -5149.66 + 29936.92 * eq - 54087.36 * eqsq + 31324.56 * eoc;
|
| 348 |
}
|
| 349 |
|
| 350 |
double g533;
|
| 351 |
double g521;
|
| 352 |
double g532;
|
| 353 |
|
| 354 |
if (eq < 0.7)
|
| 355 |
{
|
| 356 |
g533 = -919.2277 + 4988.61 * eq - 9064.77 * eqsq + 5542.21 * eoc;
|
| 357 |
g521 = -822.71072 + 4568.6173 * eq - 8491.4146 * eqsq + 5337.524 * eoc;
|
| 358 |
g532 = -853.666 + 4690.25 * eq - 8624.77 * eqsq + 5341.4 * eoc;
|
| 359 |
}
|
| 360 |
else
|
| 361 |
{
|
| 362 |
g533 = -37995.78 + 161616.52 * eq - 229838.2 * eqsq + 109377.94 * eoc;
|
| 363 |
g521 = -51752.104 + 218913.95 * eq - 309468.16 * eqsq + 146349.42 * eoc;
|
| 364 |
g532 = -40023.88 + 170470.89 * eq - 242699.48 * eqsq + 115605.82 * eoc;
|
| 365 |
}
|
| 366 |
|
| 367 |
double sini2 = siniq * siniq;
|
| 368 |
f220 = 0.75*(1.0 + 2.0 * cosiq + cosq2);
|
| 369 |
double f221 = 1.5 * sini2;
|
| 370 |
double f321 = 1.875 * siniq*(1.0 - 2.0 * cosiq - 3.0 * cosq2);
|
| 371 |
double f322 = -1.875 * siniq*(1.0 + 2.0 * cosiq - 3.0 * cosq2);
|
| 372 |
double f441 = 35.0 * sini2 * f220;
|
| 373 |
double f442 = 39.3750 * sini2 * sini2;
|
| 374 |
double f522 = 9.84375 * siniq*(sini2*(1.0 - 2.0 * cosiq - 5.0 * cosq2) +
|
| 375 |
0.33333333*(-2.0 + 4.0 * cosiq + 6.0 * cosq2));
|
| 376 |
double f523 = siniq*(4.92187512 * sini2*(-2.0 - 4.0 * cosiq + 10.0 * cosq2) +
|
| 377 |
6.56250012 * (1.0 + 2.0 * cosiq - 3.0 * cosq2));
|
| 378 |
double f542 = 29.53125 * siniq*(2.0 - 8.0 * cosiq + cosq2 * (-12.0 + 8.0 * cosiq + 10.0 * cosq2));
|
| 379 |
double f543 = 29.53125 * siniq*(-2.0 - 8.0 * cosiq + cosq2 * (12.0 + 8.0 * cosiq - 10.0 * cosq2));
|
| 380 |
double xno2 = m_xnodp * m_xnodp;
|
| 381 |
double ainv2 = aqnv * aqnv;
|
| 382 |
double temp1 = 3.0 * xno2 * ainv2;
|
| 383 |
double temp = temp1 * root22;
|
| 384 |
|
| 385 |
dp_d2201 = temp * f220 * g201;
|
| 386 |
dp_d2211 = temp * f221 * g211;
|
| 387 |
temp1 = temp1 * aqnv;
|
| 388 |
temp = temp1 * root32;
|
| 389 |
dp_d3210 = temp * f321 * g310;
|
| 390 |
dp_d3222 = temp * f322 * g322;
|
| 391 |
temp1 = temp1 * aqnv;
|
| 392 |
temp = 2.0 * temp1 * root44;
|
| 393 |
dp_d4410 = temp * f441 * g410;
|
| 394 |
dp_d4422 = temp * f442 * g422;
|
| 395 |
temp1 = temp1 * aqnv;
|
| 396 |
temp = temp1 * root52;
|
| 397 |
dp_d5220 = temp * f522 * g520;
|
| 398 |
dp_d5232 = temp * f523 * g532;
|
| 399 |
temp = 2.0 * temp1 * root54;
|
| 400 |
dp_d5421 = temp * f542 * g521;
|
| 401 |
dp_d5433 = temp * f543 * g533;
|
| 402 |
dp_xlamo = xmao + m_Orbit.RAAN() + m_Orbit.RAAN() - dp_thgr - dp_thgr;
|
| 403 |
bfact = xlldot + xnodot + xnodot - thdt - thdt;
|
| 404 |
bfact = bfact + dp_ssl + dp_ssh + dp_ssh;
|
| 405 |
}
|
| 406 |
}
|
| 407 |
else
|
| 408 |
{
|
| 409 |
// Synchronous resonance terms initialization
|
| 410 |
dp_iresfl = true;
|
| 411 |
dp_isynfl = true;
|
| 412 |
double g200 = 1.0 + eqsq * (-2.5 + 0.8125 * eqsq);
|
| 413 |
g310 = 1.0 + 2.0 * eqsq;
|
| 414 |
double g300 = 1.0 + eqsq * (-6.0 + 6.60937 * eqsq);
|
| 415 |
f220 = 0.75 * (1.0 + cosiq) * (1.0 + cosiq);
|
| 416 |
double f311 = 0.9375 * siniq * siniq * (1.0 + 3 * cosiq) - 0.75 * (1.0 + cosiq);
|
| 417 |
double f330 = 1.0 + cosiq;
|
| 418 |
f330 = 1.875 * f330 * f330 * f330;
|
| 419 |
dp_del1 = 3.0 * m_xnodp * m_xnodp * aqnv * aqnv;
|
| 420 |
dp_del2 = 2.0 * dp_del1 * f220 * g200 * q22;
|
| 421 |
dp_del3 = 3.0 * dp_del1 * f330 * g300 * q33 * aqnv;
|
| 422 |
dp_del1 = dp_del1 * f311 * g310 * q31 * aqnv;
|
| 423 |
dp_fasx2 = 0.13130908;
|
| 424 |
dp_fasx4 = 2.8843198;
|
| 425 |
dp_fasx6 = 0.37448087;
|
| 426 |
dp_xlamo = xmao + m_Orbit.RAAN() + m_Orbit.ArgPerigee() - dp_thgr;
|
| 427 |
bfact = xlldot + xpidot - thdt;
|
| 428 |
bfact = bfact + dp_ssl + dp_ssg + dp_ssh;
|
| 429 |
}
|
| 430 |
|
| 431 |
if (bInitOnExit)
|
| 432 |
{
|
| 433 |
dp_xfact = bfact - m_xnodp;
|
| 434 |
|
| 435 |
// Initialize integrator
|
| 436 |
dp_xli = dp_xlamo;
|
| 437 |
dp_xni = m_xnodp;
|
| 438 |
dp_atime = 0.0;
|
| 439 |
dp_stepp = 720.0;
|
| 440 |
dp_stepn = -720.0;
|
| 441 |
dp_step2 = 259200.0;
|
| 442 |
}
|
| 443 |
|
| 444 |
*eosq = eqsq;
|
| 445 |
*sinio = siniq;
|
| 446 |
*cosio = cosiq;
|
| 447 |
*betao = rteqsq;
|
| 448 |
*aodp = ao;
|
| 449 |
*theta2 = cosq2;
|
| 450 |
*sing = sinomo;
|
| 451 |
*cosg = cosomo;
|
| 452 |
*betao2 = bsq;
|
| 453 |
*xmdot = xlldot;
|
| 454 |
*omgdot = omgdt;
|
| 455 |
*xnodott = xnodot;
|
| 456 |
|
| 457 |
return true;
|
| 458 |
}
|
| 459 |
|
| 460 |
//////////////////////////////////////////////////////////////////////////////
|
| 461 |
bool cNoradSDP4::DeepCalcDotTerms(double *pxndot, double *pxnddt, double *pxldot)
|
| 462 |
{
|
| 463 |
// Dot terms calculated
|
| 464 |
if (dp_isynfl)
|
| 465 |
{
|
| 466 |
*pxndot = dp_del1 * sin(dp_xli - dp_fasx2) +
|
| 467 |
dp_del2 * sin(2.0 * (dp_xli - dp_fasx4)) +
|
| 468 |
dp_del3 * sin(3.0 * (dp_xli - dp_fasx6));
|
| 469 |
*pxnddt = dp_del1 * cos(dp_xli - dp_fasx2) +
|
| 470 |
2.0 * dp_del2 * cos(2.0 * (dp_xli - dp_fasx4)) +
|
| 471 |
3.0 * dp_del3 * cos(3.0 * (dp_xli - dp_fasx6));
|
| 472 |
}
|
| 473 |
else
|
| 474 |
{
|
| 475 |
double xomi = dp_omegaq + omgdt * dp_atime;
|
| 476 |
double x2omi = xomi + xomi;
|
| 477 |
double x2li = dp_xli + dp_xli;
|
| 478 |
|
| 479 |
*pxndot = dp_d2201 * sin(x2omi + dp_xli - g22) +
|
| 480 |
dp_d2211 * sin(dp_xli - g22) +
|
| 481 |
dp_d3210 * sin(xomi + dp_xli - g32) +
|
| 482 |
dp_d3222 * sin(-xomi + dp_xli - g32) +
|
| 483 |
dp_d4410 * sin(x2omi + x2li - g44) +
|
| 484 |
dp_d4422 * sin(x2li - g44) +
|
| 485 |
dp_d5220 * sin(xomi + dp_xli - g52) +
|
| 486 |
dp_d5232 * sin(-xomi + dp_xli - g52) +
|
| 487 |
dp_d5421 * sin(xomi + x2li - g54) +
|
| 488 |
dp_d5433 * sin(-xomi + x2li - g54);
|
| 489 |
|
| 490 |
*pxnddt = dp_d2201 * cos(x2omi + dp_xli - g22) +
|
| 491 |
dp_d2211 * cos(dp_xli - g22) +
|
| 492 |
dp_d3210 * cos(xomi + dp_xli - g32) +
|
| 493 |
dp_d3222 * cos(-xomi + dp_xli - g32) +
|
| 494 |
dp_d5220 * cos(xomi + dp_xli - g52) +
|
| 495 |
dp_d5232 * cos(-xomi + dp_xli - g52) +
|
| 496 |
2.0 * (dp_d4410 * cos(x2omi + x2li - g44) +
|
| 497 |
dp_d4422 * cos(x2li - g44) +
|
| 498 |
dp_d5421 * cos(xomi + x2li - g54) +
|
| 499 |
dp_d5433 * cos(-xomi + x2li - g54));
|
| 500 |
}
|
| 501 |
|
| 502 |
*pxldot = dp_xni + dp_xfact;
|
| 503 |
*pxnddt = (*pxnddt) * (*pxldot);
|
| 504 |
|
| 505 |
return true;
|
| 506 |
}
|
| 507 |
|
| 508 |
//////////////////////////////////////////////////////////////////////////////
|
| 509 |
void cNoradSDP4::DeepCalcIntegrator(double *pxndot, double *pxnddt,
|
| 510 |
double *pxldot, const double &delt)
|
| 511 |
{
|
| 512 |
DeepCalcDotTerms(pxndot, pxnddt, pxldot);
|
| 513 |
|
| 514 |
dp_xli = dp_xli + (*pxldot) * delt + (*pxndot) * dp_step2;
|
| 515 |
dp_xni = dp_xni + (*pxndot) * delt + (*pxnddt) * dp_step2;
|
| 516 |
dp_atime = dp_atime + delt;
|
| 517 |
}
|
| 518 |
|
| 519 |
//////////////////////////////////////////////////////////////////////////////
|
| 520 |
bool cNoradSDP4::DeepSecular(double *xmdf, double *omgadf, double *xnode,
|
| 521 |
double *emm, double *xincc, double *xnn,
|
| 522 |
double *tsince)
|
| 523 |
{
|
| 524 |
xll = *xmdf;
|
| 525 |
omgasm = *omgadf;
|
| 526 |
xnodes = *xnode;
|
| 527 |
xn = *xnn;
|
| 528 |
t = *tsince;
|
| 529 |
|
| 530 |
// Deep space secular effects
|
| 531 |
xll = xll + dp_ssl * t;
|
| 532 |
omgasm = omgasm + dp_ssg * t;
|
| 533 |
xnodes = xnodes + dp_ssh * t;
|
| 534 |
_em = m_Orbit.Eccentricity() + dp_sse * t;
|
| 535 |
xinc = m_Orbit.Inclination() + dp_ssi * t;
|
| 536 |
|
| 537 |
if (xinc < 0.0)
|
| 538 |
{
|
| 539 |
xinc = -xinc;
|
| 540 |
xnodes = xnodes + PI;
|
| 541 |
omgasm = omgasm - PI;
|
| 542 |
}
|
| 543 |
|
| 544 |
double xnddt = 0.0;
|
| 545 |
double xndot = 0.0;
|
| 546 |
double xldot = 0.0;
|
| 547 |
double ft = 0.0;
|
| 548 |
double delt = 0.0;
|
| 549 |
|
| 550 |
bool fDone = false;
|
| 551 |
|
| 552 |
if (dp_iresfl)
|
| 553 |
{
|
| 554 |
while (!fDone)
|
| 555 |
{
|
| 556 |
if ((dp_atime == 0.0) ||
|
| 557 |
((t >= 0.0) && (dp_atime < 0.0)) ||
|
| 558 |
((t < 0.0) && (dp_atime >= 0.0)))
|
| 559 |
{
|
| 560 |
if (t < 0)
|
| 561 |
delt = dp_stepn;
|
| 562 |
else
|
| 563 |
delt = dp_stepp;
|
| 564 |
|
| 565 |
// Epoch restart
|
| 566 |
dp_atime = 0.0;
|
| 567 |
dp_xni = m_xnodp;
|
| 568 |
dp_xli = dp_xlamo;
|
| 569 |
|
| 570 |
fDone = true;
|
| 571 |
}
|
| 572 |
else
|
| 573 |
{
|
| 574 |
if (fabs(t) < fabs(dp_atime))
|
| 575 |
{
|
| 576 |
delt = dp_stepp;
|
| 577 |
|
| 578 |
if (t >= 0.0)
|
| 579 |
delt = dp_stepn;
|
| 580 |
|
| 581 |
DeepCalcIntegrator(&xndot, &xnddt, &xldot, delt);
|
| 582 |
}
|
| 583 |
else
|
| 584 |
{
|
| 585 |
delt = dp_stepn;
|
| 586 |
|
| 587 |
if (t > 0.0)
|
| 588 |
delt = dp_stepp;
|
| 589 |
|
| 590 |
fDone = true;
|
| 591 |
}
|
| 592 |
}
|
| 593 |
}
|
| 594 |
|
| 595 |
while (fabs(t - dp_atime) >= dp_stepp)
|
| 596 |
{
|
| 597 |
DeepCalcIntegrator(&xndot, &xnddt, &xldot, delt);
|
| 598 |
}
|
| 599 |
|
| 600 |
ft = t - dp_atime;
|
| 601 |
|
| 602 |
DeepCalcDotTerms(&xndot, &xnddt, &xldot);
|
| 603 |
|
| 604 |
xn = dp_xni + xndot * ft + xnddt * ft * ft * 0.5;
|
| 605 |
|
| 606 |
double xl = dp_xli + xldot * ft + xndot * ft * ft * 0.5;
|
| 607 |
double temp = -xnodes + dp_thgr + t * thdt;
|
| 608 |
|
| 609 |
xll = xl - omgasm + temp;
|
| 610 |
|
| 611 |
if (!dp_isynfl)
|
| 612 |
xll = xl + temp + temp;
|
| 613 |
}
|
| 614 |
|
| 615 |
*xmdf = xll;
|
| 616 |
*omgadf = omgasm;
|
| 617 |
*xnode = xnodes;
|
| 618 |
*emm = _em;
|
| 619 |
*xincc = xinc;
|
| 620 |
*xnn = xn;
|
| 621 |
*tsince = t;
|
| 622 |
|
| 623 |
return true;
|
| 624 |
}
|
| 625 |
|
| 626 |
//////////////////////////////////////////////////////////////////////////////
|
| 627 |
bool cNoradSDP4::DeepPeriodics(double *e, double *xincc,
|
| 628 |
double *omgadf, double *xnode,
|
| 629 |
double *xmam)
|
| 630 |
{
|
| 631 |
_em = *e;
|
| 632 |
xinc = *xincc;
|
| 633 |
omgasm = *omgadf;
|
| 634 |
xnodes = *xnode;
|
| 635 |
xll = *xmam;
|
| 636 |
|
| 637 |
// Lunar-solar periodics
|
| 638 |
double sinis = sin(xinc);
|
| 639 |
double cosis = cos(xinc);
|
| 640 |
|
| 641 |
double sghs = 0.0;
|
| 642 |
double shs = 0.0;
|
| 643 |
double sh1 = 0.0;
|
| 644 |
double pe = 0.0;
|
| 645 |
double pinc = 0.0;
|
| 646 |
double pl = 0.0;
|
| 647 |
double sghl = 0.0;
|
| 648 |
|
| 649 |
if (fabs(dp_savtsn - t) >= 30.0)
|
| 650 |
{
|
| 651 |
dp_savtsn = t;
|
| 652 |
|
| 653 |
double zm = dp_zmos + zns * t;
|
| 654 |
double zf = zm + 2.0 * zes * sin(zm);
|
| 655 |
double sinzf = sin(zf);
|
| 656 |
double f2 = 0.5 * sinzf * sinzf - 0.25;
|
| 657 |
double f3 = -0.5 * sinzf * cos(zf);
|
| 658 |
double ses = dp_se2 * f2 + dp_se3 * f3;
|
| 659 |
double sis = dp_si2 * f2 + dp_si3 * f3;
|
| 660 |
double sls = dp_sl2 * f2 + dp_sl3 * f3 + dp_sl4 * sinzf;
|
| 661 |
|
| 662 |
sghs = dp_sgh2 * f2 + dp_sgh3 * f3 + dp_sgh4 * sinzf;
|
| 663 |
shs = dp_sh2 * f2 + dp_sh3 * f3;
|
| 664 |
zm = dp_zmol + znl * t;
|
| 665 |
zf = zm + 2.0 * zel * sin(zm);
|
| 666 |
sinzf = sin(zf);
|
| 667 |
f2 = 0.5 * sinzf * sinzf - 0.25;
|
| 668 |
f3 = -0.5 * sinzf * cos(zf);
|
| 669 |
|
| 670 |
double sel = dp_ee2 * f2 + dp_e3 * f3;
|
| 671 |
double sil = dp_xi2 * f2 + dp_xi3 * f3;
|
| 672 |
double sll = dp_xl2 * f2 + dp_xl3 * f3 + dp_xl4 * sinzf;
|
| 673 |
|
| 674 |
sghl = dp_xgh2 * f2 + dp_xgh3 * f3 + dp_xgh4 * sinzf;
|
| 675 |
sh1 = dp_xh2 * f2 + dp_xh3 * f3;
|
| 676 |
pe = ses + sel;
|
| 677 |
pinc = sis + sil;
|
| 678 |
pl = sls + sll;
|
| 679 |
}
|
| 680 |
|
| 681 |
double pgh = sghs + sghl;
|
| 682 |
double ph = shs + sh1;
|
| 683 |
xinc = xinc + pinc;
|
| 684 |
_em = _em + pe;
|
| 685 |
|
| 686 |
if (dp_xqncl >= 0.2)
|
| 687 |
{
|
| 688 |
// Apply periodics directly
|
| 689 |
ph = ph / siniq;
|
| 690 |
pgh = pgh - cosiq * ph;
|
| 691 |
omgasm = omgasm + pgh;
|
| 692 |
xnodes = xnodes + ph;
|
| 693 |
xll = xll + pl;
|
| 694 |
}
|
| 695 |
else
|
| 696 |
{
|
| 697 |
// Apply periodics with Lyddane modification
|
| 698 |
double sinok = sin(xnodes);
|
| 699 |
double cosok = cos(xnodes);
|
| 700 |
double alfdp = sinis * sinok;
|
| 701 |
double betdp = sinis * cosok;
|
| 702 |
double dalf = ph * cosok + pinc * cosis * sinok;
|
| 703 |
double dbet = -ph * sinok + pinc * cosis * cosok;
|
| 704 |
|
| 705 |
alfdp = alfdp + dalf;
|
| 706 |
betdp = betdp + dbet;
|
| 707 |
|
| 708 |
double xls = xll + omgasm + cosis * xnodes;
|
| 709 |
double dls = pl + pgh - pinc * xnodes * sinis;
|
| 710 |
|
| 711 |
xls = xls + dls;
|
| 712 |
xnodes = AcTan(alfdp, betdp);
|
| 713 |
xll = xll + pl;
|
| 714 |
omgasm = xls - xll - cos(xinc) * xnodes;
|
| 715 |
}
|
| 716 |
|
| 717 |
*e = _em;
|
| 718 |
*xincc = xinc;
|
| 719 |
*omgadf = omgasm;
|
| 720 |
*xnode = xnodes;
|
| 721 |
*xmam = xll;
|
| 722 |
|
| 723 |
return true;
|
| 724 |
}
|
| 725 |
|
| 726 |
//////////////////////////////////////////////////////////////////////////////
|
| 727 |
// getPosition()
|
| 728 |
// This procedure returns the ECI position and velocity for the satellite
|
| 729 |
// in the orbit at the given number of minutes since the TLE epoch time
|
| 730 |
// using the NORAD Simplified General Perturbation 4, "deep space" orbit
|
| 731 |
// model.
|
| 732 |
//
|
| 733 |
// tsince - Time in minutes since the TLE epoch (GMT).
|
| 734 |
// pECI - pointer to location to store the ECI data.
|
| 735 |
// To convert the returned ECI position vector to km,
|
| 736 |
// multiply each component by:
|
| 737 |
// (XKMPER_WGS72 / AE).
|
| 738 |
// To convert the returned ECI velocity vector to km/sec,
|
| 739 |
// multiply each component by:
|
| 740 |
// (XKMPER_WGS72 / AE) * (MIN_PER_DAY / 86400).
|
| 741 |
bool cNoradSDP4::getPosition(double tsince, cEci &eci)
|
| 742 |
{
|
| 743 |
DeepInit(&m_eosq, &m_sinio, &m_cosio, &m_betao, &m_aodp, &m_theta2,
|
| 744 |
&m_sing, &m_cosg, &m_betao2, &m_xmdot, &m_omgdot, &m_xnodot);
|
| 745 |
|
| 746 |
// Update for secular gravity and atmospheric drag
|
| 747 |
double xmdf = m_Orbit.mnAnomaly() + m_xmdot * tsince;
|
| 748 |
double omgadf = m_Orbit.ArgPerigee() + m_omgdot * tsince;
|
| 749 |
double xnoddf = m_Orbit.RAAN() + m_xnodot * tsince;
|
| 750 |
double tsq = tsince * tsince;
|
| 751 |
double xnode = xnoddf + m_xnodcf * tsq;
|
| 752 |
double tempa = 1.0 - m_c1 * tsince;
|
| 753 |
double tempe = m_Orbit.BStar() * m_c4 * tsince;
|
| 754 |
double templ = m_t2cof * tsq;
|
| 755 |
double xn = m_xnodp;
|
| 756 |
double em;
|
| 757 |
double xinc;
|
| 758 |
|
| 759 |
DeepSecular(&xmdf, &omgadf, &xnode, &em, &xinc, &xn, &tsince);
|
| 760 |
|
| 761 |
double a = pow(XKE / xn, TWOTHRD) * sqr(tempa);
|
| 762 |
double e = em - tempe;
|
| 763 |
double xmam = xmdf + m_xnodp * templ;
|
| 764 |
|
| 765 |
DeepPeriodics(&e, &xinc, &omgadf, &xnode, &xmam);
|
| 766 |
|
| 767 |
double xl = xmam + omgadf + xnode;
|
| 768 |
|
| 769 |
xn = XKE / pow(a, 1.5);
|
| 770 |
|
| 771 |
return FinalPosition(xinc, omgadf, e, a, xl, xnode, xn, tsince, eci);
|
| 772 |
}
|
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