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sgp4/SGDP4.cpp

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#include "SGDP4.h"
#include "Vector.h"
#include "SatelliteException.h"
#include <math.h>
SGDP4::SGDP4(void) {
first_run_ = true;
}
SGDP4::~SGDP4(void) {
}
void SGDP4::SetTle(const Tle& tle) {
/*
* extract and format tle data
*/
mean_anomoly_ = tle.GetField(Tle::FLD_M, Tle::U_RAD);
ascending_node_ = tle.GetField(Tle::FLD_RAAN, Tle::U_RAD);
argument_perigee_ = tle.GetField(Tle::FLD_ARGPER, Tle::U_RAD);
eccentricity_ = tle.GetField(Tle::FLD_E);
inclination_ = tle.GetField(Tle::FLD_I, Tle::U_RAD);
mean_motion_ = tle.GetField(Tle::FLD_MMOTION) / (1440.0 / Globals::TWOPI());
bstar_ = tle.GetField(Tle::FLD_BSTAR);
epoch_ = tle.GetEpoch();
/*
* recover original mean motion (xnodp) and semimajor axis (aodp)
* from input elements
*/
double a1 = pow(Globals::XKE() / MeanMotion(), Globals::TOTHRD());
i_cosio_ = cos(Inclination());
i_sinio_ = sin(Inclination());
double theta2 = i_cosio_ * i_cosio_;
i_x3thm1_ = 3.0 * theta2 - 1.0;
double eosq = Eccentricity() * Eccentricity();
double betao2 = 1.0 - eosq;
double betao = sqrt(betao2);
double del1 = 1.5 * Globals::CK2() * i_x3thm1_ / (a1 * a1 * betao * betao2);
double ao = a1 * (1.0 - del1 * (0.5 * Globals::TOTHRD() + del1 * (1.0 + 134.0 / 81.0 * del1)));
double delo = 1.5 * Globals::CK2() * i_x3thm1_ / (ao * ao * betao * betao2);
recovered_mean_motion_ = MeanMotion() / (1.0 + delo);
recovered_semi_major_axis_ = ao / (1.0 - delo);
/*
* find perigee and period
*/
perigee_ = (RecoveredSemiMajorAxis() * (1.0 - Eccentricity()) - Globals::AE()) * Globals::XKMPER();
period_ = Globals::TWOPI() / RecoveredMeanMotion();
Initialize(theta2, betao2, betao, eosq);
}
void SGDP4::Initialize(const double& theta2, const double& betao2, const double& betao, const double& eosq) {
if (Period() >= 225.0) {
i_use_deep_space_ = true;
} else {
i_use_deep_space_ = false;
i_use_simple_model_ = false;
/*
* for perigee less than 220 kilometers, the simple_model flag is set and
* the equations are truncated to linear variation in sqrt a and
* quadratic variation in mean anomly. also, the c3 term, the
* delta omega term and the delta m term are dropped
*/
if (Perigee() < 220.0) {
i_use_simple_model_ = true;
}
}
double s4 = Globals::S();
double qoms24 = Globals::QOMS2T();
/*
* for perigee below 156km, the values of
* s4 and qoms2t are altered
*/
if (Perigee() < 156.0) {
s4 = Perigee() - 78.0;
if (Perigee() <= 98.0) {
s4 = 20.0;
}
qoms24 = pow((120.0 - s4) * Globals::AE() / Globals::XKMPER(), 4.0);
s4 = s4 / Globals::XKMPER() + Globals::AE();
}
double pinvsq = 1.0 / (RecoveredSemiMajorAxis() * RecoveredSemiMajorAxis() * betao2 * betao2);
double tsi = 1.0 / (RecoveredSemiMajorAxis() - s4);
i_eta_ = RecoveredSemiMajorAxis() * Eccentricity() * tsi;
double etasq = i_eta_ * i_eta_;
double eeta = Eccentricity() * i_eta_;
double psisq = fabs(1.0 - etasq);
double coef = qoms24 * pow(tsi, 4.0);
double coef1 = coef / pow(psisq, 3.5);
double c2 = coef1 * RecoveredMeanMotion() * (RecoveredSemiMajorAxis() *
(1.0 + 1.5 * etasq + eeta * (4.0 + etasq)) +
0.75 * Globals::CK2() * tsi / psisq *
i_x3thm1_ * (8.0 + 3.0 * etasq *
(8.0 + etasq)));
i_c1_ = BStar() * c2;
i_a3ovk2_ = -Globals::XJ3() / Globals::CK2() * pow(Globals::AE(), 3.0);
i_x1mth2_ = 1.0 - theta2;
i_c4_ = 2.0 * RecoveredMeanMotion() * coef1 * RecoveredSemiMajorAxis() * betao2 *
(i_eta_ * (2.0 + 0.5 * etasq) + Eccentricity() * (0.5 + 2.0 * etasq) -
2.0 * Globals::CK2() * tsi / (RecoveredSemiMajorAxis() * psisq) *
(-3.0 * i_x3thm1_ * (1.0 - 2.0 * eeta + etasq *
(1.5 - 0.5 * eeta)) + 0.75 * i_x1mth2_ * (2.0 * etasq - eeta *
(1.0 + etasq)) * cos(2.0 * ArgumentPerigee())));
double theta4 = theta2 * theta2;
double temp1 = 3.0 * Globals::CK2() * pinvsq * RecoveredMeanMotion();
double temp2 = temp1 * Globals::CK2() * pinvsq;
double temp3 = 1.25 * Globals::CK4() * pinvsq * pinvsq * RecoveredMeanMotion();
i_xmdot_ = RecoveredMeanMotion() + 0.5 * temp1 * betao *
i_x3thm1_ + 0.0625 * temp2 * betao *
(13.0 - 78.0 * theta2 + 137.0 * theta4);
double x1m5th = 1.0 - 5.0 * theta2;
i_omgdot_ = -0.5 * temp1 * x1m5th +
0.0625 * temp2 * (7.0 - 114.0 * theta2 + 395.0 * theta4) +
temp3 * (3.0 - 36.0 * theta2 + 49.0 * theta4);
double xhdot1_ = -temp1 * i_cosio_;
i_xnodot_ = xhdot1_ + (0.5 * temp2 * (4.0 - 19.0 * theta2) + 2.0 * temp3 *
(3.0 - 7.0 * theta2)) * i_cosio_;
i_xnodcf_ = 3.5 * betao2 * xhdot1_ * i_c1_;
i_t2cof_ = 1.5 * i_c1_;
if (fabs(i_cosio_ + 1.0) > 1.5e-12)
i_xlcof_ = 0.125 * i_a3ovk2_ * i_sinio_ * (3.0 + 5.0 * i_cosio_) / (1.0 + i_cosio_);
else
i_xlcof_ = 0.125 * i_a3ovk2_ * i_sinio_ * (3.0 + 5.0 * i_cosio_) / 1.5e-12;
i_aycof_ = 0.25 * i_a3ovk2_ * i_sinio_;
i_x7thm1_ = 7.0 * theta2 - 1.0;
if (i_use_deep_space_) {
i_gsto_ = Epoch().ToGMST();
double sing = sin(ArgumentPerigee());
double cosg = cos(ArgumentPerigee());
DeepSpaceInitialize(eosq, i_sinio_, i_cosio_, betao,
theta2, sing, cosg, betao2,
i_xmdot_, i_omgdot_, i_xnodot_);
} else {
double c3 = 0.0;
if (Eccentricity() > 1.0e-4) {
c3 = coef * tsi * i_a3ovk2_ * RecoveredMeanMotion() * Globals::AE() *
i_a3ovk2_ / Eccentricity();
}
i_c5_ = 2.0 * coef1 * RecoveredSemiMajorAxis() * betao2 * (1.0 + 2.75 *
(etasq + eeta) + eeta * etasq);
i_omgcof_ = BStar() * c3 * cos(ArgumentPerigee());
i_xmcof_ = 0.0;
if (Eccentricity() > 1.0e-4)
i_xmcof_ = -Globals::TOTHRD() * coef * BStar() * Globals::AE() / eeta;
i_delmo_ = pow(1.0 + i_eta_ * (cos(MeanAnomoly())), 3.0);
i_sinmo_ = sin(MeanAnomoly());
if (!i_use_simple_model_) {
double c1sq = i_c1_ * i_c1_;
i_d2_ = 4.0 * RecoveredSemiMajorAxis() * tsi * c1sq;
double temp = i_d2_ * tsi * i_c1_ / 3.0;
i_d3_ = (17.0 * RecoveredSemiMajorAxis() + s4) * temp;
i_d4_ = 0.5 * temp * RecoveredSemiMajorAxis() *
tsi * (221.0 * RecoveredSemiMajorAxis() + 31.0 * s4) * i_c1_;
i_t3cof_ = i_d2_ + 2.0 * c1sq;
i_t4cof_ = 0.25 * (3.0 * i_d3_ + i_c1_ *
(12.0 * i_d2_ + 10.0 * c1sq));
i_t5cof_ = 0.2 * (3.0 * i_d4_ + 12.0 * i_c1_ *
i_d3_ + 6.0 * i_d2_ * i_d2_ + 15.0 *
c1sq * (2.0 * i_d2_ + c1sq));
}
}
first_run_ = false;
}
void SGDP4::FindPosition(double tsince) {
double temp;
double temp1;
double temp2;
double temp3;
/*
* local copies which we can safely modify
*/
double tsince_eccentricity = Eccentricity();
double tsince_arg_perigee = ArgumentPerigee();
double tsince_inclination = Inclination();
double tsince_ascending_node = AscendingNode();
double xl = 0.0;
double a = 0.0;
/*
* update for secular gravity and atmospheric drag
*/
double xmdf = MeanAnomoly() + i_xmdot_ * tsince;
double omgadf = ArgumentPerigee() + i_omgdot_ * tsince;
double xnoddf = tsince_ascending_node + i_xnodot_ * tsince;
double tsq = tsince * tsince;
double xnode = xnoddf + i_xnodcf_ * tsq;
double tempa = 1.0 - i_c1_ * tsince;
double tempe = BStar() * i_c4_ * tsince;
double templ = i_t2cof_ * tsq;
tsince_arg_perigee = omgadf;
if (i_use_deep_space_) {
double xn = RecoveredMeanMotion();
#if 0
CALL DPSEC(xmdf, tsince_arg_perigee, XNODE, tle_data_tsince_.eo, tsince_inclination, xn, tsince);
#endif
a = pow(Globals::XKE() / xn, Globals::TOTHRD()) * pow(tempa, 2.0);
tsince_eccentricity -= tempe;
double xmam = xmdf + RecoveredMeanMotion() * templ;
DeepPeriodics(sinio_, cosio_, tsince, tsince_eccentricity,
tsince_inclination, tsince_arg_perigee, tsince_ascending_node, xmam);
xl = xmam + tsince_arg_perigee + xnode;
/*
* re-compute the perturbed values
*/
sinio_ = sin(tsince_inclination);
cosio_ = cos(tsince_inclination);
double theta2 = cosio_ * cosio_;
x3thm1_ = 3.0 * theta2 - 1.0;
x1mth2_ = 1.0 - theta2;
x7thm1_ = 7.0 * theta2 - 1.0;
if (fabs(cosio_ + 1.0) > 1.5e-12)
xlcof_ = 0.125 * i_a3ovk2_ * sinio_ * (3.0 + 5.0 * cosio_) / (1.0 + cosio_);
else
xlcof_ = 0.125 * i_a3ovk2_ * sinio_ * (3.0 + 5.0 * cosio_) / 1.5e-12;
aycof_ = 0.25 * i_a3ovk2_ * sinio_;
} else {
double xmp = xmdf;
if (!i_use_simple_model_) {
double delomg = omgcof_ * tsince;
double delm = xmcof_ * (pow(1.0 + i_eta_ * cos(xmdf), 3.0) - delmo_);
double temp1 = delomg + delm;
xmp = xmdf + temp1;
tsince_arg_perigee -= temp1;
double tcube = tsq * tsince;
double tfour = tsince * tcube;
tempa -= i_d2_ * tsq - i_d3_ * tcube - i_d4_ * tfour;
tempe += BStar() * i_c5_ * (sin(xmp) - sinmo_);
templ += i_t3cof_ * tcube + tfour * (i_t4cof_ + tsince * i_t5cof_);
}
a = RecoveredSemiMajorAxis() * pow(tempa, 2.0);
tsince_eccentricity = Eccentricity() - tempe;
xl = xmp + tsince_arg_perigee + xnode + RecoveredMeanMotion() * templ;
}
if (a < 1.0) {
throw new SatelliteException("Error: Satellite crashed (a < 1.0)");
}
if (tsince_eccentricity < -1.0e-3) {
throw new SatelliteException("Error: Modified eccentricity too low (e < -1.0e-3)");
}
/*
* create limits to modified eccentricity
*/
if (tsince_eccentricity < 1.0e-6) {
tsince_eccentricity = 1.0e-6;
} else if (tsince_eccentricity > 1.0 - 1.0e-6) {
tsince_eccentricity = 1.0 - 1.0e-6;
}
double beta = sqrt(1.0 - tsince_eccentricity * tsince_eccentricity);
double xn = Globals::XKE() / pow(a, 1.5);
/*
* long period periodics
*/
double axn = tsince_eccentricity * cos(tsince_arg_perigee);
temp = 1.0 / (a * beta * beta);
double xll = temp * xlcof_ * axn;
double aynl = temp * aycof_;
double xlt = xl + xll;
double ayn = tsince_eccentricity * sin(tsince_arg_perigee) + aynl;
double elsq = axn * axn + ayn * ayn;
if (elsq >= 1.0) {
throw new SatelliteException("Error: sqrt(e) >= 1 (elsq >= 1.0)");
}
/*
* solve keplers equation
* - solve using Newton-Raphson root solving
* - here capu is almost the mean anomoly
* - initialise the eccentric anomaly term epw
* - The fmod saves reduction of angle to +/-2pi in sin/cos() and prevents
* convergence problems.
*/
double capu = fmod(xlt - xnode, Globals::TWOPI());
double epw = capu;
double sinepw = 0.0;
double cosepw = 0.0;
double ecose = 0.0;
double esine = 0.0;
/*
* sensibility check for N-R correction
*/
double maxnr = sqrt(elsq);
bool kepler_running = true;
for (int i = 0; i < 10 && kepler_running; i++) {
sinepw = sin(epw);
cosepw = cos(epw);
ecose = axn * cosepw + ayn * sinepw;
esine = axn * sinepw - ayn * cosepw;
double f = capu - epw + esine;
if (fabs(f) < 1.0e-12) {
kepler_running = false;
} else {
/*
* 1st order Newton-Raphson correction
*/
double df = 1.0 - ecose;
double nr = f / df;
/*
* 2nd order Newton-Raphson correction.
* f / (df - 0.5 * d2f * f/df)
*/
if (i == 0 && fabs(nr) > 1.25 * maxnr)
nr = fabs(maxnr, nr);
else
nr = f / (df + 0.5 * esine * nr);
/*
* Newton-Raphson correction of -F/DF
*/
epw += nr;
}
}
/*
* short period preliminary quantities
*/
temp = 1.0 - elsq;
double pl = a * temp;
double r = a * (1.0 - ecose);
temp1 = 1.0 / r;
double rdot = Globals::XKE() * sqrt(a) * esine * temp1;
double rfdot = Globals::XKE() * sqrt(pl) * temp1;
temp2 = a * temp1;
double betal = sqrt(temp1);
temp3 = 1.0 / (1.0 + betal);
double cosu = temp2 * (cosepw - axn + ayn * esine * temp3);
double sinu = temp2 * (sinepw - ayn - axn * esine * temp3);
double u = atan2(sinu, cosu);
double sin2u = 2.0 * sinu * cosu;
double cos2u = 2.0 * cosu * cosu - 1.0;
/*
* update for short periodics
*/
temp = 1.0 / pl;
temp1 = Globals::CK2() * temp;
temp2 = temp1 * temp;
double rk = r * (1.0 - 1.5 * temp2 * betal * x3thm1_) + 0.5 * temp1 * x1mth2_ * cos2u;
double uk = u - 0.25 * temp2 * x7thm1_ * sin2u;
double xnodek = xnode + 1.5 * temp2 * cosio_ * sin2u;
double xinck = tsince_inclination + 1.5 * temp2 * cosio_ * sinio_ * cos2u;
double rdotk = rdot - xn * temp1 * x1mth2_ * sin2u;
double rfdotk = rfdot + xn * temp1 * (x1mth2_ * cos2u + 1.5 * x3thm1_);
if (rk < 0.0) {
throw new SatelliteException("Error: satellite decayed (rk < 0.0)");
}
/*
* orientation vectors
*/
double sinuk = sin(uk);
double cosuk = cos(uk);
double sinik = sin(xinck);
double cosik = cos(xinck);
double sinnok = sin(xnodek);
double cosnok = cos(xnodek);
double xmx = -sinnok * cosik;
double xmy = cosnok * cosik;
double ux = xmx * sinuk + cosnok * cosuk;
double uy = xmy * sinuk + sinnok * cosuk;
double uz = sinik * sinuk;
double vx = xmx * cosuk - cosnok * sinuk;
double vy = xmy * cosuk - sinnok * sinuk;
double vz = sinik * cosuk;
/*
* position and velocity
*/
double x = rk * ux * Globals::XKMPER();
double y = rk * uy * Globals::XKMPER();
double z = rk * uz * Globals::XKMPER();
Vector position(x, y, z);
double xdot = (rdotk * ux + rfdotk * vx) * Globals::XKMPER() / 60.0;
double ydot = (rdotk * uy + rfdotk * vy) * Globals::XKMPER() / 60.0;
double zdot = (rdotk * uz + rfdotk * vz) * Globals::XKMPER() / 60.0;
Vector velocity(xdot, ydot, zdot);
}
/*
* deep space initialization
*/
void SGDP4::DeepSpaceInitialize(const double& eosq, const double& sinio, const double& cosio, const double& betao,
const double& theta2, const double& sing, const double& cosg, const double& betao2,
const double& xmdot, const double& omgdot, const double& xnodot) {
double se = 0.0;
double si = 0.0;
double sl = 0.0;
double sgh = 0.0;
double shdq = 0.0;
double bfact = 0.0;
double ZNS = 1.19459E-5;
double C1SS = 2.9864797E-6;
double ZES = 0.01675;
double ZNL = 1.5835218E-4;
double C1L = 4.7968065E-7;
double ZEL = 0.05490;
double ZCOSIS = 0.91744867;
double ZSINI = 0.39785416;
double ZSINGS = -0.98088458;
double ZCOSGS = 0.1945905;
double Q22 = 1.7891679E-6;
double Q31 = 2.1460748E-6;
double Q33 = 2.2123015E-7;
double ROOT22 = 1.7891679E-6;
double ROOT32 = 3.7393792E-7;
double ROOT44 = 7.3636953E-9;
double ROOT52 = 1.1428639E-7;
double ROOT54 = 2.1765803E-9;
double THDT = 4.3752691E-3;
double aqnv = 1.0 / RecoveredSemiMajorAxis();
double xpidot = omgdot + xnodot;
double sinq = sin(AscendingNode());
double cosq = cos(AscendingNode());
/*
* initialize lunar / solar terms
*/
d_day_ = Epoch().FromJan1_12h_1900();
double xnodce = 4.5236020 - 9.2422029e-4 * d_day_;
double stem = sin(xnodce);
double ctem = cos(xnodce);
double zcosil = 0.91375164 - 0.03568096 * ctem;
double zsinil = sqrt(1.0 - zcosil * zcosil);
double zsinhl = 0.089683511 * stem / zsinil;
double zcoshl = sqrt(1.0 - zsinhl * zsinhl);
double c = 4.7199672 + 0.22997150 * d_day_;
double gam = 5.8351514 + 0.0019443680 * d_day_;
double zmol = Globals::Fmod2p(c - gam);
double zx = 0.39785416 * stem / zsinil;
double zy = zcoshl * ctem + 0.91744867 * zsinhl * stem;
/*
* todo: check
*/
zx = atan2(zx, zy);
zx = fmod(gam + zx - xnodce, Globals::TWOPI());
double zcosgl = cos(zx);
double zsingl = sin(zx);
double zmos = 6.2565837 + 0.017201977 * d_day_;
zmos = Globals::Fmod2p(zmos);
/*
* do solar terms
*/
d_savtsn_ = 1.0e20;
double zcosg = ZCOSGS;
double zsing = ZSINGS;
double zcosi = ZCOSIS;
double zsini = ZSINI;
double zcosh = cosq;
double zsinh = sinq;
double cc = C1SS;
double zn = ZNS;
double ze = ZES;
double zmo = d_zmos_;
double xnoi = 1.0 / RecoveredMeanMotion();
for (int cnt = 0; cnt < 2; cnt++) {
/*
* solar terms are done a second time after lunar terms are done
*/
double a1 = zcosg * zcosh + zsing * zcosi * zsinh;
double a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
double a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
double a8 = zsing * zsini;
double a9 = zsing * zsinh + zcosg * zcosi*zcosh;
double a10 = zcosg * zsini;
double a2 = cosio * a7 + sinio * a8;
double a4 = cosio * a9 + sinio * a10;
double a5 = -sinio * a7 + cosio * a8;
double a6 = -sinio * a9 + cosio * a10;
double x1 = a1 * cosg + a2 * sing;
double x2 = a3 * cosg + a4 * sing;
double x3 = -a1 * sing + a2 * cosg;
double x4 = -a3 * sing + a4 * cosg;
double x5 = a5 * sing;
double x6 = a6 * sing;
double x7 = a5 * cosg;
double x8 = a6 * cosg;
double z31 = 12.0 * x1 * x1 - 3. * x3 * x3;
double z32 = 24.0 * x1 * x2 - 6. * x3 * x4;
double z33 = 12.0 * x2 * x2 - 3. * x4 * x4;
double z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * eosq;
double z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * eosq;
double z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * eosq;
double z11 = -6.0 * a1 * a5 + eosq * (-24. * x1 * x7 - 6. * x3 * x5);
double z12 = -6.0 * (a1 * a6 + a3 * a5) + eosq * (-24. * (x2 * x7 + x1 * x8) - 6. * (x3 * x6 + x4 * x5));
double z13 = -6.0 * a3 * a6 + eosq * (-24. * x2 * x8 - 6. * x4 * x6);
double z21 = 6.0 * a2 * a5 + eosq * (24. * x1 * x5 - 6. * x3 * x7);
double z22 = 6.0 * (a4 * a5 + a2 * a6) + eosq * (24. * (x2 * x5 + x1 * x6) - 6. * (x4 * x7 + x3 * x8));
double z23 = 6.0 * a4 * a6 + eosq * (24. * x2 * x6 - 6. * x4 * x8);
z1 = z1 + z1 + betao2 * z31;
z2 = z2 + z2 + betao2 * z32;
z3 = z3 + z3 + betao2 * z33;
double s3 = cc * xnoi;
double s2 = -0.5 * s3 / betao;
double s4 = s3 * betao;
double s1 = -15.0 * Eccentricity() * s4;
double s5 = x1 * x3 + x2 * x4;
double s6 = x2 * x3 + x1 * x4;
double s7 = x2 * x4 - x1 * x3;
double se = s1 * zn * s5;
double si = s2 * zn * (z11 + z13);
double sl = -zn * s3 * (z1 + z3 - 14.0 - 6.0 * eosq);
double sgh = s4 * zn * (z31 + z33 - 6.0);
/*
* replaced
* sh = -zn * s2 * (z21 + z23
* with
* shdq = (-zn * s2 * (z21 + z23)) / sinio
*/
if (Inclination() < 5.2359877e-2 || Inclination() > Globals::PI() - 5.2359877e-2) {
shdq = 0.0;
} else {
shdq = (-zn * s2 * (z21 + z23)) / sinio;
}
d_ee2_ = 2.0 * s1 * s6;
d_e3_ = 2.0 * s1 * s7;
d_xi2_ = 2.0 * s2 * z12;
d_xi3_ = 2.0 * s2 * (z13 - z11);
d_xl2_ = -2.0 * s3 * z2;
d_xl3_ = -2.0 * s3 * (z3 - z1);
d_xl4_ = -2.0 * s3 * (-21.0 - 9.0 * eosq) * ze;
d_xgh2_ = 2.0 * s4 * z32;
d_xgh3_ = 2.0 * s4 * (z33 - z31);
d_xgh4_ = -18.0 * s4 * ze;
d_xh2_ = -2.0 * s2 * z22;
d_xh3_ = -2.0 * s2 * (z23 - z21);
if (cnt == 1)
break;
/*
* do lunar terms
*/
d_sse_ = se;
d_ssi_ = si;
d_ssl_ = sl;
d_ssh_ = shdq;
d_ssg_ = sgh - cosio * d_ssh_;
d_se2_ = d_ee2_;
d_si2_ = d_xi2_;
d_sl2_ = d_xl2_;
d_sgh2_ = d_xgh2_;
d_sh2_ = d_xh2_;
d_se3_ = d_e3_;
d_si3_ = d_xi3_;
d_sl3_ = d_xl3_;
d_sgh3_ = d_xgh3_;
d_sh3_ = d_xh3_;
d_sl4_ = d_xl4_;
d_sgh4_ = d_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;
zmo = zmol;
}
d_sse_ += se;
d_ssi_ += si;
d_ssl_ += sl;
d_ssg_ += sgh - cosio * shdq;
d_ssh_ += shdq;
/*
* geopotential resonance initialization for 12 hour orbits
*/
bool resonance_flag = false;
bool synchronous_flag = false;
bool initialize_integrator = true;
if (RecoveredMeanMotion() < 0.0052359877 && RecoveredMeanMotion() > 0.0034906585) {
if (RecoveredMeanMotion() < 8.26e-3 || RecoveredMeanMotion() > 9.24e-3 || Eccentricity() < 0.5) {
initialize_integrator = false;
} else {
/*
* geopotential resonance initialization for 12 hour orbits
*/
resonance_flag = true;
double eoc = Eccentricity() * eosq;
double g211;
double g310;
double g322;
double g410;
double g422;
double g520;
double g201 = -0.306 - (Eccentricity() - 0.64) * 0.440;
if (Eccentricity() <= 0.65) {
g211 = 3.616 - 13.247 * Eccentricity() + 16.290 * eosq;
g310 = -19.302 + 117.390 * Eccentricity() - 228.419 * eosq + 156.591 * eoc;
g322 = -18.9068 + 109.7927 * Eccentricity() - 214.6334 * eosq + 146.5816 * eoc;
g410 = -41.122 + 242.694 * Eccentricity() - 471.094 * eosq + 313.953 * eoc;
g422 = -146.407 + 841.880 * Eccentricity() - 1629.014 * eosq + 1083.435 * eoc;
g520 = -532.114 + 3017.977 * Eccentricity() - 5740 * eosq + 3708.276 * eoc;
} else {
g211 = -72.099 + 331.819 * Eccentricity() - 508.738 * eosq + 266.724 * eoc;
g310 = -346.844 + 1582.851 * Eccentricity() - 2415.925 * eosq + 1246.113 * eoc;
g322 = -342.585 + 1554.908 * Eccentricity() - 2366.899 * eosq + 1215.972 * eoc;
g410 = -1052.797 + 4758.686 * Eccentricity() - 7193.992 * eosq + 3651.957 * eoc;
g422 = -3581.69 + 16178.11 * Eccentricity() - 24462.77 * eosq + 12422.52 * eoc;
if (Eccentricity() <= 0.715) {
g520 = 1464.74 - 4664.75 * Eccentricity() + 3763.64 * eosq;
} else {
g520 = -5149.66 + 29936.92 * Eccentricity() - 54087.36 * eosq + 31324.56 * eoc;
}
}
double g533;
double g521;
double g532;
if (Eccentricity() < 0.7) {
g533 = -919.2277 + 4988.61 * Eccentricity() - 9064.77 * eosq + 5542.21 * eoc;
g521 = -822.71072 + 4568.6173 * Eccentricity() - 8491.4146 * eosq + 5337.524 * eoc;
g532 = -853.666 + 4690.25 * Eccentricity() - 8624.77 * eosq + 5341.4 * eoc;
} else {
g533 = -37995.78 + 161616.52 * Eccentricity() - 229838.2 * eosq + 109377.94 * eoc;
g521 = -51752.104 + 218913.95 * Eccentricity() - 309468.16 * eosq + 146349.42 * eoc;
g532 = -40023.88 + 170470.89 * Eccentricity() - 242699.48 * eosq + 115605.82 * eoc;
}
double sini2 = sinio * sinio;
double f220 = 0.75 * (1.0 + 2.0 * cosio + theta2);
double f221 = 1.5 * sini2;
double f321 = 1.875 * sinio * (1.0 - 2.0 * cosio - 3.0 * theta2);
double f322 = -1.875 * sinio * (1.0 + 2.0 * cosio - 3.0 * theta2);
double f441 = 35.0 * sini2 * f220;
double f442 = 39.3750 * sini2 * sini2;
double f522 = 9.84375 * sinio * (sini2 * (1.0 - 2.0 * cosio - 5.0 * theta2)
+ 0.33333333 * (-2.0 + 4.0 * cosio + 6.0 * theta2));
double f523 = sinio * (4.92187512 * sini2 * (-2.0 - 4.0 * cosio + 10.0 * theta2)
+ 6.56250012 * (1.0 + 2.0 * cosio - 3.0 * theta2));
double f542 = 29.53125 * sinio * (2.0 - 8.0 * cosio + theta2 *
(-12.0 + 8.0 * cosio + 10.0 * theta2));
double f543 = 29.53125 * sinio * (-2.0 - 8.0 * cosio + theta2 *
(12.0 + 8.0 * cosio - 10.0 * theta2));
double xno2 = RecoveredMeanMotion() * RecoveredMeanMotion();
double ainv2 = aqnv * aqnv;
double temp1 = 3.0 * xno2 * ainv2;
double temp = temp1 * ROOT22;
d_d2201_ = temp * f220 * g201;
d_d2211_ = temp * f221 * g211;
temp1 = temp1 * aqnv;
temp = temp1 * ROOT32;
d_d3210_ = temp * f321 * g310;
d_d3222_ = temp * f322 * g322;
temp1 = temp1 * aqnv;
temp = 2.0 * temp1 * ROOT44;
d_d4410_ = temp * f441 * g410;
d_d4422_ = temp * f442 * g422;
temp1 = temp1 * aqnv;
temp = temp1 * ROOT52;
d_d5220_ = temp * f522 * g520;
d_d5232_ = temp * f523 * g532;
temp = 2.0 * temp1 * ROOT54;
d_d5421_ = temp * f542 * g521;
d_d5433_ = temp * f543 * g533;
d_xlamo_ = MeanAnomoly() + AscendingNode() + AscendingNode() - i_gsto_ - i_gsto_;
bfact = xmdot + xnodot + xnodot - THDT - THDT;
bfact = bfact + d_ssl_ + d_ssh_ + d_ssh_;
}
} else {
/*
* 24h synchronous resonance terms initialization
*/
resonance_flag = true;
synchronous_flag = true;
double g200 = 1.0 + eosq * (-2.5 + 0.8125 * eosq);
double g310 = 1.0 + 2.0 * eosq;
double g300 = 1.0 + eosq * (-6.0 + 6.60937 * eosq);
double f220 = 0.75 * (1.0 + cosio) * (1.0 + cosio);
double f311 = 0.9375 * sinio * sinio * (1.0 + 3.0 * cosio) - 0.75 * (1.0 + cosio);
double f330 = 1.0 + cosio;
f330 = 1.875 * f330 * f330 * f330;
d_del1_ = 3.0 * RecoveredMeanMotion() * RecoveredMeanMotion() * aqnv * aqnv;
d_del2_ = 2.0 * d_del1_ * f220 * g200 * Q22;
d_del3_ = 3.0 * d_del1_ * f330 * g300 * Q33 * aqnv;
d_del1_ = d_del1_ * f311 * g310 * Q31 * aqnv;
d_fasx2_ = 0.13130908;
d_fasx4_ = 2.8843198;
d_fasx6_ = 0.37448087;
d_xlamo_ = MeanAnomoly() + AscendingNode() + ArgumentPerigee() - i_gsto_;
bfact = xmdot + xpidot - THDT;
bfact = bfact + d_ssl_ + d_ssg_ + d_ssh_;
}
if (initialize_integrator) {
d_xfact_ = bfact - RecoveredMeanMotion();
/*
* initialize integrator
*/
d_xli_ = d_xlamo_;
d_xni_ = RecoveredMeanMotion();
d_atime_ = 0.0;
d_stepp_ = 720.0;
d_stepn_ = -720.0;
d_step2_ = 259200.0;
}
}
/*
* lunar / solar periodics
*/
void SGDP4::DeepPeriodics(const double& sinio, const double& cosio, const double& t, double& em,
double& xinc, double& omgasm, double& xnodes, double& xll) {
double ZES = 0.01675;
double ZNS = 1.19459E-5;
double ZNL = 1.5835218E-4;
double ZEL = 0.05490;
double sghs = 0.0;
double shs = 0.0;
double sghl = 0.0;
double shl = 0.0;
double pe = 0.0;
double pinc = 0.0;
double pl = 0.0;
double sinis = sin(xinc);
double cosis = cos(xinc);
if (fabs(d_savtsn_ - t) >= 30.0) {
d_savtsn_ = t;
double zm = d_zmos_ + ZNS * t;
double zf = zm + 2.0 * ZES * sin(zm);
double sinzf = sin(zf);
double f2 = 0.5 * sinzf * sinzf - 0.25;
double f3 = -0.5 * sinzf * cos(zf);
double ses = d_se2_ * f2 + d_se3_ * f3;
double sis = d_si2_ * f2 + d_si3_ * f3;
double sls = d_sl2_ * f2 + d_sl3_ * f3 + d_sl4_ * sinzf;
sghs = d_sgh2_ * f2 + d_sgh3_ * f3 + d_sgh4_ * sinzf;
shs = d_sh2_ * f2 + d_sh3_ * f3;
zm = d_zmol_ + ZNL * t;
zf = zm + 2.0 * ZEL * sin(zm);
sinzf = sin(zf);
f2 = 0.5 * sinzf * sinzf - 0.25;
f3 = -0.5 * sinzf * cos(zf);
double sel = d_ee2_ * f2 + d_e3_ * f3;
double sil = d_xi2_ * f2 + d_xi3_ * f3;
double sll = d_xl2_ * f2 + d_xl3_ * f3 + d_xl4_ * sinzf;
sghl = d_xgh2_ * f2 + d_xgh3_ * f3 + d_xgh4_ * sinzf;
shl = d_xh2_ * f2 + d_xh3_ * f3;
pe = ses + sel;
pinc = sis + sil;
pl = sls + sll;
}
double pgh = sghs + sghl;
double ph = shs + shl;
xinc += pinc;
em += pe;
if (Inclination() >= 0.2) {
/*
* apply periodics directly
*/
ph /= sinio;
pgh -= cosio * ph;
omgasm += pgh;
xnodes += ph;
xll += pl;
} else {
/*
* apply periodics with lyddane modification
*/
double sinok = sin(xnodes);
double cosok = cos(xnodes);
double alfdp = sinis * sinok;
double betdp = sinis * cosok;
double dalf = ph * cosok + pinc * cosis * sinok;
double dbet = -ph * sinok + pinc * cosis * cosok;
alfdp += dalf;
betdp += dbet;
double xls = xll + omgasm + cosis * xnodes;
double dls = pl + pgh - pinc * xnodes * sinis;
xls += dls;
xnodes = atan2(alfdp, betdp);
xll += pl;
omgasm = xls - xll - cos(xinc) * xnodes;
}
}
/*
* deep space secular effects
ENTRY DPSEC(XLL,OMGASM,XNODES,EM,XINC,XN,T)
*/
void SGDP4::DeepSecular() {
/*
* passed in
*/
double xll;
double omgasm;
double xnodes;
double em;
double xinc;
double xn;
double t;
double xldot = 0.0;
double xndot = 0.0;
double xnddt = 0.0;
xll = xll + d_ssl_ * t;
omgasm = omgasm + d_ssg_ * t;
xnodes = xnodes + d_ssh_ * t;
em = Eccentricity() + d_sse_ * t;
xinc = Inclination() + d_ssi_ * t;
/*
* check if needed
*/
//if (xinc >= 0.0) {
// xinc = -xinc;
// xnodes = xnodes + Globals::PI();
// omgasm = omgasm - Globals::PI();
//}
if (iresfl == 0)
return;
if (fabs(d_atime_) < d_stepp_ ||
(d_atime_ < 0.0 && t < d_atime_ - 1.0) ||
(d_atime_ > 0.0 && t > d_atime_ + 1.0)) {
/*
* epoch restart
*/
d_atime_ = 0.0;
d_xni_ = xnq;
d_xli_ = d_xlamo_;
}
double ft = t - d_atime_;
double delt = 0.0;
if (fabs(ft) >= d_stepp_) {
if (t > 0.0)
delt = d_stepp_;
else
delt = d_stepn_;
do {
/*
* integrator
*/
d_xli_ = d_xli_ + xldot * delt + xndot * step2;
d_xni_ = d_xni_ + xndot * delt + xnddt * step2;
/*
* dot terms calculated
*/
if (isynfl != 0) {
xndot = d_del1_ * sin(d_xli_ - d_fasx2_) + d_del2_ * sin(2.0 * (d_xli_ - d_fasx4_))
1 + d_del3_ * sin(3.0 * (d_xli_ - d_fasx6_));
xnddt = d_del1_ * cos(d_xli_ - d_fasx2_)
+ 2.0 * d_del2_ * cos(2.0 * (d_xli_ - d_fasx4_))
+ 3.0 * d_del3_ * cos(3.0 * (d_xli_ - d_fasx6_));
} else {
double xomi = d_omegaq_ + omgdt * d_atime_;
double x2omi = xomi + xomi;
double x2li = d_xli_ + d_xli_;
xndot = d_d2201_ * sin(x2omi + d_xli_ - d_g22_)
+ d_d2211_ * sin(d_xli_ - d_g22_)
+ d_d3210_ * sin(xomi + xli - d_g32_)
+ d_d3222_ * sin(-xomi + xli - d_g32_)
+ d_d4410_ * sin(x2omi + x2li - d_g44_)
+ d_d4422_ * sin(x2li - d_g44)
+ d_d5220_ * sin(xomi + xli - d_g52_)
+ d_d5232_ * sin(-xomi + xli - d_g52_)
+ d_d5421_ * sin(xomi + x2li - d_g54_)
+ d_d5433_ * sin(-xomi + x2li - d_g54_);
xnddt = d_d2201_ * cos(x2omi + xli - d_g22_)
+ d_d2211_ * cos(xli - d_g22_)
+ d_d3210_ * cos(xomi + xli - d_g32_)
+ d_d3222_ * cos(-xomi + xli - d_g32_)
+ d_d5220_ * cos(xomi + xli - d_g52_)
+ d_d5232_ * cos(-xomi + xli - d_g52_)
+ 2.0 * (d_d4410_ * cos(x2omi + x2li - g44_)
+ d_d4422_ * cos(x2li - g44)
+ d_d5421_ * cos(xomi + x2li - d_g54_)
+ d_d5433_ * cos(-xomi + x2li - d_g54_));
}
xldot = xni + xfact;
xnddt = xnddt * xldot;
d_atime_ += delt;
ft = t - d_atime_;
} while (fabs(ft) >= d_stepp_);
}
/*
* integrator
*/
xn = d_xni_ + xndot * ft + xnddt * ft * ft * 0.5;
double xl = d_xli_ + xldot * ft + xndot * ft * ft * 0.5;
double temp = -xnodes + thgr + t * thdt;
if (isynfl == 0)
xll = xl + temp + temp;
else
xll = xl - omgasm + temp;
}
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