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sgp4/SGDP4.cpp

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#include "SGDP4.h"
#include "Vector.h"
#include "SatelliteException.h"
#include <cmath>
#include <iomanip>
#define AE (1.0)
#define Q0 (120.0)
#define S0 (78.0)
#define XKMPER (6378.135)
#define XJ2 (1.082616e-3)
#define XJ3 (-2.53881e-6)
#define XJ4 (-1.65597e-6)
#define XKE (7.43669161331734132e-2)
#define CK2 (0.5 * XJ2 * AE * AE)
#define CK4 (-0.375 * XJ4 * AE * AE * AE * AE)
#define QOMS2T (1.880279159015270643865e-9)
#define S (AE * (1.0 + S0 / XKMPER))
#define PI (3.14159265358979323846264338327950288419716939937510582)
#define TWOPI (2.0 * PI)
#define TWOTHIRD (2.0 / 3.0)
#define THDT (4.37526908801129966e-3)
SGDP4::SGDP4(void) {
first_run_ = true;
}
SGDP4::~SGDP4(void) {
}
void SGDP4::SetTle(const Tle& tle) {
/*
* reset all constants etc
*/
ResetGlobalVariables();
/*
* 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) * TWOPI / Globals::MIN_PER_DAY();
bstar_ = tle.GetField(Tle::FLD_BSTAR);
epoch_ = tle.GetEpoch();
/*
* error checks
*/
if (eccentricity_ < 0.0 || eccentricity_ > 1.0 - 1.0e-3) {
throw new SatelliteException("Eccentricity out of range");
}
if (inclination_ < 0.0 || eccentricity_ > PI) {
throw new SatelliteException("Inclination out of range");
}
/*
* recover original mean motion (xnodp) and semimajor axis (aodp)
* from input elements
*/
const double a1 = pow(XKE / MeanMotion(), TWOTHIRD);
i_cosio_ = cos(Inclination());
i_sinio_ = sin(Inclination());
const double theta2 = i_cosio_ * i_cosio_;
i_x3thm1_ = 3.0 * theta2 - 1.0;
const double eosq = Eccentricity() * Eccentricity();
const double betao2 = 1.0 - eosq;
const double betao = sqrt(betao2);
const double temp = (1.5 * CK2) * i_x3thm1_ / (betao * betao2);
const double del1 = temp / (a1 * a1);
const double a0 = a1 * (1.0 - del1 * (1.0 / 3.0 + del1 * (1.0 + del1 * 134.0 / 81.0)));
const double del0 = temp / (a0 * a0);
recovered_mean_motion_ = MeanMotion() / (1.0 + del0);
recovered_semi_major_axis_ = a0 / (1.0 - del0);
/*
* find perigee and period
*/
perigee_ = (RecoveredSemiMajorAxis() * (1.0 - Eccentricity()) - AE) * XKMPER;
period_ = 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;
}
}
/*
* for perigee below 156km, the values of
* s4 and qoms2t are altered
*/
double s4 = S;
double qoms24 = QOMS2T;
if (Perigee() < 156.0) {
s4 = Perigee() - 78.0;
if (Perigee() < 98.0) {
s4 = 20.0;
}
qoms24 = pow((120.0 - s4) * AE / XKMPER, 4.0);
s4 = s4 / XKMPER + AE;
}
/*
* generate constants
*/
const double pinvsq = 1.0 / (RecoveredSemiMajorAxis() * RecoveredSemiMajorAxis() * betao2 * betao2);
const double tsi = 1.0 / (RecoveredSemiMajorAxis() - s4);
i_eta_ = RecoveredSemiMajorAxis() * Eccentricity() * tsi;
const double etasq = i_eta_ * i_eta_;
const double eeta = Eccentricity() * i_eta_;
const double psisq = fabs(1.0 - etasq);
const double coef = qoms24 * pow(tsi, 4.0);
const double coef1 = coef / pow(psisq, 3.5);
const double c2 = coef1 * RecoveredMeanMotion() * (RecoveredSemiMajorAxis() *
(1.0 + 1.5 * etasq + eeta * (4.0 + etasq)) +
0.75 * CK2 * tsi / psisq *
i_x3thm1_ * (8.0 + 3.0 * etasq *
(8.0 + etasq)));
i_c1_ = BStar() * c2;
i_a3ovk2_ = -XJ3 / CK2 * pow(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 * 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())));
const double theta4 = theta2 * theta2;
const double temp1 = 3.0 * CK2 * pinvsq * RecoveredMeanMotion();
const double temp2 = temp1 * CK2 * pinvsq;
const double temp3 = 1.25 * 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);
const 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);
const 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_) {
d_gsto_ = Epoch().ToGreenwichSiderealTime();
DeepSpaceInitialize(eosq, i_sinio_, i_cosio_, betao,
theta2, betao2,
i_xmdot_, i_omgdot_, i_xnodot_);
} else {
double c3 = 0.0;
if (Eccentricity() > 1.0e-4) {
c3 = coef * tsi * i_a3ovk2_ * RecoveredMeanMotion() * AE *
i_sinio_ / Eccentricity();
}
n_c5_ = 2.0 * coef1 * RecoveredSemiMajorAxis() * betao2 * (1.0 + 2.75 *
(etasq + eeta) + eeta * etasq);
n_omgcof_ = BStar() * c3 * cos(ArgumentPerigee());
n_xmcof_ = 0.0;
if (Eccentricity() > 1.0e-4)
n_xmcof_ = -TWOTHIRD * coef * BStar() * AE / eeta;
n_delmo_ = pow(1.0 + i_eta_ * (cos(MeanAnomoly())), 3.0);
n_sinmo_ = sin(MeanAnomoly());
if (!i_use_simple_model_) {
const double c1sq = i_c1_ * i_c1_;
n_d2_ = 4.0 * RecoveredSemiMajorAxis() * tsi * c1sq;
const double temp = n_d2_ * tsi * i_c1_ / 3.0;
n_d3_ = (17.0 * RecoveredSemiMajorAxis() + s4) * temp;
n_d4_ = 0.5 * temp * RecoveredSemiMajorAxis() *
tsi * (221.0 * RecoveredSemiMajorAxis() + 31.0 * s4) * i_c1_;
n_t3cof_ = n_d2_ + 2.0 * c1sq;
n_t4cof_ = 0.25 * (3.0 * n_d3_ + i_c1_ *
(12.0 * n_d2_ + 10.0 * c1sq));
n_t5cof_ = 0.2 * (3.0 * n_d4_ + 12.0 * i_c1_ *
n_d3_ + 6.0 * n_d2_ * n_d2_ + 15.0 *
c1sq * (2.0 * n_d2_ + c1sq));
}
}
first_run_ = false;
}
void SGDP4::FindPosition(Eci& eci, double tsince) {
Julian tsince_epoch = Epoch();
tsince_epoch.AddMin(tsince);
double actual_tsince = tsince_epoch.SpanMin(Epoch());
if (i_use_deep_space_)
FindPositionSDP4(eci, actual_tsince);
else
FindPositionSGP4(eci, actual_tsince);
}
void SGDP4::FindPositionSDP4(Eci& eci, double tsince) {
/*
* the final values
*/
double e;
double a;
double omega;
double xl;
double xnode;
double xincl;
/*
* update for secular gravity and atmospheric drag
*/
double xmdf = MeanAnomoly() + i_xmdot_ * tsince;
double omgadf = ArgumentPerigee() + i_omgdot_ * tsince;
const double xnoddf = AscendingNode() + i_xnodot_ * tsince;
const double tsq = tsince * tsince;
xnode = xnoddf + i_xnodcf_ * tsq;
double tempa = 1.0 - i_c1_ * tsince;
double tempe = BStar() * i_c4_ * tsince;
double templ = i_t2cof_ * tsq;
double xn = RecoveredMeanMotion();
e = Eccentricity();
xincl = Inclination();
DeepSpaceSecular(tsince, xmdf, omgadf, xnode, e, xincl, xn);
if (xn <= 0.0) {
throw new SatelliteException("Error: 2 (xn <= 0.0)");
}
a = pow(XKE / xn, TWOTHIRD) * pow(tempa, 2.0);
e = e - tempe;
/*
* fix tolerance for error recognition
*/
if (e >= 1.0 || e < -0.001) {
throw new SatelliteException("Error: 1 (e >= 1.0 || e < -0.001)");
}
/*
* fix tolerance to avoid a divide by zero
*/
if (e < 1.0e-6)
e = 1.0e-6;
/*
xmdf += RecoveredMeanMotion() * templ;
double xlm = xmdf + omgadf + xnode;
xnode = fmod(xnode, TWOPI);
omgadf = fmod(omgadf, TWOPI);
xlm = fmod(xlm, TWOPI);
double xmam = fmod(xlm - omgadf - xnode, TWOPI);
*/
double xmam = xmdf + RecoveredMeanMotion() * templ;
DeepSpacePeriodics(tsince, e, xincl, omgadf, xnode, xmam);
/*
* keeping xincl positive important unless you need to display xincl
* and dislike negative inclinations
*/
if (xincl < 0.0) {
xincl = -xincl;
xnode += PI;
omgadf = omgadf - PI;
}
xl = xmam + omgadf + xnode;
omega = omgadf;
if (e < 0.0 || e > 1.0) {
throw new SatelliteException("Error: 3 (e < 0.0 || e > 1.0)");
}
/*
* re-compute the perturbed values
*/
const double perturbed_sinio = sin(xincl);
const double perturbed_cosio = cos(xincl);
const double perturbed_theta2 = perturbed_cosio * perturbed_cosio;
const double perturbed_x3thm1 = 3.0 * perturbed_theta2 - 1.0;
const double perturbed_x1mth2 = 1.0 - perturbed_theta2;
const double perturbed_x7thm1 = 7.0 * perturbed_theta2 - 1.0;
double perturbed_xlcof;
if (fabs(perturbed_cosio + 1.0) > 1.5e-12)
perturbed_xlcof = 0.125 * i_a3ovk2_ * perturbed_sinio * (3.0 + 5.0 * perturbed_cosio) / (1.0 + perturbed_cosio);
else
perturbed_xlcof = 0.125 * i_a3ovk2_ * perturbed_sinio * (3.0 + 5.0 * perturbed_cosio) / 1.5e-12;
const double perturbed_aycof = 0.25 * i_a3ovk2_ * perturbed_sinio;
/*
* using calculated values, find position and velocity
*/
CalculateFinalPositionVelocity(eci, tsince, e,
a, omega, xl, xnode,
xincl, perturbed_xlcof, perturbed_aycof,
perturbed_x3thm1, perturbed_x1mth2, perturbed_x7thm1,
perturbed_cosio, perturbed_sinio);
}
void SGDP4::FindPositionSGP4(Eci& eci, double tsince) const {
/*
* the final values
*/
double e;
double a;
double omega;
double xl;
double xnode;
double xincl;
/*
* update for secular gravity and atmospheric drag
*/
const double xmdf = MeanAnomoly() + i_xmdot_ * tsince;
const double omgadf = ArgumentPerigee() + i_omgdot_ * tsince;
const double xnoddf = AscendingNode() + i_xnodot_ * tsince;
const double tsq = tsince * tsince;
xnode = xnoddf + i_xnodcf_ * tsq;
double tempa = 1.0 - i_c1_ * tsince;
double tempe = BStar() * i_c4_ * tsince;
double templ = i_t2cof_ * tsq;
xincl = Inclination();
omega = omgadf;
double xmp = xmdf;
if (!i_use_simple_model_) {
const double delomg = n_omgcof_ * tsince;
const double delm = n_xmcof_ * (pow(1.0 + i_eta_ * cos(xmdf), 3.0) - n_delmo_);
const double temp = delomg + delm;
xmp += temp;
omega = omega - temp;
const double tcube = tsq * tsince;
const double tfour = tsince * tcube;
tempa = tempa - n_d2_ * tsq - n_d3_ * tcube - n_d4_ * tfour;
tempe += BStar() * n_c5_ * (sin(xmp) - n_sinmo_);
templ += n_t3cof_ * tcube + tfour * (n_t4cof_ + tsince * n_t5cof_);
}
a = RecoveredSemiMajorAxis() * pow(tempa, 2.0);
e = Eccentricity() - tempe;
xl = xmp + omega + xnode + RecoveredMeanMotion() * templ;
/*
* using calculated values, find position and velocity
* we can pass in constants from Initialize() as these dont change
*/
CalculateFinalPositionVelocity(eci, tsince, e,
a, omega, xl, xnode,
xincl, i_xlcof_, i_aycof_,
i_x3thm1_, i_x1mth2_, i_x7thm1_,
i_cosio_, i_sinio_);
}
void SGDP4::CalculateFinalPositionVelocity(Eci& eci, const double& tsince, const double& e,
const double& a, const double& omega, const double& xl, const double& xnode,
const double& xincl, const double& xlcof, const double& aycof,
const double& x3thm1, const double& x1mth2, const double& x7thm1,
const double& cosio, const double& sinio) const {
double temp;
double temp1;
double temp2;
double temp3;
if (a < 1.0) {
throw new SatelliteException("Error: Satellite crashed (a < 1.0)");
}
if (e < -1.0e-3) {
throw new SatelliteException("Error: Modified eccentricity too low (e < -1.0e-3)");
}
const double beta = sqrt(1.0 - e * e);
const double xn = XKE / pow(a, 1.5);
/*
* long period periodics
*/
const double axn = e * cos(omega);
temp = 1.0 / (a * beta * beta);
const double xll = temp * xlcof * axn;
const double aynl = temp * aycof;
const double xlt = xl + xll;
const double ayn = e * sin(omega) + aynl;
const 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.
*/
const double capu = fmod(xlt - xnode, 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
*/
const double max_newton_naphson = 1.25 * fabs(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
*/
const double fdot = 1.0 - ecose;
double delta_epw = f / fdot;
/*
* 2nd order Newton-Raphson correction.
* f / (fdot - 0.5 * d2f * f/fdot)
*/
if (i == 0) {
if (delta_epw > max_newton_naphson)
delta_epw = max_newton_naphson;
else if (delta_epw < -max_newton_naphson)
delta_epw = -max_newton_naphson;
} else {
delta_epw = f / (fdot + 0.5 * esine * delta_epw);
}
/*
* Newton-Raphson correction of -F/DF
*/
epw += delta_epw;
}
}
/*
* short period preliminary quantities
*/
temp = 1.0 - elsq;
const double pl = a * temp;
const double r = a * (1.0 - ecose);
temp1 = 1.0 / r;
const double rdot = XKE * sqrt(a) * esine * temp1;
const double rfdot = XKE * sqrt(pl) * temp1;
temp2 = a * temp1;
const double betal = sqrt(temp);
temp3 = 1.0 / (1.0 + betal);
const double cosu = temp2 * (cosepw - axn + ayn * esine * temp3);
const double sinu = temp2 * (sinepw - ayn - axn * esine * temp3);
const double u = atan2(sinu, cosu);
const double sin2u = 2.0 * sinu * cosu;
const double cos2u = 2.0 * cosu * cosu - 1.0;
temp = 1.0 / pl;
temp1 = CK2 * temp;
temp2 = temp1 * temp;
/*
* update for short periodics
*/
const double rk = r * (1.0 - 1.5 * temp2 * betal * x3thm1) + 0.5 * temp1 * x1mth2 * cos2u;
const double uk = u - 0.25 * temp2 * x7thm1 * sin2u;
const double xnodek = xnode + 1.5 * temp2 * cosio * sin2u;
const double xinck = xincl + 1.5 * temp2 * cosio * sinio * cos2u;
const double rdotk = rdot - xn * temp1 * x1mth2 * sin2u;
const 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
*/
const double sinuk = sin(uk);
const double cosuk = cos(uk);
const double sinik = sin(xinck);
const double cosik = cos(xinck);
const double sinnok = sin(xnodek);
const double cosnok = cos(xnodek);
const double xmx = -sinnok * cosik;
const double xmy = cosnok * cosik;
const double ux = xmx * sinuk + cosnok * cosuk;
const double uy = xmy * sinuk + sinnok * cosuk;
const double uz = sinik * sinuk;
const double vx = xmx * cosuk - cosnok * sinuk;
const double vy = xmy * cosuk - sinnok * sinuk;
const double vz = sinik * cosuk;
/*
* position and velocity
*/
const double x = rk * ux * XKMPER;
const double y = rk * uy * XKMPER;
const double z = rk * uz * XKMPER;
Vector position(x, y, z);
const double xdot = (rdotk * ux + rfdotk * vx) * XKMPER / 60.0;
const double ydot = (rdotk * uy + rfdotk * vy) * XKMPER / 60.0;
const double zdot = (rdotk * uz + rfdotk * vz) * XKMPER / 60.0;
Vector velocity(xdot, ydot, zdot);
Julian julian = Epoch();
julian.AddMin(tsince);
eci = Eci(julian, position, velocity);
}
/*
* deep space initialization
*/
void SGDP4::DeepSpaceInitialize(const double& eosq, const double& sinio, const double& cosio, const double& betao,
const double& theta2, 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;
static const double ZNS = 1.19459E-5;
static const double C1SS = 2.9864797E-6;
static const double ZES = 0.01675;
static const double ZNL = 1.5835218E-4;
static const double C1L = 4.7968065E-7;
static const double ZEL = 0.05490;
static const double ZCOSIS = 0.91744867;
static const double ZSINI = 0.39785416;
static const double ZSINGS = -0.98088458;
static const double ZCOSGS = 0.1945905;
static const double Q22 = 1.7891679E-6;
static const double Q31 = 2.1460748E-6;
static const double Q33 = 2.2123015E-7;
static const double ROOT22 = 1.7891679E-6;
static const double ROOT32 = 3.7393792E-7;
static const double ROOT44 = 7.3636953E-9;
static const double ROOT52 = 1.1428639E-7;
static const double ROOT54 = 2.1765803E-9;
const double aqnv = 1.0 / RecoveredSemiMajorAxis();
const double xpidot = omgdot + xnodot;
const double sinq = sin(AscendingNode());
const double cosq = cos(AscendingNode());
const double sing = sin(ArgumentPerigee());
const double cosg = cos(ArgumentPerigee());
/*
* initialize lunar / solar terms
*/
const double d_day_ = Epoch().FromJan1_12h_1900();
const double xnodce = 4.5236020 - 9.2422029e-4 * d_day_;
const double xnodce_temp = fmod(xnodce, TWOPI);
const double stem = sin(xnodce_temp);
const double ctem = cos(xnodce_temp);
const double zcosil = 0.91375164 - 0.03568096 * ctem;
const double zsinil = sqrt(1.0 - zcosil * zcosil);
const double zsinhl = 0.089683511 * stem / zsinil;
const double zcoshl = sqrt(1.0 - zsinhl * zsinhl);
const double c = 4.7199672 + 0.22997150 * d_day_;
const double gam = 5.8351514 + 0.0019443680 * d_day_;
d_zmol_ = Globals::Fmod2p(c - gam);
double zx = 0.39785416 * stem / zsinil;
double zy = zcoshl * ctem + 0.91744867 * zsinhl * stem;
zx = atan2(zx, zy);
zx = fmod(gam + zx - xnodce, TWOPI);
const double zcosgl = cos(zx);
const double zsingl = sin(zx);
d_zmos_ = Globals::Fmod2p(6.2565837 + 0.017201977 * d_day_);
/*
* do solar terms
*/
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;
const double xnoi = 1.0 / RecoveredMeanMotion();
for (int cnt = 0; cnt < 2; cnt++) {
/*
* solar terms are done a second time after lunar terms are done
*/
const double a1 = zcosg * zcosh + zsing * zcosi * zsinh;
const double a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
const double a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
const double a8 = zsing * zsini;
const double a9 = zsing * zsinh + zcosg * zcosi*zcosh;
const double a10 = zcosg * zsini;
const double a2 = cosio * a7 + sinio * a8;
const double a4 = cosio * a9 + sinio * a10;
const double a5 = -sinio * a7 + cosio * a8;
const double a6 = -sinio * a9 + cosio * a10;
const double x1 = a1 * cosg + a2 * sing;
const double x2 = a3 * cosg + a4 * sing;
const double x3 = -a1 * sing + a2 * cosg;
const double x4 = -a3 * sing + a4 * cosg;
const double x5 = a5 * sing;
const double x6 = a6 * sing;
const double x7 = a5 * cosg;
const double x8 = a6 * cosg;
const double z31 = 12.0 * x1 * x1 - 3. * x3 * x3;
const double z32 = 24.0 * x1 * x2 - 6. * x3 * x4;
const 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;
const double z11 = -6.0 * a1 * a5 + eosq * (-24. * x1 * x7 - 6. * x3 * x5);
const double z12 = -6.0 * (a1 * a6 + a3 * a5) + eosq * (-24. * (x2 * x7 + x1 * x8) - 6. * (x3 * x6 + x4 * x5));
const double z13 = -6.0 * a3 * a6 + eosq * (-24. * x2 * x8 - 6. * x4 * x6);
const double z21 = 6.0 * a2 * a5 + eosq * (24. * x1 * x5 - 6. * x3 * x7);
const double z22 = 6.0 * (a4 * a5 + a2 * a6) + eosq * (24. * (x2 * x5 + x1 * x6) - 6. * (x4 * x7 + x3 * x8));
const 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;
const double s3 = cc * xnoi;
const double s2 = -0.5 * s3 / betao;
const double s4 = s3 * betao;
const double s1 = -15.0 * Eccentricity() * s4;
const double s5 = x1 * x3 + x2 * x4;
const double s6 = x2 * x3 + x1 * x4;
const double s7 = x2 * x4 - x1 * x3;
se = s1 * zn * s5;
si = s2 * zn * (z11 + z13);
sl = -zn * s3 * (z1 + z3 - 14.0 - 6.0 * eosq);
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() > 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;
}
d_sse_ += se;
d_ssi_ += si;
d_ssl_ += sl;
d_ssg_ += sgh - cosio * shdq;
d_ssh_ += shdq;
d_resonance_flag_ = false;
d_synchronous_flag_ = false;
bool initialize_integrator = true;
if (RecoveredMeanMotion() < 0.0052359877 && RecoveredMeanMotion() > 0.0034906585) {
/*
* 24h synchronous resonance terms initialization
*/
d_resonance_flag_ = true;
d_synchronous_flag_ = true;
const double g200 = 1.0 + eosq * (-2.5 + 0.8125 * eosq);
const double g310 = 1.0 + 2.0 * eosq;
const double g300 = 1.0 + eosq * (-6.0 + 6.60937 * eosq);
const double f220 = 0.75 * (1.0 + cosio) * (1.0 + cosio);
const 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() - d_gsto_;
bfact = xmdot + xpidot - THDT;
bfact += d_ssl_ + d_ssg_ + d_ssh_;
} else if (RecoveredMeanMotion() < 8.26e-3 || RecoveredMeanMotion() > 9.24e-3 || Eccentricity() < 0.5) {
initialize_integrator = false;
} else {
/*
* geopotential resonance initialization for 12 hour orbits
*/
d_resonance_flag_ = true;
const 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;
}
const double sini2 = sinio * sinio;
const double f220 = 0.75 * (1.0 + 2.0 * cosio + theta2);
const double f221 = 1.5 * sini2;
const double f321 = 1.875 * sinio * (1.0 - 2.0 * cosio - 3.0 * theta2);
const double f322 = -1.875 * sinio * (1.0 + 2.0 * cosio - 3.0 * theta2);
const double f441 = 35.0 * sini2 * f220;
const double f442 = 39.3750 * sini2 * sini2;
const double f522 = 9.84375 * sinio * (sini2 * (1.0 - 2.0 * cosio - 5.0 * theta2)
+ 0.33333333 * (-2.0 + 4.0 * cosio + 6.0 * theta2));
const double f523 = sinio * (4.92187512 * sini2 * (-2.0 - 4.0 * cosio + 10.0 * theta2)
+ 6.56250012 * (1.0 + 2.0 * cosio - 3.0 * theta2));
const double f542 = 29.53125 * sinio * (2.0 - 8.0 * cosio + theta2 *
(-12.0 + 8.0 * cosio + 10.0 * theta2));
const double f543 = 29.53125 * sinio * (-2.0 - 8.0 * cosio + theta2 *
(12.0 + 8.0 * cosio - 10.0 * theta2));
const double xno2 = RecoveredMeanMotion() * RecoveredMeanMotion();
const 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() - d_gsto_ - d_gsto_;
bfact = xmdot + xnodot + xnodot - THDT - THDT;
bfact = bfact + d_ssl_ + d_ssh_ + d_ssh_;
}
if (initialize_integrator) {
/*
* initialize integrator
*/
d_xfact_ = bfact - RecoveredMeanMotion();
d_atime_ = 0.0;
d_xni_ = RecoveredMeanMotion();
d_xli_ = d_xlamo_;
}
}
void SGDP4::DeepSpaceCalculateLunarSolarTerms(const double t, double& pe, double& pinc,
double& pl, double& pgh, double& ph) const {
static const double ZES = 0.01675;
static const double ZNS = 1.19459E-5;
static const double ZNL = 1.5835218E-4;
static const double ZEL = 0.05490;
/*
* calculate solar terms for time t
*/
double zm = d_zmos_ + ZNS * t;
if (first_run_)
zm = d_zmos_;
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);
const double ses = d_se2_ * f2 + d_se3_ * f3;
const double sis = d_si2_ * f2 + d_si3_ * f3;
const double sls = d_sl2_ * f2 + d_sl3_ * f3 + d_sl4_ * sinzf;
const double sghs = d_sgh2_ * f2 + d_sgh3_ * f3 + d_sgh4_ * sinzf;
const double shs = d_sh2_ * f2 + d_sh3_ * f3;
/*
* calculate lunar terms for time t
*/
zm = d_zmol_ + ZNL * t;
if (first_run_)
zm = d_zmol_;
zf = zm + 2.0 * ZEL * sin(zm);
sinzf = sin(zf);
f2 = 0.5 * sinzf * sinzf - 0.25;
f3 = -0.5 * sinzf * cos(zf);
const double sel = d_ee2_ * f2 + d_e3_ * f3;
const double sil = d_xi2_ * f2 + d_xi3_ * f3;
const double sll = d_xl2_ * f2 + d_xl3_ * f3 + d_xl4_ * sinzf;
const double sghl = d_xgh2_ * f2 + d_xgh3_ * f3 + d_xgh4_ * sinzf;
const double shl = d_xh2_ * f2 + d_xh3_ * f3;
/*
* merge calculated values
*/
pe = ses + sel;
pinc = sis + sil;
pl = sls + sll;
pgh = sghs + sghl;
ph = shs + shl;
}
/*
* calculate lunar / solar periodics and apply
*/
void SGDP4::DeepSpacePeriodics(const double& t, double& em,
double& xinc, double& omgasm, double& xnodes, double& xll) {
/*
* storage for lunar / solar terms set by DeepSpaceCalculateLunarSolarTerms()
*/
double pe = 0.0;
double pinc = 0.0;
double pl = 0.0;
double pgh = 0.0;
double ph = 0.0;
/*
* calculate lunar / solar terms for current time
*/
DeepSpaceCalculateLunarSolarTerms(t, pe, pinc, pl, pgh, ph);
if (!first_run_) {
xinc += pinc;
em += pe;
/* Spacetrack report #3 has sin/cos from before perturbations
* added to xinc (oldxinc), but apparently report # 6 has then
* from after they are added.
* use for strn3
* if (Inclination() >= 0.2)
* use for gsfc
* if (xinc >= 0.2)
* (moved from start of function)
*/
const double sinis = sin(xinc);
const double cosis = cos(xinc);
if (xinc >= 0.2) {
/*
* apply periodics directly
*/
const double tmp_ph = ph / sinis;
omgasm += pgh - cosis * tmp_ph;
xnodes += tmp_ph;
xll += pl;
} else {
/*
* apply periodics with lyddane modification
*/
const double sinok = sin(xnodes);
const double cosok = cos(xnodes);
double alfdp = sinis * sinok;
double betdp = sinis * cosok;
const double dalf = ph * cosok + pinc * cosis * sinok;
const 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;
/*
* save old xnodes value
*/
const double oldxnodes = xnodes;
xnodes = atan2(alfdp, betdp);
/*
* Get perturbed xnodes in to same quadrant as original.
* RAAN is in the range of 0 to 360 degrees
* atan2 is in the range of -180 to 180 degrees
*/
if (fabs(oldxnodes - xnodes) > PI) {
if (xnodes < oldxnodes)
xnodes += TWOPI;
else
xnodes = xnodes - TWOPI;
}
xll += pl;
omgasm = xls - xll - cosis * xnodes;
}
}
}
/*
* deep space secular effects
*/
void SGDP4::DeepSpaceSecular(const double& t, double& xll, double& omgasm,
double& xnodes, double& em, double& xinc, double& xn) const {
static const double STEP2 = 259200.0;
static const double STEP = 720.0;
double xldot = 0.0;
double xndot = 0.0;
double xnddt = 0.0;
xll += d_ssl_ * t;
omgasm += d_ssg_ * t;
xnodes += d_ssh_ * t;
em += d_sse_ * t;
xinc += d_ssi_ * t;
if (!d_resonance_flag_)
return;
/*
* 1st condition (if t is less than one time step from epoch)
* 2nd condition (if d_atime_ and t are of opposite signs, so zero crossing required)
* 3rd condition (if t is closer to zero than d_atime_)
*/
if (fabs(t) < STEP ||
t * d_atime_ <= 0.0 ||
fabs(t) < fabs(d_atime_)) {
/*
* restart from epoch
*/
d_atime_ = 0.0;
d_xni_ = RecoveredMeanMotion();
d_xli_ = d_xlamo_;
}
double ft = t - d_atime_;
/*
* if time difference (ft) is greater than the time step (720.0)
* loop around until d_atime_ is within one time step of t
*/
if (fabs(ft) >= STEP) {
/*
* calculate step direction to allow d_atime_
* to catch up with t
*/
double delt = -STEP;
if (ft >= 0.0)
delt = STEP;
do {
DeepSpaceCalcIntegrator(delt, STEP2, xndot, xnddt, xldot);
ft = t - d_atime_;
} while (fabs(ft) >= STEP);
}
/*
* calculate dot terms
*/
DeepSpaceCalcDotTerms(xndot, xnddt, xldot);
/*
* integrator
*/
xn = d_xni_ + xndot * ft + xnddt * ft * ft * 0.5;
const double xl = d_xli_ + xldot * ft + xndot * ft * ft * 0.5;
const double temp = -xnodes + d_gsto_ + t * THDT;
if (d_synchronous_flag_)
xll = xl + temp - omgasm;
else
xll = xl + temp + temp;
}
/*
* calculate dot terms
*/
void SGDP4::DeepSpaceCalcDotTerms(double& xndot, double& xnddt, double& xldot) const {
static const double G22 = 5.7686396;
static const double G32 = 0.95240898;
static const double G44 = 1.8014998;
static const double G52 = 1.0508330;
static const double G54 = 4.4108898;
if (d_synchronous_flag_) {
xndot = d_del1_ * sin(d_xli_ - d_fasx2_) +
d_del2_ * sin(2.0 * (d_xli_ - d_fasx4_)) +
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 {
const double xomi = ArgumentPerigee() + i_omgdot_ * d_atime_;
const double x2omi = xomi + xomi;
const double x2li = d_xli_ + d_xli_;
xndot = d_d2201_ * sin(x2omi + d_xli_ - G22)
+ d_d2211_ * sin(d_xli_ - G22)
+ d_d3210_ * sin(xomi + d_xli_ - G32)
+ d_d3222_ * sin(-xomi + d_xli_ - G32)
+ d_d4410_ * sin(x2omi + x2li - G44)
+ d_d4422_ * sin(x2li - G44)
+ d_d5220_ * sin(xomi + d_xli_ - G52)
+ d_d5232_ * sin(-xomi + d_xli_ - G52)
+ d_d5421_ * sin(xomi + x2li - G54)
+ d_d5433_ * sin(-xomi + x2li - G54);
xnddt = d_d2201_ * cos(x2omi + d_xli_ - G22)
+ d_d2211_ * cos(d_xli_ - G22)
+ d_d3210_ * cos(xomi + d_xli_ - G32)
+ d_d3222_ * cos(-xomi + d_xli_ - G32)
+ d_d5220_ * cos(xomi + d_xli_ - G52)
+ d_d5232_ * cos(-xomi + d_xli_ - G52)
+ 2.0 * (d_d4410_ * cos(x2omi + x2li - G44)
+ d_d4422_ * cos(x2li - G44)
+ d_d5421_ * cos(xomi + x2li - G54)
+ d_d5433_ * cos(-xomi + x2li - G54));
}
xldot = d_xni_ + d_xfact_;
xnddt = xnddt * xldot;
}
/*
* deep space integrator for time period of delt
*/
void SGDP4::DeepSpaceCalcIntegrator(const double& delt, const double& step2, double& xndot, double& xnddt, double& xldot) const {
/*
* calculate dot terms
*/
DeepSpaceCalcDotTerms(xndot, xnddt, xldot);
/*
* integrator
*/
d_xli_ += xldot * delt + xndot * step2;
d_xni_ += xndot * delt + xnddt * step2;
/*
* increment integrator time
*/
d_atime_ += delt;
}
void SGDP4::ResetGlobalVariables() {
first_run_ = true;
i_use_simple_model_ = false;
i_use_deep_space_ = false;
i_cosio_ = i_sinio_ = i_eta_ = i_t2cof_ = i_a3ovk2_ = i_x1mth2_ =
i_x3thm1_ = i_x7thm1_ = i_aycof_ = i_xlcof_ = i_xnodcf_ = i_c1_ =
i_c4_ = i_omgdot_ = i_xnodot_ = i_xmdot_ = 0.0;
n_c5_ = n_omgcof_ = n_xmcof_ = n_delmo_ = n_sinmo_ = n_d2_ =
n_d3_ = n_d4_ = n_t3cof_ = n_t4cof_ = n_t5cof_ = 0.0;
d_gsto_ = d_zmol_ = d_zmos_ = 0.0;
d_resonance_flag_ = false;
d_synchronous_flag_ = false;
d_sse_ = d_ssi_ = d_ssl_ = d_ssg_ = d_ssh_ = 0.0;
d_se2_ = d_si2_ = d_sl2_ = d_sgh2_ = d_sh2_ = d_se3_ = d_si3_ = d_sl3_ =
d_sgh3_ = d_sh3_ = d_sl4_ = d_sgh4_ = d_ee2_ = d_e3_ = d_xi2_ =
d_xi3_ = d_xl2_ = d_xl3_ = d_xl4_ = d_xgh2_ = d_xgh3_ = d_xgh4_ =
d_xh2_ = d_xh3_ = 0.0;
d_d2201_ = d_d2211_ = d_d3210_ = d_d3222_ = d_d4410_ = d_d4422_ =
d_d5220_ = d_d5232_ = d_d5421_ = d_d5433_ = d_del1_ = d_del2_ =
d_del3_ = d_fasx2_ = d_fasx4_ = d_fasx6_ = 0.0;
d_xfact_ = d_xlamo_ = d_xli_ = d_xni_ = d_atime_ = 0.0;
mean_anomoly_ = ascending_node_ = argument_perigee_ = eccentricity_ =
inclination_ = mean_motion_ = bstar_ = recovered_semi_major_axis_ =
recovered_mean_motion_ = perigee_ = period_ = 0.0;
epoch_ = Julian();
}
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