KJ135
/
sgp4
mirror of http://172.16.0.12:5000/LAMPSARToolSoftware/sgp4.git
4
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity
sgp4/SGP4.cpp

1248 lines
45 KiB
C++
Raw Blame History

#include "SGP4.h"
#include "Util.h"
#include "Vector.h"
#include "SatelliteException.h"
#include <cmath>
#include <iomanip>
void SGP4::SetTle(const Tle& tle)
{
/*
* extract and format tle data
*/
elements_ = OrbitalElements(tle);
Initialise();
}
void SGP4::Initialise()
{
/*
* reset all constants etc
*/
Reset();
/*
* error checks
*/
if (elements_.Eccentricity() < 0.0 || elements_.Eccentricity() > 1.0 - 1.0e-3)
{
throw SatelliteException("Eccentricity out of range");
}
if (elements_.Inclination() < 0.0 || elements_.Inclination() > kPI)
{
throw SatelliteException("Inclination out of range");
}
common_consts_.cosio = cos(elements_.Inclination());
common_consts_.sinio = sin(elements_.Inclination());
const double theta2 = common_consts_.cosio * common_consts_.cosio;
common_consts_.x3thm1 = 3.0 * theta2 - 1.0;
const double eosq = elements_.Eccentricity() * elements_.Eccentricity();
const double betao2 = 1.0 - eosq;
const double betao = sqrt(betao2);
if (elements_.Period() >= 225.0)
{
use_deep_space_ = true;
}
else
{
use_deep_space_ = false;
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 (elements_.Perigee() < 220.0)
{
use_simple_model_ = true;
}
}
/*
* for perigee below 156km, the values of
* s4 and qoms2t are altered
*/
double s4 = kS;
double qoms24 = kQOMS2T;
if (elements_.Perigee() < 156.0)
{
s4 = elements_.Perigee() - 78.0;
if (elements_.Perigee() < 98.0)
{
s4 = 20.0;
}
qoms24 = pow((120.0 - s4) * kAE / kXKMPER, 4.0);
s4 = s4 / kXKMPER + kAE;
}
/*
* generate constants
*/
const double pinvsq = 1.0 / (elements_.RecoveredSemiMajorAxis() * elements_.RecoveredSemiMajorAxis() * betao2 * betao2);
const double tsi = 1.0 / (elements_.RecoveredSemiMajorAxis() - s4);
common_consts_.eta = elements_.RecoveredSemiMajorAxis() * elements_.Eccentricity() * tsi;
const double etasq = common_consts_.eta * common_consts_.eta;
const double eeta = elements_.Eccentricity() * common_consts_.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 * elements_.RecoveredMeanMotion() * (elements_.RecoveredSemiMajorAxis() *
(1.0 + 1.5 * etasq + eeta * (4.0 + etasq)) +
0.75 * kCK2 * tsi / psisq *
common_consts_.x3thm1 * (8.0 + 3.0 * etasq *
(8.0 + etasq)));
common_consts_.c1 = elements_.BStar() * c2;
common_consts_.a3ovk2 = -kXJ3 / kCK2 * pow(kAE, 3.0);
common_consts_.x1mth2 = 1.0 - theta2;
common_consts_.c4 = 2.0 * elements_.RecoveredMeanMotion() * coef1 * elements_.RecoveredSemiMajorAxis() * betao2 *
(common_consts_.eta * (2.0 + 0.5 * etasq) + elements_.Eccentricity() * (0.5 + 2.0 * etasq) -
2.0 * kCK2 * tsi / (elements_.RecoveredSemiMajorAxis() * psisq) *
(-3.0 * common_consts_.x3thm1 * (1.0 - 2.0 * eeta + etasq *
(1.5 - 0.5 * eeta)) + 0.75 * common_consts_.x1mth2 * (2.0 * etasq - eeta *
(1.0 + etasq)) * cos(2.0 * elements_.ArgumentPerigee())));
const double theta4 = theta2 * theta2;
const double temp1 = 3.0 * kCK2 * pinvsq * elements_.RecoveredMeanMotion();
const double temp2 = temp1 * kCK2 * pinvsq;
const double temp3 = 1.25 * kCK4 * pinvsq * pinvsq * elements_.RecoveredMeanMotion();
common_consts_.xmdot = elements_.RecoveredMeanMotion() + 0.5 * temp1 * betao *
common_consts_.x3thm1 + 0.0625 * temp2 * betao *
(13.0 - 78.0 * theta2 + 137.0 * theta4);
const double x1m5th = 1.0 - 5.0 * theta2;
common_consts_.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 * common_consts_.cosio;
common_consts_.xnodot = xhdot1 + (0.5 * temp2 * (4.0 - 19.0 * theta2) + 2.0 * temp3 *
(3.0 - 7.0 * theta2)) * common_consts_.cosio;
common_consts_.xnodcf = 3.5 * betao2 * xhdot1 * common_consts_.c1;
common_consts_.t2cof = 1.5 * common_consts_.c1;
if (fabs(common_consts_.cosio + 1.0) > 1.5e-12)
{
common_consts_.xlcof = 0.125 * common_consts_.a3ovk2 * common_consts_.sinio * (3.0 + 5.0 * common_consts_.cosio) / (1.0 + common_consts_.cosio);
}
else
{
common_consts_.xlcof = 0.125 * common_consts_.a3ovk2 * common_consts_.sinio * (3.0 + 5.0 * common_consts_.cosio) / 1.5e-12;
}
common_consts_.aycof = 0.25 * common_consts_.a3ovk2 * common_consts_.sinio;
common_consts_.x7thm1 = 7.0 * theta2 - 1.0;
if (use_deep_space_)
{
deepspace_consts_.gsto = elements_.Epoch().ToGreenwichSiderealTime();
DeepSpaceInitialise(eosq, common_consts_.sinio, common_consts_.cosio, betao,
theta2, betao2,
common_consts_.xmdot, common_consts_.omgdot, common_consts_.xnodot);
}
else
{
double c3 = 0.0;
if (elements_.Eccentricity() > 1.0e-4)
{
c3 = coef * tsi * common_consts_.a3ovk2 * elements_.RecoveredMeanMotion() * kAE *
common_consts_.sinio / elements_.Eccentricity();
}
nearspace_consts_.c5 = 2.0 * coef1 * elements_.RecoveredSemiMajorAxis() * betao2 * (1.0 + 2.75 *
(etasq + eeta) + eeta * etasq);
nearspace_consts_.omgcof = elements_.BStar() * c3 * cos(elements_.ArgumentPerigee());
nearspace_consts_.xmcof = 0.0;
if (elements_.Eccentricity() > 1.0e-4)
{
nearspace_consts_.xmcof = -kTWOTHIRD * coef * elements_.BStar() * kAE / eeta;
}
nearspace_consts_.delmo = pow(1.0 + common_consts_.eta * (cos(elements_.MeanAnomoly())), 3.0);
nearspace_consts_.sinmo = sin(elements_.MeanAnomoly());
if (!use_simple_model_)
{
const double c1sq = common_consts_.c1 * common_consts_.c1;
nearspace_consts_.d2 = 4.0 * elements_.RecoveredSemiMajorAxis() * tsi * c1sq;
const double temp = nearspace_consts_.d2 * tsi * common_consts_.c1 / 3.0;
nearspace_consts_.d3 = (17.0 * elements_.RecoveredSemiMajorAxis() + s4) * temp;
nearspace_consts_.d4 = 0.5 * temp * elements_.RecoveredSemiMajorAxis() *
tsi * (221.0 * elements_.RecoveredSemiMajorAxis() + 31.0 * s4) * common_consts_.c1;
nearspace_consts_.t3cof = nearspace_consts_.d2 + 2.0 * c1sq;
nearspace_consts_.t4cof = 0.25 * (3.0 * nearspace_consts_.d3 + common_consts_.c1 *
(12.0 * nearspace_consts_.d2 + 10.0 * c1sq));
nearspace_consts_.t5cof = 0.2 * (3.0 * nearspace_consts_.d4 + 12.0 * common_consts_.c1 *
nearspace_consts_.d3 + 6.0 * nearspace_consts_.d2 * nearspace_consts_.d2 + 15.0 *
c1sq * (2.0 * nearspace_consts_.d2 + c1sq));
}
}
}
Eci SGP4::FindPosition(double tsince) const
{
if (use_deep_space_)
{
return FindPositionSDP4(tsince);
}
else
{
return FindPositionSGP4(tsince);
}
}
Eci SGP4::FindPosition(const Julian& date) const
{
Timespan diff = date - elements_.Epoch();
return FindPosition(diff.GetTotalMinutes());
}
Eci SGP4::FindPositionSDP4(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
*/
double xmdf = elements_.MeanAnomoly() + common_consts_.xmdot * tsince;
double omgadf = elements_.ArgumentPerigee() + common_consts_.omgdot * tsince;
const double xnoddf = elements_.AscendingNode() + common_consts_.xnodot * tsince;
const double tsq = tsince * tsince;
xnode = xnoddf + common_consts_.xnodcf * tsq;
double tempa = 1.0 - common_consts_.c1 * tsince;
double tempe = elements_.BStar() * common_consts_.c4 * tsince;
double templ = common_consts_.t2cof * tsq;
double xn = elements_.RecoveredMeanMotion();
e = elements_.Eccentricity();
xincl = elements_.Inclination();
DeepSpaceSecular(tsince, &xmdf, &omgadf, &xnode, &e, &xincl, &xn);
if (xn <= 0.0)
{
throw SatelliteException("Error: #2 (xn <= 0.0)");
}
a = pow(kXKE / xn, kTWOTHIRD) * pow(tempa, 2.0);
e -= tempe;
double xmam = xmdf + elements_.RecoveredMeanMotion() * templ;
/*
* fix tolerance for error recognition
*/
if (e >= 1.0 || e < -0.001)
{
throw 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;
}
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 += kPI;
omgadf -= kPI;
}
xl = xmam + omgadf + xnode;
omega = omgadf;
if (e < 0.0 || e > 1.0)
{
throw 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 * common_consts_.a3ovk2 * perturbed_sinio * (3.0 + 5.0 * perturbed_cosio) / (1.0 + perturbed_cosio);
}
else
{
perturbed_xlcof = 0.125 * common_consts_.a3ovk2 * perturbed_sinio * (3.0 + 5.0 * perturbed_cosio) / 1.5e-12;
}
const double perturbed_aycof = 0.25 * common_consts_.a3ovk2 * perturbed_sinio;
/*
* using calculated values, find position and velocity
*/
return CalculateFinalPositionVelocity(tsince, e,
a, omega, xl, xnode,
xincl, perturbed_xlcof, perturbed_aycof,
perturbed_x3thm1, perturbed_x1mth2, perturbed_x7thm1,
perturbed_cosio, perturbed_sinio);
}
Eci SGP4::FindPositionSGP4(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 = elements_.MeanAnomoly() + common_consts_.xmdot * tsince;
const double omgadf = elements_.ArgumentPerigee() + common_consts_.omgdot * tsince;
const double xnoddf = elements_.AscendingNode() + common_consts_.xnodot * tsince;
const double tsq = tsince * tsince;
xnode = xnoddf + common_consts_.xnodcf * tsq;
double tempa = 1.0 - common_consts_.c1 * tsince;
double tempe = elements_.BStar() * common_consts_.c4 * tsince;
double templ = common_consts_.t2cof * tsq;
xincl = elements_.Inclination();
omega = omgadf;
double xmp = xmdf;
if (!use_simple_model_)
{
const double delomg = nearspace_consts_.omgcof * tsince;
const double delm = nearspace_consts_.xmcof * (pow(1.0 + common_consts_.eta * cos(xmdf), 3.0) - nearspace_consts_.delmo);
const double temp = delomg + delm;
xmp += temp;
omega -= temp;
const double tcube = tsq * tsince;
const double tfour = tsince * tcube;
tempa = tempa - nearspace_consts_.d2 * tsq - nearspace_consts_.d3 * tcube - nearspace_consts_.d4 * tfour;
tempe += elements_.BStar() * nearspace_consts_.c5 * (sin(xmp) - nearspace_consts_.sinmo);
templ += nearspace_consts_.t3cof * tcube + tfour * (nearspace_consts_.t4cof + tsince * nearspace_consts_.t5cof);
}
a = elements_.RecoveredSemiMajorAxis() * pow(tempa, 2.0);
e = elements_.Eccentricity() - tempe;
xl = xmp + omega + xnode + elements_.RecoveredMeanMotion() * templ;
if (xl <= 0.0)
{
throw SatelliteException("Error: #2 (xl <= 0.0)");
}
/*
* fix tolerance for error recognition
*/
if (e >= 1.0 || e < -0.001)
{
throw 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;
}
/*
* using calculated values, find position and velocity
* we can pass in constants from Initialise() as these dont change
*/
return CalculateFinalPositionVelocity(tsince, e,
a, omega, xl, xnode,
xincl, common_consts_.xlcof, common_consts_.aycof,
common_consts_.x3thm1, common_consts_.x1mth2, common_consts_.x7thm1,
common_consts_.cosio, common_consts_.sinio);
}
Eci SGP4::CalculateFinalPositionVelocity(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
{
const double beta = sqrt(1.0 - e * e);
const double xn = kXKE / pow(a, 1.5);
/*
* long period periodics
*/
const double axn = e * cos(omega);
const double temp11 = 1.0 / (a * beta * beta);
const double xll = temp11 * xlcof * axn;
const double aynl = temp11 * aycof;
const double xlt = xl + xll;
const double ayn = e * sin(omega) + aynl;
const double elsq = axn * axn + ayn * ayn;
/*
* 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, kTWOPI);
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
*/
const double temp21 = 1.0 - elsq;
const double pl = a * temp21;
if (pl < 0.0)
{
throw SatelliteException("Error: #4 (pl < 0.0)");
}
const double r = a * (1.0 - ecose);
const double temp31 = 1.0 / r;
const double rdot = kXKE * sqrt(a) * esine * temp31;
const double rfdot = kXKE * sqrt(pl) * temp31;
const double temp32 = a * temp31;
const double betal = sqrt(temp21);
const double temp33 = 1.0 / (1.0 + betal);
const double cosu = temp32 * (cosepw - axn + ayn * esine * temp33);
const double sinu = temp32 * (sinepw - ayn - axn * esine * temp33);
const double u = atan2(sinu, cosu);
const double sin2u = 2.0 * sinu * cosu;
const double cos2u = 2.0 * cosu * cosu - 1.0;
/*
* update for short periodics
*/
const double temp41 = 1.0 / pl;
const double temp42 = kCK2 * temp41;
const double temp43 = temp42 * temp41;
const double rk = r * (1.0 - 1.5 * temp43 * betal * x3thm1) + 0.5 * temp42 * x1mth2 * cos2u;
const double uk = u - 0.25 * temp43 * x7thm1 * sin2u;
const double xnodek = xnode + 1.5 * temp43 * cosio * sin2u;
const double xinck = xincl + 1.5 * temp43 * cosio * sinio * cos2u;
const double rdotk = rdot - xn * temp42 * x1mth2 * sin2u;
const double rfdotk = rfdot + xn * temp42 * (x1mth2 * cos2u + 1.5 * x3thm1);
if (rk < 1.0)
{
throw SatelliteException("Error: #6 Satellite decayed (rk < 1.0)");
}
/*
* 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 * kXKMPER;
const double y = rk * uy * kXKMPER;
const double z = rk * uz * kXKMPER;
Vector position(x, y, z);
const double xdot = (rdotk * ux + rfdotk * vx) * kXKMPER / 60.0;
const double ydot = (rdotk * uy + rfdotk * vy) * kXKMPER / 60.0;
const double zdot = (rdotk * uz + rfdotk * vz) * kXKMPER / 60.0;
Vector velocity(xdot, ydot, zdot);
Julian julian(elements_.Epoch());
julian.AddMin(tsince);
Eci eci(julian, position, velocity);
return eci;
}
static inline double EvaluateCubicPolynomial(const double x, const double constant,
const double linear, const double squared, const double cubed)
{
return constant + x * (linear + x * (squared + x * cubed));
}
/*
* deep space initialisation
*/
void SGP4::DeepSpaceInitialise(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 / elements_.RecoveredSemiMajorAxis();
const double xpidot = omgdot + xnodot;
const double sinq = sin(elements_.AscendingNode());
const double cosq = cos(elements_.AscendingNode());
const double sing = sin(elements_.ArgumentPerigee());
const double cosg = cos(elements_.ArgumentPerigee());
/*
* initialize lunar / solar terms
*/
const double jday = elements_.Epoch().FromJan1_12h_1900();
const double xnodce = 4.5236020 - 9.2422029e-4 * jday;
const double xnodce_temp = fmod(xnodce, kTWOPI);
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 * jday;
const double gam = 5.8351514 + 0.0019443680 * jday;
deepspace_consts_.zmol = Util::WrapTwoPI(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, kTWOPI);
const double zcosgl = cos(zx);
const double zsingl = sin(zx);
deepspace_consts_.zmos = Util::WrapTwoPI(6.2565837 + 0.017201977 * jday);
/*
* 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 / elements_.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 * elements_.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 (elements_.Inclination() < 5.2359877e-2 || elements_.Inclination() > kPI - 5.2359877e-2)
{
shdq = 0.0;
}
else
{
shdq = (-zn * s2 * (z21 + z23)) / sinio;
}
deepspace_consts_.ee2 = 2.0 * s1 * s6;
deepspace_consts_.e3 = 2.0 * s1 * s7;
deepspace_consts_.xi2 = 2.0 * s2 * z12;
deepspace_consts_.xi3 = 2.0 * s2 * (z13 - z11);
deepspace_consts_.xl2 = -2.0 * s3 * z2;
deepspace_consts_.xl3 = -2.0 * s3 * (z3 - z1);
deepspace_consts_.xl4 = -2.0 * s3 * (-21.0 - 9.0 * eosq) * ze;
deepspace_consts_.xgh2 = 2.0 * s4 * z32;
deepspace_consts_.xgh3 = 2.0 * s4 * (z33 - z31);
deepspace_consts_.xgh4 = -18.0 * s4 * ze;
deepspace_consts_.xh2 = -2.0 * s2 * z22;
deepspace_consts_.xh3 = -2.0 * s2 * (z23 - z21);
if (cnt == 1)
{
break;
}
/*
* do lunar terms
*/
deepspace_consts_.sse = se;
deepspace_consts_.ssi = si;
deepspace_consts_.ssl = sl;
deepspace_consts_.ssh = shdq;
deepspace_consts_.ssg = sgh - cosio * deepspace_consts_.ssh;
deepspace_consts_.se2 = deepspace_consts_.ee2;
deepspace_consts_.si2 = deepspace_consts_.xi2;
deepspace_consts_.sl2 = deepspace_consts_.xl2;
deepspace_consts_.sgh2 = deepspace_consts_.xgh2;
deepspace_consts_.sh2 = deepspace_consts_.xh2;
deepspace_consts_.se3 = deepspace_consts_.e3;
deepspace_consts_.si3 = deepspace_consts_.xi3;
deepspace_consts_.sl3 = deepspace_consts_.xl3;
deepspace_consts_.sgh3 = deepspace_consts_.xgh3;
deepspace_consts_.sh3 = deepspace_consts_.xh3;
deepspace_consts_.sl4 = deepspace_consts_.xl4;
deepspace_consts_.sgh4 = deepspace_consts_.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;
}
deepspace_consts_.sse += se;
deepspace_consts_.ssi += si;
deepspace_consts_.ssl += sl;
deepspace_consts_.ssg += sgh - cosio * shdq;
deepspace_consts_.ssh += shdq;
deepspace_consts_.resonance_flag = false;
deepspace_consts_.synchronous_flag = false;
bool initialise_integrator = true;
if (elements_.RecoveredMeanMotion() < 0.0052359877 && elements_.RecoveredMeanMotion() > 0.0034906585)
{
/*
* 24h synchronous resonance terms initialisation
*/
deepspace_consts_.resonance_flag = true;
deepspace_consts_.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;
deepspace_consts_.del1 = 3.0 * elements_.RecoveredMeanMotion() * elements_.RecoveredMeanMotion() * aqnv * aqnv;
deepspace_consts_.del2 = 2.0 * deepspace_consts_.del1 * f220 * g200 * Q22;
deepspace_consts_.del3 = 3.0 * deepspace_consts_.del1 * f330 * g300 * Q33 * aqnv;
deepspace_consts_.del1 = deepspace_consts_.del1 * f311 * g310 * Q31 * aqnv;
integrator_consts_.xlamo = elements_.MeanAnomoly() + elements_.AscendingNode() + elements_.ArgumentPerigee() - deepspace_consts_.gsto;
bfact = xmdot + xpidot - kTHDT;
bfact += deepspace_consts_.ssl + deepspace_consts_.ssg + deepspace_consts_.ssh;
}
else if (elements_.RecoveredMeanMotion() < 8.26e-3 || elements_.RecoveredMeanMotion() > 9.24e-3 || elements_.Eccentricity() < 0.5)
{
initialise_integrator = false;
}
else
{
/*
* geopotential resonance initialisation for 12 hour orbits
*/
deepspace_consts_.resonance_flag = true;
double g211;
double g310;
double g322;
double g410;
double g422;
double g520;
double g201 = -0.306 - (elements_.Eccentricity() - 0.64) * 0.440;
if (elements_.Eccentricity() <= 0.65)
{
g211 = EvaluateCubicPolynomial(elements_.Eccentricity(), 3.616, -13.247, +16.290, 0.0);
g310 = EvaluateCubicPolynomial(elements_.Eccentricity(), -19.302, 117.390, -228.419, 156.591);
g322 = EvaluateCubicPolynomial(elements_.Eccentricity(), -18.9068, 109.7927, -214.6334, 146.5816);
g410 = EvaluateCubicPolynomial(elements_.Eccentricity(), -41.122, 242.694, -471.094, 313.953);
g422 = EvaluateCubicPolynomial(elements_.Eccentricity(), -146.407, 841.880, -1629.014, 1083.435);
g520 = EvaluateCubicPolynomial(elements_.Eccentricity(), -532.114, 3017.977, -5740.032, 3708.276);
}
else
{
g211 = EvaluateCubicPolynomial(elements_.Eccentricity(), -72.099, 331.819, -508.738, 266.724);
g310 = EvaluateCubicPolynomial(elements_.Eccentricity(), -346.844, 1582.851, -2415.925, 1246.113);
g322 = EvaluateCubicPolynomial(elements_.Eccentricity(), -342.585, 1554.908, -2366.899, 1215.972);
g410 = EvaluateCubicPolynomial(elements_.Eccentricity(), -1052.797, 4758.686, -7193.992, 3651.957);
g422 = EvaluateCubicPolynomial(elements_.Eccentricity(), -3581.69, 16178.11, -24462.77, 12422.52);
if (elements_.Eccentricity() <= 0.715)
{
g520 = EvaluateCubicPolynomial(elements_.Eccentricity(), 1464.74, -4664.75, 3763.64, 0.0);
}
else
{
g520 = EvaluateCubicPolynomial(elements_.Eccentricity(), -5149.66, 29936.92, -54087.36, 31324.56);
}
}
double g533;
double g521;
double g532;
if (elements_.Eccentricity() < 0.7)
{
g533 = EvaluateCubicPolynomial(elements_.Eccentricity(), -919.2277, 4988.61, -9064.77, 5542.21);
g521 = EvaluateCubicPolynomial(elements_.Eccentricity(), -822.71072, 4568.6173, -8491.4146, 5337.524);
g532 = EvaluateCubicPolynomial(elements_.Eccentricity(), -853.666, 4690.25, -8624.77, 5341.4);
}
else
{
g533 = EvaluateCubicPolynomial(elements_.Eccentricity(), -37995.78, 161616.52, -229838.2, 109377.94);
g521 = EvaluateCubicPolynomial(elements_.Eccentricity(), -51752.104, 218913.95, -309468.16, 146349.42);
g532 = EvaluateCubicPolynomial(elements_.Eccentricity(), -40023.88, 170470.89, -242699.48, 115605.82);
}
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 = elements_.RecoveredMeanMotion() * elements_.RecoveredMeanMotion();
const double ainv2 = aqnv * aqnv;
double temp1 = 3.0 * xno2 * ainv2;
double temp = temp1 * ROOT22;
deepspace_consts_.d2201 = temp * f220 * g201;
deepspace_consts_.d2211 = temp * f221 * g211;
temp1 = temp1 * aqnv;
temp = temp1 * ROOT32;
deepspace_consts_.d3210 = temp * f321 * g310;
deepspace_consts_.d3222 = temp * f322 * g322;
temp1 = temp1 * aqnv;
temp = 2.0 * temp1 * ROOT44;
deepspace_consts_.d4410 = temp * f441 * g410;
deepspace_consts_.d4422 = temp * f442 * g422;
temp1 = temp1 * aqnv;
temp = temp1 * ROOT52;
deepspace_consts_.d5220 = temp * f522 * g520;
deepspace_consts_.d5232 = temp * f523 * g532;
temp = 2.0 * temp1 * ROOT54;
deepspace_consts_.d5421 = temp * f542 * g521;
deepspace_consts_.d5433 = temp * f543 * g533;
integrator_consts_.xlamo = elements_.MeanAnomoly() + elements_.AscendingNode() + elements_.AscendingNode() - deepspace_consts_.gsto - deepspace_consts_.gsto;
bfact = xmdot + xnodot + xnodot - kTHDT - kTHDT;
bfact = bfact + deepspace_consts_.ssl + deepspace_consts_.ssh + deepspace_consts_.ssh;
}
if (initialise_integrator)
{
/*
* initialise integrator
*/
integrator_consts_.xfact = bfact - elements_.RecoveredMeanMotion();
integrator_params_.atime = 0.0;
integrator_params_.xni = elements_.RecoveredMeanMotion();
integrator_params_.xli = integrator_consts_.xlamo;
/*
* precompute dot terms for epoch
*/
DeepSpaceCalcDotTerms(&integrator_consts_.values_0);
}
}
void SGP4::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 = deepspace_consts_.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);
const double ses = deepspace_consts_.se2 * f2 + deepspace_consts_.se3 * f3;
const double sis = deepspace_consts_.si2 * f2 + deepspace_consts_.si3 * f3;
const double sls = deepspace_consts_.sl2 * f2 + deepspace_consts_.sl3 * f3 + deepspace_consts_.sl4 * sinzf;
const double sghs = deepspace_consts_.sgh2 * f2 + deepspace_consts_.sgh3 * f3 + deepspace_consts_.sgh4 * sinzf;
const double shs = deepspace_consts_.sh2 * f2 + deepspace_consts_.sh3 * f3;
/*
* calculate lunar terms for time t
*/
zm = deepspace_consts_.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);
const double sel = deepspace_consts_.ee2 * f2 + deepspace_consts_.e3 * f3;
const double sil = deepspace_consts_.xi2 * f2 + deepspace_consts_.xi3 * f3;
const double sll = deepspace_consts_.xl2 * f2 + deepspace_consts_.xl3 * f3 + deepspace_consts_.xl4 * sinzf;
const double sghl = deepspace_consts_.xgh2 * f2 + deepspace_consts_.xgh3 * f3 + deepspace_consts_.xgh4 * sinzf;
const double shl = deepspace_consts_.xh2 * f2 + deepspace_consts_.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 SGP4::DeepSpacePeriodics(const double& t, double* em,
double* xinc, double* omgasm, double* xnodes, double* xll) const
{
/*
* 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);
(*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 (elements_.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;
(*xnodes) = Util::WrapTwoPI((*xnodes));
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);
if ((*xnodes) < 0.0)
{
(*xnodes) += kTWOPI;
}
/*
* 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)) > kPI)
{
if ((*xnodes) < oldxnodes)
{
(*xnodes) += kTWOPI;
}
else
{
(*xnodes) -= kTWOPI;
}
}
(*xll) += pl;
(*omgasm) = xls - (*xll) - cosis * (*xnodes);
}
}
/*
* deep space secular effects
*/
void SGP4::DeepSpaceSecular(const double& t, double* xll, double* omgasm,
double* xnodes, double* em, double* xinc, double* xn) const
{
static const double STEP = 720.0;
static const double STEP2 = 259200.0;
(*xll) += deepspace_consts_.ssl * t;
(*omgasm) += deepspace_consts_.ssg * t;
(*xnodes) += deepspace_consts_.ssh * t;
(*em) += deepspace_consts_.sse * t;
(*xinc) += deepspace_consts_.ssi * t;
if (!deepspace_consts_.resonance_flag)
{
return;
}
/*
* 1st condition (if t is less than one time step from epoch)
* 2nd condition (if integrator_params_.atime and t are of opposite signs, so zero crossing required)
* 3rd condition (if t is closer to zero than integrator_params_.atime, only integrate away from zero)
*/
if (fabs(t) < STEP ||
t * integrator_params_.atime <= 0.0 ||
fabs(t) < fabs(integrator_params_.atime))
{
/*
* restart from epoch
*/
integrator_params_.atime = 0.0;
integrator_params_.xni = elements_.RecoveredMeanMotion();
integrator_params_.xli = integrator_consts_.xlamo;
/*
* restore precomputed values for epoch
*/
integrator_params_.values_t = integrator_consts_.values_0;
}
double ft = t - integrator_params_.atime;
/*
* if time difference (ft) is greater than the time step (720.0)
* loop around until integrator_params_.atime is within one time step of t
*/
if (fabs(ft) >= STEP)
{
/*
* calculate step direction to allow integrator_params_.atime
* to catch up with t
*/
double delt = -STEP;
if (ft >= 0.0)
{
delt = STEP;
}
do
{
/*
* integrate using current dot terms
*/
DeepSpaceIntegrator(delt, STEP2, integrator_params_.values_t);
/*
* calculate dot terms for next integration
*/
DeepSpaceCalcDotTerms(&integrator_params_.values_t);
ft = t - integrator_params_.atime;
} while (fabs(ft) >= STEP);
}
/*
* integrator
*/
(*xn) = integrator_params_.xni + integrator_params_.values_t.xndot * ft + integrator_params_.values_t.xnddt * ft * ft * 0.5;
const double xl = integrator_params_.xli + integrator_params_.values_t.xldot * ft + integrator_params_.values_t.xndot * ft * ft * 0.5;
const double temp = -(*xnodes) + deepspace_consts_.gsto + t * kTHDT;
if (deepspace_consts_.synchronous_flag)
{
(*xll) = xl + temp - (*omgasm);
}
else
{
(*xll) = xl + temp + temp;
}
}
/*
* calculate dot terms
*/
void SGP4::DeepSpaceCalcDotTerms(struct IntegratorValues *values) 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;
static const double FASX2 = 0.13130908;
static const double FASX4 = 2.8843198;
static const double FASX6 = 0.37448087;
if (deepspace_consts_.synchronous_flag)
{
values->xndot = deepspace_consts_.del1 * sin(integrator_params_.xli - FASX2) +
deepspace_consts_.del2 * sin(2.0 * (integrator_params_.xli - FASX4)) +
deepspace_consts_.del3 * sin(3.0 * (integrator_params_.xli - FASX6));
values->xnddt = deepspace_consts_.del1 * cos(integrator_params_.xli - FASX2) + 2.0 *
deepspace_consts_.del2 * cos(2.0 * (integrator_params_.xli - FASX4)) + 3.0 *
deepspace_consts_.del3 * cos(3.0 * (integrator_params_.xli - FASX6));
}
else
{
const double xomi = elements_.ArgumentPerigee() + common_consts_.omgdot * integrator_params_.atime;
const double x2omi = xomi + xomi;
const double x2li = integrator_params_.xli + integrator_params_.xli;
values->xndot = deepspace_consts_.d2201 * sin(x2omi + integrator_params_.xli - G22)
+ deepspace_consts_.d2211 * sin(integrator_params_.xli - G22)
+ deepspace_consts_.d3210 * sin(xomi + integrator_params_.xli - G32)
+ deepspace_consts_.d3222 * sin(-xomi + integrator_params_.xli - G32)
+ deepspace_consts_.d4410 * sin(x2omi + x2li - G44)
+ deepspace_consts_.d4422 * sin(x2li - G44)
+ deepspace_consts_.d5220 * sin(xomi + integrator_params_.xli - G52)
+ deepspace_consts_.d5232 * sin(-xomi + integrator_params_.xli - G52)
+ deepspace_consts_.d5421 * sin(xomi + x2li - G54)
+ deepspace_consts_.d5433 * sin(-xomi + x2li - G54);
values->xnddt = deepspace_consts_.d2201 * cos(x2omi + integrator_params_.xli - G22)
+ deepspace_consts_.d2211 * cos(integrator_params_.xli - G22)
+ deepspace_consts_.d3210 * cos(xomi + integrator_params_.xli - G32)
+ deepspace_consts_.d3222 * cos(-xomi + integrator_params_.xli - G32)
+ deepspace_consts_.d5220 * cos(xomi + integrator_params_.xli - G52)
+ deepspace_consts_.d5232 * cos(-xomi + integrator_params_.xli - G52)
+ 2.0 * (deepspace_consts_.d4410 * cos(x2omi + x2li - G44)
+ deepspace_consts_.d4422 * cos(x2li - G44)
+ deepspace_consts_.d5421 * cos(xomi + x2li - G54)
+ deepspace_consts_.d5433 * cos(-xomi + x2li - G54));
}
values->xldot = integrator_params_.xni + integrator_consts_.xfact;
values->xnddt *= values->xldot;
}
/*
* deep space integrator for time period of delt
*/
void SGP4::DeepSpaceIntegrator(const double delt, const double step2,
const struct IntegratorValues &values) const
{
/*
* integrator
*/
integrator_params_.xli += values.xldot * delt + values.xndot * step2;
integrator_params_.xni += values.xndot * delt + values.xnddt * step2;
/*
* increment integrator time
*/
integrator_params_.atime += delt;
}
void SGP4::Reset()
{
/*
* common variables
*/
use_simple_model_ = false;
use_deep_space_ = false;
}
Reference in New Issue View Git Blame Copy Permalink