// ///////////////////////////////////////////////////////////////////////////
private bool DeepPeriodics(ref double e, ref double xincc,
ref double omgadf, ref double xnode,
ref double xmam, double tsince)
{
// Lunar-solar periodics
double sinis = Math.Sin(xincc);
double cosis = Math.Cos(xincc);
double sghs = 0.0;
double shs = 0.0;
double sh1 = 0.0;
double pe = 0.0;
double pinc = 0.0;
double pl = 0.0;
double sghl = 0.0;
double zm = dp_zmos + zns * tsince;
double zf = zm + 2.0 * zes * Math.Sin(zm);
double sinzf = Math.Sin(zf);
double f2 = 0.5 * sinzf * sinzf - 0.25;
double f3 = -0.5 * sinzf * Math.Cos(zf);
double ses = dp_se2 * f2 + dp_se3 * f3;
double sis = dp_si2 * f2 + dp_si3 * f3;
double sls = dp_sl2 * f2 + dp_sl3 * f3 + dp_sl4 * sinzf;
sghs = dp_sgh2 * f2 + dp_sgh3 * f3 + dp_sgh4 * sinzf;
shs = dp_sh2 * f2 + dp_sh3 * f3;
zm = dp_zmol + znl * tsince;
zf = zm + 2.0 * zel * Math.Sin(zm);
sinzf = Math.Sin(zf);
f2 = 0.5 * sinzf * sinzf - 0.25;
f3 = -0.5 * sinzf * Math.Cos(zf);
double sel = dp_ee2 * f2 + dp_e3 * f3;
double sil = dp_xi2 * f2 + dp_xi3 * f3;
double sll = dp_xl2 * f2 + dp_xl3 * f3 + dp_xl4 * sinzf;
sghl = dp_xgh2 * f2 + dp_xgh3 * f3 + dp_xgh4 * sinzf;
sh1 = dp_xh2 * f2 + dp_xh3 * f3;
pe = ses + sel;
pinc = sis + sil;
pl = sls + sll;
double pgh = sghs + sghl;
double ph = shs + sh1;
xincc = xincc + pinc;
e = e + pe;
if (dp_xqncl >= 0.2)
{
// Apply periodics directly
ph = ph / m_sinio;
pgh = pgh - m_cosio * ph;
omgadf = omgadf + pgh;
xnode = xnode + ph;
xmam = xmam + pl;
}
else
{
// Apply periodics with Lyddane modification
double sinok = Math.Sin(xnode);
double cosok = Math.Cos(xnode);
double alfdp = sinis * sinok;
double betdp = sinis * cosok;
double dalf = ph * cosok + pinc * cosis * sinok;
double dbet = -ph * sinok + pinc * cosis * cosok;
alfdp = alfdp + dalf;
betdp = betdp + dbet;
double xls = xmam + omgadf + cosis * xnode;
double dls = pl + pgh - pinc * xnode * sinis;
xls = xls + dls;
xnode = Globals.AcTan(alfdp, betdp);
xmam = xmam + pl;
omgadf = xls - xmam - Math.Cos(xincc) * xnode;
}
return(true);
}
bool gp_sync; // geopotential synchronous
// ///////////////////////////////////////////////////////////////////////////
public NoradSDP4(Orbit orbit) :
base(orbit)
{
double sinarg = Math.Sin(Orbit.ArgPerigee);
double cosarg = Math.Cos(Orbit.ArgPerigee);
// Deep space initialization
Julian jd = Orbit.Epoch;
dp_thgr = jd.ToGmst();
double eq = Orbit.Eccentricity;
double aqnv = 1.0 / Orbit.SemiMajor;
dp_xqncl = Orbit.Inclination;
double xmao = Orbit.MeanAnomaly;
double xpidot = m_omgdot + m_xnodot;
double sinq = Math.Sin(Orbit.RAAN);
double cosq = Math.Cos(Orbit.RAAN);
dp_omegaq = Orbit.ArgPerigee;
#region Lunar / Solar terms
// Initialize lunar solar terms
double day = jd.FromJan0_12h_1900();
double dpi_xnodce = 4.5236020 - 9.2422029E-4 * day;
double dpi_stem = Math.Sin(dpi_xnodce);
double dpi_ctem = Math.Cos(dpi_xnodce);
double dpi_zcosil = 0.91375164 - 0.03568096 * dpi_ctem;
double dpi_zsinil = Math.Sqrt(1.0 - dpi_zcosil * dpi_zcosil);
double dpi_zsinhl = 0.089683511 * dpi_stem / dpi_zsinil;
double dpi_zcoshl = Math.Sqrt(1.0 - dpi_zsinhl * dpi_zsinhl);
double dpi_c = 4.7199672 + 0.22997150 * day;
double dpi_gam = 5.8351514 + 0.0019443680 * day;
dp_zmol = Globals.Fmod2p(dpi_c - dpi_gam);
double dpi_zx = 0.39785416 * dpi_stem / dpi_zsinil;
double dpi_zy = dpi_zcoshl * dpi_ctem + 0.91744867 * dpi_zsinhl * dpi_stem;
dpi_zx = Globals.AcTan(dpi_zx, dpi_zy) + dpi_gam - dpi_xnodce;
double dpi_zcosgl = Math.Cos(dpi_zx);
double dpi_zsingl = Math.Sin(dpi_zx);
dp_zmos = 6.2565837 + 0.017201977 * day;
dp_zmos = Globals.Fmod2p(dp_zmos);
const double zcosis = 0.91744867;
const double zsinis = 0.39785416;
const double zsings = -0.98088458;
const double zcosgs = 0.1945905;
const double c1ss = 2.9864797E-6;
double zcosg = zcosgs;
double zsing = zsings;
double zcosi = zcosis;
double zsini = zsinis;
double zcosh = cosq;
double zsinh = sinq;
double cc = c1ss;
double zn = zns;
double ze = zes;
double xnoi = 1.0 / Orbit.MeanMotion;
double a1; double a3; double a7; double a8; double a9; double a10;
double a2; double a4; double a5; double a6; double x1; double x2;
double x3; double x4; double x5; double x6; double x7; double x8;
double z31; double z32; double z33; double z1; double z2; double z3;
double z11; double z12; double z13; double z21; double z22; double z23;
double s3; double s2; double s4; double s1; double s5; double s6;
double s7;
double se = 0.0;
double si = 0.0;
double sl = 0.0;
double sgh = 0.0;
double sh = 0.0;
double eosq = Globals.Sqr(Orbit.Eccentricity);
// Apply the solar and lunar terms on the first pass, then re-apply the
// solar terms again on the second pass.
for (int pass = 1; pass <= 2; pass++)
{
// Do solar terms
a1 = zcosg * zcosh + zsing * zcosi * zsinh;
a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
a8 = zsing * zsini;
a9 = zsing * zsinh + zcosg * zcosi * zcosh;
a10 = zcosg * zsini;
a2 = m_cosio * a7 + m_sinio * a8;
a4 = m_cosio * a9 + m_sinio * a10;
a5 = -m_sinio * a7 + m_cosio * a8;
a6 = -m_sinio * a9 + m_cosio * a10;
x1 = a1 * cosarg + a2 * sinarg;
x2 = a3 * cosarg + a4 * sinarg;
x3 = -a1 * sinarg + a2 * cosarg;
x4 = -a3 * sinarg + a4 * cosarg;
x5 = a5 * sinarg;
x6 = a6 * sinarg;
x7 = a5 * cosarg;
x8 = a6 * cosarg;
z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3;
z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4;
z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4;
z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * eosq;
z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * eosq;
z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * eosq;
z11 = -6.0 * a1 * a5 + eosq * (-24.0 * x1 * x7 - 6.0 * x3 * x5);
z12 = -6.0 * (a1 * a6 + a3 * a5) +
eosq * (-24.0 * (x2 * x7 + x1 * x8) - 6.0 * (x3 * x6 + x4 * x5));
z13 = -6.0 * a3 * a6 + eosq * (-24.0 * x2 * x8 - 6.0 * x4 * x6);
z21 = 6.0 * a2 * a5 + eosq * (24.0 * x1 * x5 - 6.0 * x3 * x7);
z22 = 6.0 * (a4 * a5 + a2 * a6) +
eosq * (24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8));
z23 = 6.0 * a4 * a6 + eosq * (24.0 * x2 * x6 - 6.0 * x4 * x8);
z1 = z1 + z1 + m_betao2 * z31;
z2 = z2 + z2 + m_betao2 * z32;
z3 = z3 + z3 + m_betao2 * z33;
s3 = cc * xnoi;
s2 = -0.5 * s3 / m_betao;
s4 = s3 * m_betao;
s1 = -15.0 * eq * s4;
s5 = x1 * x3 + x2 * x4;
s6 = x2 * x3 + x1 * x4;
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);
if (Orbit.Inclination < 5.2359877E-2)
{
sh = 0.0;
}
else
{
sh = -zn * s2 * (z21 + z23);
}
dp_ee2 = 2.0 * s1 * s6;
dp_e3 = 2.0 * s1 * s7;
dp_xi2 = 2.0 * s2 * z12;
dp_xi3 = 2.0 * s2 * (z13 - z11);
dp_xl2 = -2.0 * s3 * z2;
dp_xl3 = -2.0 * s3 * (z3 - z1);
dp_xl4 = -2.0 * s3 * (-21.0 - 9.0 * eosq) * ze;
dp_xgh2 = 2.0 * s4 * z32;
dp_xgh3 = 2.0 * s4 * (z33 - z31);
dp_xgh4 = -18.0 * s4 * ze;
dp_xh2 = -2.0 * s2 * z22;
dp_xh3 = -2.0 * s2 * (z23 - z21);
if (pass == 1)
{
// Do lunar terms
dp_sse = se;
dp_ssi = si;
dp_ssl = sl;
dp_ssh = sh / m_sinio;
dp_ssg = sgh - m_cosio * dp_ssh;
dp_se2 = dp_ee2;
dp_si2 = dp_xi2;
dp_sl2 = dp_xl2;
dp_sgh2 = dp_xgh2;
dp_sh2 = dp_xh2;
dp_se3 = dp_e3;
dp_si3 = dp_xi3;
dp_sl3 = dp_xl3;
dp_sgh3 = dp_xgh3;
dp_sh3 = dp_xh3;
dp_sl4 = dp_xl4;
dp_sgh4 = dp_xgh4;
zcosg = dpi_zcosgl;
zsing = dpi_zsingl;
zcosi = dpi_zcosil;
zsini = dpi_zsinil;
zcosh = dpi_zcoshl * cosq + dpi_zsinhl * sinq;
zsinh = sinq * dpi_zcoshl - cosq * dpi_zsinhl;
zn = znl;
const double c1l = 4.7968065E-7;
cc = c1l;
ze = zel;
}
}
#endregion
dp_sse = dp_sse + se;
dp_ssi = dp_ssi + si;
dp_ssl = dp_ssl + sl;
dp_ssg = dp_ssg + sgh - m_cosio / m_sinio * sh;
dp_ssh = dp_ssh + sh / m_sinio;
// Geopotential resonance initialization for 12 hour orbits
gp_reso = false;
gp_sync = false;
double g310;
double f220;
double bfact = 0.0;
// Determine if orbit is 12- or 24-hour resonant.
// Mean motion is given in radians per minute.
if ((Orbit.MeanMotion > 0.0034906585) && (Orbit.MeanMotion < 0.0052359877))
{
// Orbit is within the Clarke Belt (period is 24-hour resonant).
// Synchronous resonance terms initialization
gp_reso = true;
gp_sync = true;
#region 24-hour resonant
double g200 = 1.0 + eosq * (-2.5 + 0.8125 * eosq);
g310 = 1.0 + 2.0 * eosq;
double g300 = 1.0 + eosq * (-6.0 + 6.60937 * eosq);
f220 = 0.75 * (1.0 + m_cosio) * (1.0 + m_cosio);
double f311 = 0.9375 * m_sinio * m_sinio * (1.0 + 3 * m_cosio) - 0.75 * (1.0 + m_cosio);
double f330 = 1.0 + m_cosio;
f330 = 1.875 * f330 * f330 * f330;
const double q22 = 1.7891679e-06;
const double q33 = 2.2123015e-07;
const double q31 = 2.1460748e-06;
dp_del1 = 3.0 * m_xnodp * m_xnodp * aqnv * aqnv;
dp_del2 = 2.0 * dp_del1 * f220 * g200 * q22;
dp_del3 = 3.0 * dp_del1 * f330 * g300 * q33 * aqnv;
dp_del1 = dp_del1 * f311 * g310 * q31 * aqnv;
dp_xlamo = xmao + Orbit.RAAN + Orbit.ArgPerigee - dp_thgr;
bfact = m_xmdot + xpidot - thdt;
bfact = bfact + dp_ssl + dp_ssg + dp_ssh;
#endregion
}
else if (((Orbit.MeanMotion >= 8.26E-3) && (Orbit.MeanMotion <= 9.24E-3)) && (eq >= 0.5))
{
// Period is 12-hour resonant
gp_reso = true;
#region 12-hour resonant
double eoc = eq * eosq;
double g201 = -0.306 - (eq - 0.64) * 0.440;
double g211; double g322;
double g410; double g422;
double g520;
if (eq <= 0.65)
{
g211 = 3.616 - 13.247 * eq + 16.290 * eosq;
g310 = -19.302 + 117.390 * eq - 228.419 * eosq + 156.591 * eoc;
g322 = -18.9068 + 109.7927 * eq - 214.6334 * eosq + 146.5816 * eoc;
g410 = -41.122 + 242.694 * eq - 471.094 * eosq + 313.953 * eoc;
g422 = -146.407 + 841.880 * eq - 1629.014 * eosq + 1083.435 * eoc;
g520 = -532.114 + 3017.977 * eq - 5740.0 * eosq + 3708.276 * eoc;
}
else
{
g211 = -72.099 + 331.819 * eq - 508.738 * eosq + 266.724 * eoc;
g310 = -346.844 + 1582.851 * eq - 2415.925 * eosq + 1246.113 * eoc;
g322 = -342.585 + 1554.908 * eq - 2366.899 * eosq + 1215.972 * eoc;
g410 = -1052.797 + 4758.686 * eq - 7193.992 * eosq + 3651.957 * eoc;
g422 = -3581.69 + 16178.11 * eq - 24462.77 * eosq + 12422.52 * eoc;
if (eq <= 0.715)
{
g520 = 1464.74 - 4664.75 * eq + 3763.64 * eosq;
}
else
{
g520 = -5149.66 + 29936.92 * eq - 54087.36 * eosq + 31324.56 * eoc;
}
}
double g533;
double g521;
double g532;
if (eq < 0.7)
{
g533 = -919.2277 + 4988.61 * eq - 9064.77 * eosq + 5542.21 * eoc;
g521 = -822.71072 + 4568.6173 * eq - 8491.4146 * eosq + 5337.524 * eoc;
g532 = -853.666 + 4690.25 * eq - 8624.77 * eosq + 5341.4 * eoc;
}
else
{
g533 = -37995.78 + 161616.52 * eq - 229838.2 * eosq + 109377.94 * eoc;
g521 = -51752.104 + 218913.95 * eq - 309468.16 * eosq + 146349.42 * eoc;
g532 = -40023.88 + 170470.89 * eq - 242699.48 * eosq + 115605.82 * eoc;
}
double sini2 = m_sinio * m_sinio;
double cosi2 = m_cosio * m_cosio;
f220 = 0.75 * (1.0 + 2.0 * m_cosio + cosi2);
double f221 = 1.5 * sini2;
double f321 = 1.875 * m_sinio * (1.0 - 2.0 * m_cosio - 3.0 * cosi2);
double f322 = -1.875 * m_sinio * (1.0 + 2.0 * m_cosio - 3.0 * cosi2);
double f441 = 35.0 * sini2 * f220;
double f442 = 39.3750 * sini2 * sini2;
double f522 = 9.84375 * m_sinio * (sini2 * (1.0 - 2.0 * m_cosio - 5.0 * cosi2) +
0.33333333 * (-2.0 + 4.0 * m_cosio + 6.0 * cosi2));
double f523 = m_sinio * (4.92187512 * sini2 * (-2.0 - 4.0 * m_cosio + 10.0 * cosi2) +
6.56250012 * (1.0 + 2.0 * m_cosio - 3.0 * cosi2));
double f542 = 29.53125 * m_sinio * (2.0 - 8.0 * m_cosio + cosi2 * (-12.0 + 8.0 * m_cosio + 10.0 * cosi2));
double f543 = 29.53125 * m_sinio * (-2.0 - 8.0 * m_cosio + cosi2 * (12.0 + 8.0 * m_cosio - 10.0 * cosi2));
double xno2 = m_xnodp * m_xnodp;
double ainv2 = aqnv * aqnv;
double temp1 = 3.0 * xno2 * ainv2;
const double root22 = 1.7891679E-6;
const double root32 = 3.7393792E-7;
const double root44 = 7.3636953E-9;
const double root52 = 1.1428639E-7;
const double root54 = 2.1765803E-9;
double temp = temp1 * root22;
dp_d2201 = temp * f220 * g201;
dp_d2211 = temp * f221 * g211;
temp1 = temp1 * aqnv;
temp = temp1 * root32;
dp_d3210 = temp * f321 * g310;
dp_d3222 = temp * f322 * g322;
temp1 = temp1 * aqnv;
temp = 2.0 * temp1 * root44;
dp_d4410 = temp * f441 * g410;
dp_d4422 = temp * f442 * g422;
temp1 = temp1 * aqnv;
temp = temp1 * root52;
dp_d5220 = temp * f522 * g520;
dp_d5232 = temp * f523 * g532;
temp = 2.0 * temp1 * root54;
dp_d5421 = temp * f542 * g521;
dp_d5433 = temp * f543 * g533;
dp_xlamo = xmao + Orbit.RAAN + Orbit.RAAN - dp_thgr - dp_thgr;
bfact = m_xmdot + m_xnodot + m_xnodot - thdt - thdt;
bfact = bfact + dp_ssl + dp_ssh + dp_ssh;
#endregion
}
if (gp_reso || gp_sync)
{
dp_xfact = bfact - m_xnodp;
// Initialize integrator
dp_xli = dp_xlamo;
dp_xni = m_xnodp;
// dp_atime = 0.0; // performed by runtime
dp_stepp = 720.0;
dp_stepn = -720.0;
dp_step2 = 259200.0;
}
}