void SolarRadiationPressure::doCompute(UTCTime utc, EarthBody& rb, Spacecraft& sc)
{
crossArea = sc.getDragArea();
dryMass = sc.getDryMass();
reflectCoeff = sc.getReflectCoeff();
Vector<double> r_sun = ReferenceFrames::getJ2kPosition(utc.asTDB(),SolarSystem::Sun);
Vector<double> r_moon = ReferenceFrames::getJ2kPosition(utc.asTDB(),SolarSystem::Moon);
// from km to m
r_sun = r_sun*1000.0;
r_moon = r_moon*1000.0;
// a
a = accelSRP(sc.R(),r_sun)*getShadowFunction(sc.R(),r_sun,r_moon,SM_CONICAL);
// da_dr reference to Montenbruck P248
// and it's in the same way as the gravitational attraction of the sun
da_dr.resize(3,3,0.0);
double au2 = ASConstant::AU * ASConstant::AU;
double factor = -1.0*reflectCoeff * (crossArea/dryMass) * ASConstant::P_Sol*au2;
Vector<double> d = sc.R() - r_sun;
double dmag = norm(d);
double dcubed = dmag * dmag *dmag;
Vector<double> temp1 = d / dcubed; // detRJ/detRJ^3
double muod3 = factor / dcubed;
double jk = 3.0 * muod3/dmag/dmag;
double xx = d(0);
double yy = d(1);
double zz = d(2);
da_dr(0,0) = jk * xx * xx - muod3;
da_dr(0,1) = jk * xx * yy;
da_dr(0,2) = jk * xx * zz;
da_dr(1,0) = da_dr(0,1);
da_dr(1,1) = jk * yy * yy - muod3;
da_dr(1,2) = jk * yy * zz;
da_dr(2,0) = da_dr(0,2);
da_dr(2,1) = da_dr(1,2);
da_dr(2,2) = jk * zz * zz - muod3;
// da_dv
da_dv.resize(3,3,0.0);
// da_dp
dadcr.resize(3,0.0);
dadcr = a /reflectCoeff;
da_dcr(0,0) = dadcr(0);
da_dcr(1,0) = dadcr(1);
da_dcr(2,0) = dadcr(2);
} // End of method 'SolarRadiationPressure::doCompute()'
/* Call the relevant methods to compute the acceleration.
* @param t Time reference class
* @param bRef Body reference class
* @param sc Spacecraft parameters and state
* @return the acceleration [m/s^s]
*/
void MoonForce::doCompute(UTCTime utc, EarthBody& rb, Spacecraft& sc)
{
/* Oliver P69 and P248
* a = GM*( (s-r)/norm(s-r)^3 - s/norm(s)^3 )
*
* da/dr = -GM*( I/norm(r-s)^3 - 3(r-s)transpose(r-s)/norm(r-s)^5)
*/
Vector<double> r_moon = ReferenceFrames::getJ2kPosition(utc.asTDB(), SolarSystem::Moon);
r_moon = r_moon * 1000.0; // from km to m
Vector<double> d = sc.R() - r_moon;
double dmag = norm(d);
double dcubed = dmag * dmag *dmag;
Vector<double> temp1 = d / dcubed; // detRJ/detRJ^3
double smag = norm(r_moon);
double scubed = smag * smag * smag;
Vector<double> temp2 = r_moon / scubed; // Rj/Rj^3
Vector<double> sum = temp1 + temp2;
a = sum * (-mu); // a
// da_dr
da_dr.resize(3,3,0.0);
double muod3 = mu / dcubed;
double jk = 3.0 * muod3/dmag/dmag;
double xx = d(0);
double yy = d(1);
double zz = d(2);
da_dr(0,0) = jk * xx * xx - muod3;
da_dr(0,1) = jk * xx * yy;
da_dr(0,2) = jk * xx * zz;
da_dr(1,0) = da_dr(0,1);
da_dr(1,1) = jk * yy * yy - muod3;
da_dr(1,2) = jk * yy * zz;
da_dr(2,0) = da_dr(0,2);
da_dr(2,1) = da_dr(1,2);
da_dr(2,2) = jk * zz * zz - muod3;
// da_dv
da_dv.resize(3,3,0.0);
//da_dp
} // End of method 'MoonForce::doCompute()'
// this is the real one
void AtmosphericDrag::doCompute(UTCTime utc, EarthBody& rb, Spacecraft& sc)
{
// To consist with STK
double omega_e = 7.292115E-05; // IERS 1996 conventions
//double omega_e = rb.getSpinRate(utc);
Vector<double> r = sc.R(); // satellite position in m
Vector<double> v = sc.V(); // satellite velocity in m/s
const double cd = sc.getDragCoeff();
const double area = sc.getDragArea();
const double mass = sc.getDryMass();
double rmag = norm(r);
double beta = cd * area / mass; // [m^2/kg]
// compute the atmospheric density
double rho = computeDensity(utc, rb, r, v); // [kg/m^3]
// debuging...
//rho = 6.3097802844338E-12;
// compute the relative velocity vector and magnitude
Vector<double> we(3,0.0);
we(2)= omega_e;
Vector<double> wxr = cross(we,r);
Vector<double> vr = v - wxr;
double vrmag = norm(vr);
// form -1/2 (Cd*A/m) rho
double coeff = -0.5 * beta * rho;
double coeff2 = coeff * vrmag;
// compute the acceleration in ECI frame (km/s^2)
a = vr * coeff2; ///////// a
// Partial reference: Montenbruck,P248
// form partial of drag wrt v
// da_dv = -0.5*Cd*(A/M)*p*(vr*transpose(vr)/vr+vr1)
Matrix<double> tr(3,1,0.0);
tr(0,0)=vr(0);
tr(1,0)=vr(1);
tr(2,0)=vr(2);
Matrix<double> vrvrt = tr*transpose(tr);
vrvrt = vrvrt / vrmag;
double eye3[3*3] = {1,0,0,0,1,0,0,0,1};
Matrix<double> vrm(3,3,0.0);
vrm = eye3;
vrm = vrm * vrmag;
da_dv = (vrvrt + vrm) * coeff; //////// da_dv
// da_dr
// da_dr = -0.5*Cd*(A/M)*vr*dp_dr-da_dv*X(w)
da_dr.resize(3,3,0.0);
Matrix<double> X(3,3,0.0);
X(0,1) = -we(2); // -wz
X(0,2) = +we(1); // wy
X(1,0) = +we(2); // +wz
X(1,2) = -we(0); // -wx
X(2,0) = -we(1); // -wy
X(2,1) = +we(0); // +wx
Matrix<double> part1(3,3,0.0);
Matrix<double> part2(3,3,0.0);
// Get the J2000 to TOD transformation
Matrix<double> N = ReferenceFrames::J2kToTODMatrix(utc);
// Transform r from J2000 to TOD
Vector<double> r_tod = N * r;
Position geoidPos(r_tod(0),r_tod(1),r_tod(3));
// Satellite height
double height = geoidPos.getAltitude()/1000.0; // convert to [km]
const int n = CIRA_SIZE; ;
int bracket = 0;
if (height >= h0[n-1])
{
bracket = n - 1;
}
else
{
for (int i = 0; i < (n-1); i++)
{
if ((height >= h0[i]) && (height < h0[i+1]))
{
bracket = i;
}
}
} // End 'if (height >= h0[n-1]) '
double Hh = H[bracket];
double coeff4 = -1.0 / (Hh * rmag);
Vector<double> drhodr = r*coeff4;
Matrix<double> tr2(3,1,0.0);
tr2(0,0) = drhodr(0);
tr2(1,0) = drhodr(1);
tr2(2,0) = drhodr(2);
part1 = tr*transpose(tr2); // //Matrix part1 = vr.outerProduct(drhodr);
part1 = part1*coeff2;
//part1 = dp_dr*a/rho;
part2 =-da_dv*X;
da_dr = part1-part2;
// form partial of drag wrt cd
double coeff3 = coeff2 / cd;
this->dadcd = vr*coeff3; //////// da_dcd
this->da_dcd(0,0) = dadcd(0);
this->da_dcd(1,0) = dadcd(1);
this->da_dcd(2,0) = dadcd(2);
} // End of method 'AtmosphericDrag::doCompute()'
// this is the real one
void RelativityEffect::doCompute(UTCTime utc, EarthBody& rb, Spacecraft& sc)
{
/* reference: Jisheng,Li P110 Bernese5 GENREL.f
a_rl = a_rl1 + a_rl2 + a_rl3
a_rl2 and a_rl3 are ignored for precise orbit determination
*/
const double GM = ASConstant::GM_Earth;
const double C = ASConstant::SPEED_OF_LIGHT;
Vector<double> r = sc.R();
Vector<double> v = sc.V();
double beta = 1.0;
double gama = 1.0;
double c2 = C * C;
double r2 = dot(r,r);
double v2 = dot(v,v);
double r_mag = norm(r);
double r3 = r2 * r_mag;
double p = GM/c2/r3;
// a
a.resize(3,0.0);
double pr = 2.0 * (beta + gama) * GM / r_mag - gama * v2;
double pv = 2.0 * (1.0 + gama) * dot(r,v);
a = p * ( pr * r + pv * v );
// da_dr
da_dr.resize(3,3,0.0);
double prr = -(GM/r_mag)*(GM/r_mag)*(2.0*(beta+gama)/c2);
double pvv = (GM/r3)*(2.0*(1.0+gama)/c2);
double par = -3.0/r2;
double ppr = (GM/r3)*((GM/r_mag)*(2.0*(beta+gama)/c2)-gama*v2/c2);
for(int i=0; i<3; i++)
{
for(int j=0; j<3; j++)
{
double det = (i == j) ? 1.0 : 0.0;
da_dr(i,j) = prr*r(i)*r(j)
+ pvv*v(i)*v(j)
+ par*a(i)*r(j)
+ ppr*det;
}
}
// da_dv
da_dv.resize(3,3,0.0);
double prv = -(GM/r3)*(2.0*gama/c2);
double pvr = (GM/r3)*(2.0*(1.0+gama)/c2);
double ppv = pvr*dot(r,v);
for(int i=0;i<3;i++)
{
for(int j=0;j<3;j++)
{
double det = (i == j) ? 1.0 : 0.0;
da_dr(i,j) = prv*r(i)*v(j)
+ pvr*v(i)*r(j)
+ ppv*det;
}
}
// da_dp add it later...
//da_GM da_dbeta da_gama
} // End of method 'RelativityEffect::doCompute()'