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/***********************************************/
/**
* @file kepler.cpp
*
* @brief Keplerian elements and orbits.
*
* @author Torsten Mayer-Guerr
* @date 2004-09-12
*
*/
/***********************************************/
#include "base/importStd.h"
#include "base/vector3d.h"
#include "base/time.h"
#include "base/kepler.h"
#include "base/equinoctial.h"
/***********************************************/
Kepler::Kepler() :
GM(DEFAULT_GM),
Omega(0),
i(0),
omega(0),
a(0),
e(0),
tau()
{
}
/***********************************************/
Kepler::Kepler(Double _Omega, Double _i, Double _omega, Double _a, Double _e, const Time &_tau, Double _GM) :
GM(_GM),
Omega(_Omega),
i( _i),
omega(_omega),
a(_a),
e(_e),
tau(_tau)
{
}
/***********************************************/
Kepler::Kepler(const Time &time, Double _Omega, Double _i, Double _omega, Double _a, Double _e, Double _M, Double _GM) :
GM(_GM),
Omega(_Omega),
i( _i),
omega(_omega),
a(_a),
e(_e),
tau(time - seconds2time(_M*sqrt(a*a*a/GM)))
{
}
/***********************************************/
Kepler::Kepler(const Equinoctial &equinoctial) :
GM(equinoctial.GM),
a(equinoctial.a),
tau(equinoctial.tau)
{
e = sqrt(equinoctial.h*equinoctial.h+equinoctial.k*equinoctial.k);
i = 2*atan(sqrt(equinoctial.p*equinoctial.p+equinoctial.q*equinoctial.q));
const Double sinOmega = equinoctial.p/sqrt(equinoctial.p*equinoctial.p+equinoctial.q*equinoctial.q);
const Double cosOmega = equinoctial.q/sqrt(equinoctial.p*equinoctial.p+equinoctial.q*equinoctial.q);
Omega = atan2(sinOmega,cosOmega);
const Double sinXi = equinoctial.h / sqrt(equinoctial.h*equinoctial.h+equinoctial.k*equinoctial.k);
const Double cosXi = equinoctial.k / sqrt(equinoctial.h*equinoctial.h+equinoctial.k*equinoctial.k);
const Double xi = atan2(sinXi,cosXi);
const Double M = static_cast<Double>(equinoctial.l0) - xi;
omega = xi - Omega; //equinoctial.l0 - Omega;
tau = tau - seconds2time(M*sqrt(a*a*a/GM));
if(Omega<0) Omega += 2*PI;
if(omega<0) omega += 2*PI;
if(i<0) i += 2*PI;
}
/***********************************************/
Kepler::Kepler(const Time &time, const Vector3d &position, const Vector3d &velocity, Double _GM) : GM(_GM)
{
const Double r = position.r();
const Vector3d C = crossProduct(position, velocity);
i = atan2(sqrt(C.x()*C.x()+C.y()*C.y()), C.z());
Omega = atan2(C.x(), -C.y());
// major semi axis
a = 1/(2/position.r()-inner(velocity,velocity)/GM);
// excentricity
const Double p = inner(C,C)/GM;
e = sqrt((a-p)/a);
// true anomaly
const Double v = atan2(p*inner(position,velocity)/C.r(), p-r);
// oribt system
const Vector3d P = (e+cos(v))/p * position - r*sin(v)/C.r() * velocity;
const Vector3d Q = sin(v)/p * position + r*cos(v)/C.r() * velocity;
const Vector3d K = Vector3d(cos(Omega), sin(Omega), 0);
// argument of perigee
omega = atan2(-inner(K,Q), inner(K,P));
// excentric anomaly
Double E = atan2(inner(position,Q)/(a*sqrt(1-e*e)), inner(position,P)/a+e);
// positive angles
if(i<0) i += 2*PI;
if(Omega<0) Omega += 2*PI;
if(omega<0) omega += 2*PI;
if(E<0) E += 2*PI;
// time of perigee
const Double M = E - e*sin(E);
tau = time - seconds2time(M*sqrt(a*a*a/GM));
}
/***********************************************/
Double Kepler::meanAnomaly(const Time &time) const
{
Double M = (time-tau).seconds()*sqrt(GM/(a*a*a));
if(M<0) M += 2*PI;
return M;
}
/***********************************************/
Double Kepler::trueAnomaly(const Time &time) const
{
Double M = meanAnomaly(time);
// excentric anomaly
Double E = M;
Double E_old;
Double eps = 1e-12;
UInt iter = 0;
do
{
E_old = E;
E = M + e*sin(E);
}
while((fabs(E-E_old)>eps)&&(iter++<100));
return atan2(sqrt(1-e*e)*sin(E), cos(E)-e);
}
/***********************************************/
const Vector3d Kepler::position(const Time &time) const
{
Vector3d position, velocity;
orbit(time, position, velocity);
return position;
}
/***********************************************/
void Kepler::orbit(const Time &time, Vector3d &position, Vector3d &velocity) const
{
Vector3d acceleration;
orbit(time, position, velocity, acceleration);
}
/***********************************************/
void Kepler::orbit(const Time &time, Vector3d &position, Vector3d &velocity, Vector3d &acceleration) const
{
Double v = trueAnomaly(time);
// distance and angular momentum
Double p = a*(1-e*e);
Double r = p/(1+e*cos(v));
Double C = sqrt(GM*p);
// orbital system
Vector3d P(cos(Omega)*cos(omega)-sin(Omega)*sin(omega)*cos(i),
sin(Omega)*cos(omega)+cos(Omega)*sin(omega)*cos(i),
sin(omega)*sin(i));
Vector3d Q(-cos(Omega)*sin(omega)-sin(Omega)*cos(omega)*cos(i),
-sin(Omega)*sin(omega)+cos(Omega)*cos(omega)*cos(i),
cos(omega)*sin(i));
// position and velocity
position = (r*cos(v)) * P + (r*sin(v)) * Q;
velocity = (-C/p*sin(v)) * P + (C*(cos(v)+e)/p) * Q;
acceleration = -GM/pow(position.r(),3) * position;
}
/***********************************************/
/***********************************************/
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