keplerian.hpp File Reference

Defines a solver for differential Kepler's equation in universal variable x. More...

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Functions
GPUAPI double	C_prussing (double y)
	functions needed for kepstep More...
GPUAPI double	S_prussing (double y)
	equation 2.40b Prussing +Conway
GPUAPI void	SC_prussing (double y, double &S, double &C)
	equation 2.40a Prussing + Conway
__device__ void	SC_prussing_fast (double y, double &S, double &C)
	equation 2.40a Prussing + Conway
GPUAPI double	solvex (double r0dotv0, double alpha, double sqrtM1, double r0, double dt)
GPUAPI void	drift_kepler (double &x_old, double &y_old, double &z_old, double &vx_old, double &vy_old, double &vz_old, const double sqrtGM, const double deltaTime)
	advance a particle using f,g functions and universal variables More...

Detailed Description

Defines a solver for differential Kepler's equation in universal variable x.

solving differential Kepler's equation in universal variable x using Laguerre method as outlined by Prusing+C eqn 2.43 code adapted from Alice Quillen's Qymsym code see http://astro.pas.rochester.edu/~aquillen/qymsym/

Definition in file keplerian.hpp.

Function Documentation

GPUAPI double C_prussing

(

double

y)

functions needed for kepstep

equation 2.40a Prussing + Conway

Definition at line 42 of file keplerian.hpp.

GPUAPI void drift_kepler	(	double &	x_old,
		double &	y_old,
		double &	z_old,
		double &	vx_old,
		double &	vy_old,
		double &	vz_old,
		const double	sqrtGM,
		const double	deltaTime
	)

advance a particle using f,g functions and universal variables

if dt == 0 then f=dgdt=1 and g=dfdt=0 f,g functions equation 2.38a PC

dfdt,dgdt function equation 2.38b PC

conservation of angular momentum means that f dfdt - g dfdt =1

dfdt,dgdt function equation 2.38b PC

eqn 2.65 M+D

eqn 2.70 M+D

Replace values

Definition at line 175 of file keplerian.hpp.

References SC_prussing(), solvex(), and x.

Referenced by swarm::gpu::bppt::MVSPropagator< T, Gravitation >::advance().

GPUAPI double solvex	(	double	r0dotv0,
		double	alpha,
		double	sqrtM1,
		double	r0,
		double	dt
	)

integer n, for recommended Laguerre method

initial guess could be improved

7 iterations is probably overkill

eqn 2.41 PC

eqn 2.42 PC

equation 2.43 PC

Definition at line 120 of file keplerian.hpp.

References SC_prussing(), SC_prussing_fast(), and x.

Referenced by drift_kepler().