kep2car.m

function [r,v]=kep2car(kep,mu)

% kep2car.m
% 
% PROTOTYPE:
%   [r,v]=kep2car(kep,mu)
%
% DESCRIPTION:
% 	Function that switch keplerian parameters into cartesian coordinates 
%   (alternative mthod without v)
%
% INPUT:
%	kep[6]         Keplerian parameters of the orbit
%   mu[1]          
%
% OUTPUT:
%	r[3]           Position vector
%   v[3]           Velocity vector
%
% AUTHOR:
%   Alfonso Collogrosso
%  

a = kep(1);
e = kep(2);
i = kep(3);
OMG = kep(4);
omg = kep(5);
theta = kep(6);

% Semi latus rectum
p = a*(1 - norm(e)^2);

% Compute R position of S/C
R = p/(1 + norm(e)*cos(theta));

% Compute r perifocal
r_pf = [R*cos(theta);R*sin(theta);0];

% Compute v perifocal
v_pf = [-sqrt(mu/p)*sin(theta); sqrt(mu/p)*(norm(e) + cos(theta)); 0];

% Rotation matrix
RM_OMG = [ cos(OMG),sin(OMG), 0; -sin(OMG), cos(OMG), 0; 0, 0, 1];
RM_i = [1, 0, 0; 0, cos(i), sin(i);  0, -sin(i), cos(i)];
RM_omg = [cos(omg), sin(omg), 0; -sin(omg), cos(omg), 0; 0, 0, 1];
T = RM_OMG'*RM_i'*RM_omg';

% Compute v and r in geoceter equatorial system
r = T*r_pf;
v = T*v_pf;

end