par2car.m

function [rr,vv]=par2car(orb,mu)

    % Trasformation from Keplerian coordinates to cartesian parameters
    %
    % [rr,vv]=par2car(orb,mu)
    % ---------------------------------------------------------------------
    % Input arguments:
    % orb         [6x1]   orbital parameters                [-]
    % mu          [1x1]   gravitational parameter           [km^3/s^2]    
    %
    % ---------------------------------------------------------------------
    % Output argumets:
    % rr          [3x1]   position vector                   [km]
    % vv          [3x1]   velocity vector                   [km/s]
    
    a=orb(1);
    e=orb(2);
    i=orb(3);
    OM=orb(4);
    om=orb(5);
    th=orb(6);
    
    R_OM=[cos(OM) sin(OM) 0; -sin(OM) cos(OM) 0; 0 0 1];
    R_i=[1 0 0; 0 cos(i) sin(i); 0 -sin(i) cos(i)];
    R_om=[cos(om) sin(om) 0; -sin(om) cos(om) 0; 0 0 1];
    
    T_ECI_PF=R_om*R_i*R_OM;
    T_PF_ECI=T_ECI_PF';
    
    p=a*(1-e^2);
    
    r=p/(1+e*cos(th));
    
    r_PF=r*[cos(th);sin(th);0];
    v_PF=sqrt(mu/p)*[-sin(th);e+cos(th);0];
    
    rr=T_PF_ECI*r_PF;
    vv=T_PF_ECI*v_PF;
    
end