f_and_g_ta.m

% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  function [f, g] = f_and_g_ta(r0, v0, dt, mu)
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%{
  This function calculates the Lagrange f and g coefficients from the
  change in true anomaly since time t0

  mu  - gravitational parameter (km^3/s^2)
  dt  - change in true anomaly (degrees)
  r0  - position vector at time t0 (km)
  v0  - velocity vector at time t0 (km/s)
  h   - angular momentum (km^2/s)
  vr0 - radial component of v0 (km/s)
  r   - radial position after the change in true anomaly
  f   - the Lagrange f coefficient (dimensionless)
  g   - the Lagrange g coefficient (s)

  User M-functions required:  None
%}
% --------------------------------------------

h   = norm(cross(r0,v0));
vr0 = dot(v0,r0)/norm(r0);
r0  = norm(r0);
s   = sind(dt);
c   = cosd(dt);

%...Equation 2.152:
r   = h^2/mu/(1 + (h^2/mu/r0 - 1)*c - h*vr0*s/mu);

%...Equations 2.158a & b:
f   = 1 - mu*r*(1 - c)/h^2;
g   = r*r0*s/h;

end
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~