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
    %
    % Jeremy Penn
    % 19/11/2017
    %
    % function [f, g] = f_and_g_ta(r0, v0, dt, mu)
    %
    % Inputs:   o mu  - gravitational parameter (km^3/s^2)
    %           o dt  - change in true anomaly (degrees)
    %           o r0  - position vector at time t0 (km)
    %           o v0  - velocity vector at time t0 (km/s)
    %
    % Outputs:  o f   - the Lagrange f coefficient (dimensionless)
    %           o g   - the Lagrange g coefficient (s)
    %
    
    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