function [ dX ] = CartDynamics( X, F )
%cart dynamics 
m1 = 2;  % cart
m2 = 1;  % ball
L = 1;   % length

% X = [x, q, dx, dq]
x = X(1);
q = X(2);
dx = X(3);
dq = X(4);
g = 9.8;
M = [m1+m2, m2*L*cos(q); m2*L*cos(q), m2*L*L];
A = [dq*dq*m2*L*sin(q); g*L*m2*sin(q)];
B = [1;0];
d2X = inv(M) * (A + B*F);
dX = [dx; dq; d2X];
end