function [ dX ] = CartDynamics( X, F )
%cart dynamics  (Sp24 version)
% cart = 4kg
% ball = 1kg
% length = 1.3m
% X = [x, q, dx, dq]
x = X(1);
q = X(2);
dx = X(3);
dq = X(4);
g = 9.8;
M = [5, 1.3*cos(q); 1.3*cos(q), 1.69];
A = [1.3*dq*dq*sin(q); 1.3*g*sin(q)];
B = [1;0];
d2X = inv(M) * (A + B*F);
dX = [dx; dq; d2X];
end