I would like to simulate a system which comes at the following form:
where the Mass Matrix (M) is a 2x2 matrix. I simulated the system by using the inverse of the M matrix (it is positive definite, so I can do that) but I would also like to simulate it by using the 'Mass' matrix option that can be provided to the ode solver. If I use the inverse of the matrix, then the system breaks down to 4 first order ODEs and it's beiing simulated. How can I break the system to first order ODEs and use the mass matrix option ? My issue is that as far as I know, ODE solvers solve first order ODEs. The q variable denotes angles of a 2-DOF robotic manipulator, so its dimension is 2x1.