A method of solving optimal manoeuvre control of linear underactuated mechanical systems is presented. The nonintegrable constraints present in such systems are handled by adding dummy actuators and then by applying Lagrange multipliers to reduce their action to zero. The open- and closed-loop control schemes can be analyzed. https://www.roneverhart.com/Albert-s-Ice-Cubes-Chocolates-5-Pack-12-Piece-Display/