<p>In this paper Modelica and Optimica are used to solve two different optimal control problems for a system consisting of a pendulum and a cart. These optimizations will demonstrate that Optimica is easy to use and powerful when optimizing systems with highly non-linear dynamics. The optimal control trajectories are applied to a real pendulum and cart system, in open loop as well as in closed loop with an MPC-controller. The experiments show that optimal trajectories from Optimica together with MPC feedback is a suitable control structure when optimal transitions through non-linear dynamics are desired.</p>