On variational integrators for optimal control of mechanical control systems - Colombo, Leonardo (2011)
In this paper we study discrete second-order vakonomic mechanics, that is, constrained variational problems for second-order lagrangian systems. One of the main applications of the presented theory will be optimal control of underactuated mechanical control systems. We derive geometric integrators which are symplectic and preserve the momentum map. Additional, we show the applicability of the proposed theory in an example, the planar rigid body.