Optimal control of affine connection control systems from the point of   view of Lie algebroids
  The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field. 
L. Abrunheiro and M. Camarinha
math.OC math-ph math.DG math.MP math.SG