Modeling and Solution of Some Mechanical Problems on Lie Groups

We apply Munthe-Kaas and Crouch-Grossman methods in the solution of some mechanical problems. These methods are quite new, and they exploit intrinsic properties of the manifolds defined by the mechanical problems, thus ensuring that the numerical solution obey underlying constraints. A brief introduction to the methods is presented, and numerical simulations show some of the properties they possess. We also discuss error estimation and stepsize selection for some of these methods.