Application of Geometric Integration to some Mechanical Problems
Abstract
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 are
presented, and numerical simulations show some of the properties they
possess. We also discuss error estimation and stepsize selection for
some of these methods.