Abstract

this article we show how such an ambient Riemannian metric can be used to frame the popular "leapfrog" method in the category of Riemannian manifolds, thus creating new intrinsic methods applicable to mechanical systems with configuration spaces as general as homogeneous spaces of semisimple Lie groups. This new method, shown in Figure (1), is implicit, second order, time-reversing, symplectic and respects those symmetries of the system which are also isometries of the ambient metric. For arbitrary potential energy, but where the kinetic energy metric of the mechanical system is proportional to the ambient metric, our method is explicit, and is equivalent to the splitting method corresponding to the splitting of the Hamiltonian into kinetic and potential energy. 2. Context and Notation

Citations