turkmath.org

The talk will be consisting of two main parts. In the first one, a gentle introduction to the geometric mechanics will be presented. Accordingly, some basic notions of the theory namely, Lie groups, Lie algebras, Poisson manifolds, and Hamiltonian systems will be summarized. Several examples will be provided. In the second part, we shall address the problem of determining the matched equations of motion of two interacting systems (whose configuration spaces are Lie groups) governing the coupled system starting with the individual equations of motions in Hamiltonian form. The configuration spaces of the systems being Lie groups is imperative here in order to define the mutual actions. We shall present the theory of matched dynamics and particularly write the matched Lie-Poisson equations. It will be shown that the theory of matched dynamics is a generalization of the well-developed semi-direct product theory.