turkmath.org

The problem presented in this talk is to determine 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 Lagrangian or/and Hamiltonian forms). The configuration spaces of the systems being Lie groups is imperative here in order to define the mutual actions. To this end, we first recall some basics such as Lie groups, Lie algebras, Poisson manifolds and Hamiltonian systems. Then we will study reduced Lagrangian and reduced Hamiltonian dynamics by introducing Euler-Poincaré and Lie-Poisson equations, respectively. We introduce the matched pairs of Lie groups, and write the matched Euler-Poincaré and the matched Lie-Poisson equations. (joint work with Serkan Sütlü)