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The talk will be consisting of two main parts. In the first one, a gentle introduction to Geometric Mechanics will be presented. Accordingly, some basic notions of the theory namely, Lie groups, Lie algebras, Euler-Poincaré equations, will be exhibited. 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 (higher-order) Lagrangian 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, what I call, (higher-order) matched Euler-Poincaré equations. It will be shown that the theory of matched dynamics is a generalization of the well-developed semi-direct product theory. This talk is part of a project pursued jointly Serkan Sütlü.
References
O. Esen, Kudeyt, M., Sütlü, S. (2019). Matched Higher Order Lagrangian Dynamics. arXiv preprint arXiv:1909.10375.
O. Esen, S. Sütlü, (2018). Matched pairs of discrete dynamical systems. arXiv preprint arXiv:1809.00521.
O. Esen, S. Sütlü, (2017), Lagrangian Dynamics on Matched Pairs, Journal of Geometry and Physics 111C (2017) pp. 142-157.
O. Esen, S. Sütlü, (2016), Hamiltonian dynamics on matched pairs, International Journal of Geometric Methods in Modern Physics, Vol. 13, No. 10 (2016) 1650128 (24 pages)