Seminarium KMMF "Teoria Dwoistości"

The geometric description of the Euler-Lagrange equations of a mechanical system determined by a Lagrangian function relies on the velocity phase space TM of a configuration manifold M. In discrete mechanics, the starting point is to replace TM by M \times M, taking two nearby points as the discrete analogue of a velocity vector. Discrete mechanics has been developed on Lie groups and Lie groupoids as well. My talk is about the generalization of the discrete mechanics on Lie groups to non-associative objects, smooth loops, generalizing Lie groups. This shows that the associativity assumption is not crucial for mechanics and opens new perspectives. The motivating example is octonions, I will show how to construct the discrete Lagrangian and Hamiltonian mechanics on unitary octonions. To attend our seminar, please use the Zoom link: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09