Nonsmooth Herglotz variational principle
arXiv:2208.02033 · doi:10.23919/ACC55779.2023.10156228
Abstract
In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems. In particular, we develop a Herglotz variational principle for non-smooth action-dependent Lagrangians which leads to the preservation of energy and momentum at impacts. By defining appropriately a Legendre transform, we can obtain the Hamilton equations of motion for the corresponding non-smooth Hamiltonian system. We apply the result to a billiard problem in the presence of dissipation.
7 pages, 1 figure. Preprint submitted to a conference. Comments welcome!
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