论文标题
非平滑性Herglotz变分原理
Nonsmooth Herglotz variational principle
论文作者
论文摘要
在本文中，平稳的依赖动作的拉格朗日力学理论（也称为接触拉格朗日人）扩展到适合碰撞问题的非平滑环境。特别是，我们为非平滑动作依赖的拉格朗日人开发了一个Herglotz变分原理，从而导致影响能量和动力。通过适当定义Legendre变换，我们可以为相应的非平滑汉密尔顿系统获得汉密尔顿运动方程。在耗散存在的情况下，我们将结果应用于台球问题。
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.
