论文标题
联系Lagrangian系统受到冲动限制
Contact Lagrangian systems subject to impulsive constraints
论文作者
论文摘要
我们描述了在冲动力和约束下的几何接触拉格朗日系统以及沿构型空间并不统一的瞬时非单学约束。在这两种情况下，描述触点拉格朗日系统动力学的矢量场是通过定义投影仪来通过使用Riemannian度量来评估约束的。特别是，我们介绍了接触拉格朗日系统的HERGLOTZ方程，但受到瞬时非语言约束。此外，我们为受冲动力和约束的接触拉格朗日系统提供了Carnot-type定理，该系统表征了由于接触型耗散和冲动力而导致的能量变化。我们说明了该方法的适用性，尤其是在弹簧表面上的滚动缸和不均匀表面上的滚动球，均具有耗散。
We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constraints by using a Riemannian metric. In particular, we introduce the Herglotz equations for contact Lagrangian systems subject to instantaneous nonholonomic constraints. Moreover, we provide a Carnot-type theorem for contact Lagrangian systems subject to impulsive forces and constraints, which characterizes the changes of energy due to contact-type dissipation and impulsive forces. We illustrate the applicability of the method with practical examples, in particular, a rolling cylinder on a springily surface and a rolling sphere on a non-uniform surface, both with dissipation.
