事件空间中非完整力学系统的Herglotz-d′Alembert原理与守恒律

研究事件空间中非完整力学系统的Herglotz型守恒律.给出事件空间中Herglotz型广义变分原理,引入非完整约束并采用交换关系的H9lder定义,导出事件空间中非完整力学系统的新型微分变分原理—Herglotz-d′Alembert原理.引进事件空间中的空间生成元和参数生成元,建立Herglotz-d′Alembert原理不变性条件的变换.基于该原理构建了事件空间中非完整非保守力学系统的Herglotz型守恒定理及其逆定理.作为特例,给出了位形空间的Herglotz型守恒量和事件空间中完整力学系统的Herglotz型守恒量.文末还给出了一个算例.

HERGLOTZ-D'ALEMBERT PRINCIPLE AND CONSERVATION LAW FOR NONHOLONOMIC MECHANICAL SYSTEMS IN EVENT SPACE

Herglotz conservation laws of nonholonomic mechanical systems in event space are studied. The Herglotz generalized variational principle in event space is given, and the Herglotz -d'' Alembert principle, a new differential variational principle for nonholonomic mechanical systems in event space, is derived by introducing non-holonomic constraints and using the Holder definition of commutative relation. The transformation of the invariance condition of Herglotz-d'' Alembert principle is established by introducing space generators and parameter generators in the event space. Herglotz conservation theorem and its inverse for nonholonomic nonconservative mechanical systems in event space are constructed based on this principle. As particular cases, the Herglotz conservation laws in configuration space and the Herglotz conservation laws for holonomic mechanical system in event space are given. An example is given at the end of the paper to illustrate the application of Herglotz conservation laws.