广义混合动量映射与带非弹性碰撞的受迫力学系统的对称性约化
Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions
AI总结：
该研究针对带非弹性碰撞的受迫力学系统的对称性约化问题，引入广义混合动量映射与混合运动常数，给出哈密顿、拉格朗日及时变系统的约化条件，并通过实例与仿真验证了方法的适用性。
摘要：
本文讨论了具有非弹性碰撞的自治与非自治受迫力学系统的对称性约化问题。具体而言，我们引入了广义混合动量映射和混合运动常数的概念，给出了受非保守外力与非弹性碰撞作用的哈密顿系统和拉格朗日系统能否进行对称性约化的一般条件，并将其推广到受时变外力与时变非弹性碰撞作用的时变力学系统。我们通过实例和数值仿真验证了该方法的适用性。
英文摘要：
This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion to give general conditions on whether it is possible to perform symmetry reduction for Hamiltonian and Lagrangian systems subject to non-conservative external forces and non-elastic impacts, as well as its extension to time-dependent mechanical systems subject to time-dependent external forces and time-dependent inelastic collisions. We illustrate the applicability of the method with examples and numerical simulations.
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