论文标题
简单混合劳斯系统中的对称性和周期轨道
Symmetries and periodic orbits in simple hybrid Routhian systems
论文作者
论文摘要
在广泛的非线性系统中，对称性无处不在。特别是在动力学由拉格朗日或哈密顿功能决定的系统中。对于具有带环变量的拉格朗日函数确定的连续时间动力学的混合系统，可以通过称为\ textit {hybrid ruthian降低}的方法来降低相应混合拉格朗日系统的自由度。在本文中，我们研究了充分的条件，以表现出杂交ruthian系统中的周期性轨道，这些轨道也表现出时间反转对称性。同样，我们通过对相应的线性庞加莱映射的特征值的特征来探索此类轨道的一些稳定性方面。最后，我们将结果应用于在杂种不足的Routhian控制系统中找到周期性解决方案。
Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a Lagrangian function, with a cyclic variable, the degrees of freedom for the corresponding hybrid Lagrangian system can be reduced by means of a method known as \textit{hybrid Routhian reduction}. In this paper we study sufficient conditions for the existence of periodic orbits in hybrid Routhian systems which also exhibit time-reversal symmetry. Likewise, we explore some stability aspects of such orbits through the characterization of the eigenvalues for the corresponding linearized Poincaré map. Finally, we apply the results to find periodic solutions in underactuated hybrid Routhian control systems.
