标题： LR 和 L+R 系统 显示英文标题

标题： LR and L+R Systems

摘要： 我们考虑在李群乘积上的耦合非完整LR系统。 作为例子，我们研究了球形支撑系统和橡胶Chaplygin球的$n$维变体。 对于惯性算子的特殊选择，证明了在约化和时间重参数化后，橡胶Chaplygin球成为$(n-1)$维球面上的一个可积哈密顿系统。 此外，我们表明Fedorov引入的任意L+R系统可以看作是适当耦合LR系统的约化系统。 显示英文摘要

摘要： We consider coupled nonholonomic LR systems on the product of Lie groups. As examples, we study $n$-dimensional variants of the spherical support system and the rubber Chaplygin sphere. For a special choice of the inertia operator, it is proved that the rubber Chaplygin sphere, after reduction and a time reparametrization becomes an integrable Hamiltonian system on the $(n-1)$--dimensional sphere. Also, we showed that an arbitrary L+R system introduced by Fedorov can be seen as a reduced system of an appropriate coupled LR system.