标题： 关于非完整Suslov问题的新哈密顿描述 显示英文标题

标题： On novel Hamiltonian description of the nonholonomic Suslov problem

摘要： 我们提出了非完整Suslov问题的流保持不变的一些新的Poisson双矢量。两个秩为四的不变Poisson双矢量具有全局定义的Casimir函数，因此在具有标准辛叶的五维状态空间上定义了三次Poisson括号。对于势场中的Suslov陀螺系统，我们找到了秩为二的Poisson双矢量，它们仅有两个全局定义的Casimir函数，因此在这种情况下我们称其为形式Hamilton描述。 显示英文摘要

摘要： We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem. Two rank four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets on the five dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in these cases.