非完整力学系统的Hamilton对称性

Symmetry of Hamiltonians of a nonholonomic mechanical system

研究非完整力学系统的Hamilton对称性与守恒量.将非完整系统纳入广义Birkhoff系统,建立了用正则变量表示的运动微分方程,给出了系统的Hamilton对称性的定义和判据,导出了非完整力学系统的Hamilton对称性导致守恒量的条件及其形式.作为特例,文章给出了非保守力学系统和Hamilton系统的Hamilton对称性与守恒量.文末举例说明结果的应用.

This paper focuses on studying a symmetry of Hamiltonians and corresponding conserved quantity of a nonholonomic mechanical system. The nonholonomic system is considered as a special generalized Birkhoffian system, and the differential equations of motion of the system expressed by the canonical variables are established. The definition and the criterion of the symmetry of Hamiltonians of the system are given. The condition under which a symmetry of Hamiltonians can lead to a new conserved quantity is deduced and the form of the new conserved quantity is presented. As a special case, the symmetry of Hamiltonians and corresponding conserved quantity for a nonconservative mechanical system and a Hamiltonian system are given. At the end of the paper, two examples are given to illustrate the application of the results.