相空间中准坐标下非完整系统的Noether对称性

Noether Symmetry of Nonholonomic System under Quasi - coordinate in Phase Space

研究相空间中准坐标下完整系统和非完整系统的Noether对称性。首先,在相空间中引入准速度和准坐标,定义了用准速度表示的广义Hamilton函数和广义Hamilton作用量;基于广义Hamilton作用量在无限小变换下的不变性,得到了完整系统和非完整系统广义Hamilton作用量变分的基本原理;给出了相空间中准坐标下完整系统和非完整系统的Noether对称性、Noether准对称性和Noether广义准对称性的定义、判据及其Noether定理;并研究了该系统的Noether对称性逆问题。

Noether symmetry of holonomic and nonholomic system under quasi - coordinate in phase space is studied. First, the quasi - speed and quasi - coordinate are introduced in phase space and generalized Hamilton function and action in expression of quasi - speed are defined. Basing on the invariability of generalized Hamilton action under the condition of infinitesimal transformation, the basic principle of the variation of Noether symmetry of holonomic and nonholomic system. The definition and criterion of Noether symmetry, Noether pseudo - symmetry and Noether generalized pseudo - symmetry of holonomic and nonholomic system under quasi - coordinate in phase space are given as well as Noether theorem and the counter question of Noether symmetry of this system is studied.