El-Nabulsi动力学模型下非Chetaev型非完整系统的精确不变量与绝热不变量

Exact invariants and adiabatic invariants for nonholonomic systems in non-Chetaev's type based on El-Nabulsi dynamical models

研究El-Nabulsi动力学模型下非Chetaev型非完整系统精确不变量与绝热不变量问题.首先,导出El-Nabulsi-d’Alembert-Lagrange原理并建立系统的运动微分方程.其次,建立El-Nabulsi模型下未受扰动的非Chetaev型非完整系统的Noether对称性与Noether对称性导致的精确不变量之间的关系;再次,引入力学系统的绝热不变量概念,研究受小扰动作用下非Chetaev型非完整系统Noether对称性的摄动导致绝热不变量问题,给出了绝热不变量存在的条件及其形式.作为特例,本文讨论了El-Nabulsi模型下Chetaev型非完整系统的精确不变量与绝热不变量问题.最后分别给出非Chetaev型和Chetaev型两种约束下的算例以说明结果的应用.

In this paper, the problem of exact invariants and adiabatic invariants for nonholonomic system in non-Chetaev＇s type based on the El-Nabulsi dynamical model is studied. First, the El-Nabulsi-d＇Alembert-Lagrange principle is deduced and the differential equations of motion of the system are established. Then, the relation between the Noether symmetry and the exact invariant that is led directly by the symmetry for undisturbed nonholonomic system in non-Chetaev＇s type is given. Furthermore, by introducing the concept of high-order adiabatic invariant of a mechanical system, the conditions that the perturbation of symmetry leads to the adiabatic invariant and its formulation are studied for the nonholonomic system in non-Chetaev＇s type under the action of small disturbance. As a special case, the problem of the exact invariants and the adiabatic invariants for the nonholonomic system in Chetaev＇s type in El-Nabulsi model is discussed. At the end of the paper, two examples for the nonholonomic systems in non-Chetaev＇s type constraints and also the Chetaev＇s type constraints are given respectively to show the application of the methods and the results of this paper.