Perturbation of Symmetries and Adiabatic Invariants for a System of Generalized Classical Mechanics

Yi Zhang

《Chinese Journal of Physics》 49卷5期 (2011/10) Pp. 1005-1017

並列摘要

This paper focuses on studying the perturbation of symmetries and adiabatic invariants for a system of generalized classical mechanics. Firstly, by using the invariance of the Pfaffian action under the infinitesimal transformations, the Noether symmetry and the corresponding conserved quantity of the generalized classical mechanical system is established, the perturbation of the Noether symmetry of the system with the action of a small disturbance is investigated, and a type of Noether higher-order adiabatic invariant of the system is obtained. Secondly, by using the invariance of differential equations under infinitesimal transformations, the Lie symmetry of the generalized classical mechanical system is established, and the Hojman conserved quantity directly obtained by the Lie symmetry of the system is given. The perturbation of the Lie symmetry of the system with the action of a small disturbance is investigated, and a type of Hojman higher-order adiabatic invariant of the system is obtained. Some examples are given to illustrate the application of the results.