约束力学系统的Lie对称性和全局分析

This project belongs to basic research problems for analytical mechanics. It has studied the restrictions on Lie symmetries imposed by nonholonomic constraints, given the formulations and solutions of Lie symmetry problems and inverse problems for various constrained systems, founded the relation between Noether symmetries and Lie symmetries, studied the effects of.non-conservative forces and nonholonomic constraints on Lie symmetries and conserved quantities. It has made a global analysis for the Birkhoff system, studied the existence of periodic solution for the higher order Birkhoff systems, the chaotic.behavior, the Poincaré bifurcation, the perturbation of the symmetry and adiabatic invariants of the lower order Birkhoff systems, given the differential geometric structure for the system. It has made a preliminary global analysis for nonholonomic.systems, given the perturbation of the symmetry, adiabatic invariants and the.differential geometric representation for holonomic and nonholonomic systems with variable mass. In addition, it has studied the next new problem in advance. The achievements of this project are 67 papers, in which 26 papers is cited by SCI, 22 papers by EI, 1 paper by ISTP.

研究约束力学系统，特别是非完整约束力学系统和Birkhoff 系统的Lie对称性与守恒量两辔侍狻蒐ie对称性求守恒量的正问题以及由已知守恒量求Lie 对称性的逆问题，建立约束力学系统一整套Lie 理论。研究约束力学系统的全局特性，包括非完整约束系统和Birkhoff 系统的全局稳定性，分叉与混沌，使对约束力学系统的研究上一个新台阶。