中国物理B ›› 2006, Vol. 15 ›› Issue (3): 470-474.doi: 10.1088/1009-1963/15/3/002
陈向炜, 刘翠梅, 李彦敏
Chen Xiang-Wei (陈向炜), Liu Cui-Mei (刘翠梅), Li Yan-Min (李彦敏)
摘要: Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincar\'{e} equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.
中图分类号: (Partial differential equations)