Application of canonical coordinates for solving single-freedom constraint mechanical systems  

作　　者：高芳 张晓波 傅景礼 

机构地区：[1]Institute of Mathematical Physics,Zhejiang Sci-Tech University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第8期1029-1038,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11072218 and 11272287);the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT)(No.IRT13097)

摘　　要：This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.

关 键 词：canonical coordinates first integral Lie symmetry constraint mechanical system 

分 类 号：O316[理学—一般力学与力学基础]