Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems  

作　　者：刘畅 常鹏 刘世兴 郭永新 

机构地区：[1]College of Physics,Liaoning University [2]Department of Applied Mechanics,Beijing Institute of Technology

出　　处：《Chinese Physics B》2010年第3期21-26,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos. 10872084 and 10472040);the Outstanding Young Talents Training Fund of Liaoning Province,China (Grant No. 3040005);the Research Program of Higher Education of Liaoning Province,China (Grant No. 2008S098)

摘　　要：This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost- Poisson structure for generalised Chaplygin＇s systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noneanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion.This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost- Poisson structure for generalised Chaplygin＇s systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noneanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion.

关 键 词：almost-Poisson structure non-self-adjointness Jacobi identity generalised Chaplygin＇snonholonomic systems 

分 类 号：O316[理学—一般力学与力学基础]