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

doi:10.1088/1674-1056/19/3/030302

中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30302-030302.doi: 10.1088/1674-1056/19/3/030302

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

常鹏¹, 刘世兴¹, 郭永新¹, 刘畅²

(1)College of Physics, Liaoning University, Shenyang 110036, China; (2)College of Physics, Liaoning University, Shenyang 110036, China;Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2009-02-03 修回日期:2009-05-16 出版日期:2010-03-15 发布日期:2010-03-15
基金资助:
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) and the Research Program of Higher Education of Liaoning Province, China (Grant No.~2008S098).

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

Liu Chang(刘畅)^a)b), Chang Peng(常鹏)^a), Liu Shi-Xing(刘世兴)^a), and Guo Yong-Xin(郭永新)^a)^†

^a College of Physics, Liaoning University, Shenyang 110036, China; ^b Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China

Received:2009-02-03 Revised:2009-05-16 Online:2010-03-15 Published:2010-03-15
Supported by:
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) and the Research Program of Higher Education of Liaoning Province, China (Grant No.~2008S098).

摘要/Abstract

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 noncanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion.

Abstract: 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 noncanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion.

Key words: almost-Poisson structure, non-self-adjointness, Jacobi identity, generalised Chaplygin's nonholonomic systems

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

02.30.Jr (Partial differential equations)

刘畅, 常鹏, 刘世兴, 郭永新. Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems[J]. 中国物理B, 2010, 19(3): 30302-030302.

Liu Chang(刘畅), Chang Peng(常鹏), Liu Shi-Xing(刘世兴), and Guo Yong-Xin(郭永新). Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems[J]. Chin. Phys. B, 2010, 19(3): 30302-030302.

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

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

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