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

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

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.

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

Received: 03 February 2009
Revised: 16 May 2009
Accepted manuscript online:

PACS:	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	02.30.Jr	(Partial differential equations)

Fund: 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).

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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 2010 Chin. Phys. B 19 030302

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

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