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

作者：Liu Chang; Chang Peng; Liu Shi Xing; Guo Yong Xin^*

来源：Chinese Physics B, 2010, 19(3): 030302.

DOI：10.1088/1674-1056/19/3/030302

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

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.

• 出版日期2010-3
• 单位辽宁大学; 北京理工大学