中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30302-030302.doi: 10.1088/1674-1056/19/3/030302
常鹏1, 刘世兴1, 郭永新1, 刘畅2
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)†
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.
中图分类号: (Lagrangian and Hamiltonian mechanics)