SYMPLECTIC STRUCTURE OF POISSON SYSTEM

• Published in: Applied mathematics and mechanics Vol. 26; no. 11; pp. 1484 - 1490
• Main Author: 孙建强 马中骐 田益民 秦孟兆 GU Yuan-xian
• Format: Journal Article
• Language: English
• Published: Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R.China%Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100039, P.R.China%Institute of Software, Chinese Academy of Sciences,Beijing 100080, P.R.China%Institute of Computational Mathematics, Chinese Academy of Sciences,Beijing 100080, P.R.China 01.11.2005; Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100039, P.R.China
• Subjects: Poisson系统; Poisson结构; 刚性体; 对称结构; 非线性传播; Poisson system; symplectic method; nonlinear transformation; rigid body problem
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/BF03246255

When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform. Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform.