Abstract
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.
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Communicated by !GU Yuan-xian
Project supported by the National Natural Science Foundation of China (Nos. 10401033, 90103003 and 10471145)
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Sun, Jq., Ma, Zq., Tian, Ym. et al. Symplectic structure of poisson system. Appl. Math. Mech.-Engl. Ed. 26, 1484–1490 (2005). https://doi.org/10.1007/BF03246255
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DOI: https://doi.org/10.1007/BF03246255