Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
; Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
; Chinese Acad Sci, Inst Software, Beijing 100080, Peoples R China
; Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China
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.