Poisson系统的辛结构

1.
中国科学院高能物理研究所,北京 100039;2.应用物理与计算数学研究所,北京 100088;3.中国科学院软件研究所,北京 100080;4.中国科学院计算数学研究所,北京 100080

基金项目: 国家自然科学基金资助项目(10401033;90103003;10471145)

Symplectic Structure of Poisson System

1.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, P. R. China;

摘要: 当Poisson系统中的Poisson矩阵是非常数时,经典的辛方法如辛Runge-Kutta方法,生成函数法一般不能保持Poisson系统的Poisson结构,利用非线性变换可把非常数Poisson结构转化成辛结构,然后任意阶的辛方法可以长时间计算Poisson系统的辛结构．自由刚体问题中Euler方程被转换成辛结构并用辛中点格式进行数值求解,数值结果给出了这种非线性变换的有效性．
- Poisson系统 /
- 非线性变换 /
- 辛方法 /
- 自由刚体问题
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.
- Poisson system /
- nonlinear transformation /
- symplectic method /
- rigid body problem

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