基于对偶变量变分原理和两端动量独立变量的保辛方法

将广义位移和动量同时用拉格朗日多项式近似，并选择积分区间两端动量为独立变量，然后基于对偶变量变分原理导出了哈密顿系统的离散正则变换和对应的数值积分保辛算法．当位移和动量的拉格朗日多项式近似阶数满足一定条件时，可以自然导出保辛算法的不动点格式．通过数值算例讨论了位移和动量采用不同阶次插值所需最少Gauss积分点个数，并讨论了位移插值阶数、动量插值阶数以及Gauss积分点个数对保辛算法精度的影响，说明了上述不动点格式恰好是一种最优格式．

The symplectic and energy preserving method for the integration of hamilton system

The generalized displacements and momentum were approximated by Lagrange polynomial,and the momentum at the two ends of time interval were taken as the independent variables.Then the discrete Hamilton canonical equations and the corresponding symplectic method were derived based on the dual variable principle. A fix point iteration formula can be derived when the order of the approximate polynomials of displacements and momentum satisfy some certain conditions.In the numerical examples part,the smallest num...