中文摘要：

根据动量的不同表达式,给出3种不同的Legenda变换形式;得到3种不同形式的Hamilton系统的动力学方程;给出辛结构守恒的具体形式;二自由度非线性谐振子的例子验证基于离散变分原理的算法具有保系统的能量守恒量性质.

英文摘要：

Three types of discrete Legenda transformations are obtained when the displacement coordinates are defined implicitly by different momentum.The different forms of Hamiltonian equations are constructed based on the difference Legenda transformations.The symplectic structures of the three Hamilton systems are given,respectively.The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show the advantage of variational numerical method.