离散差分变分Hamilton系统的Lie对称性与Noether守恒量

研究离散差分Hamilton系统的Lie对称性与Noether守恒量. 根据扩展的时间离散力学变分原理构建Hamilton系统的差分动力学方程.定义离散系统运动差分方程在无限小变换群下的不变性为Lie对称性, 导出由Lie对称性得到系统离散Noether守恒量的判据. 举例说明结果的应用. 关键词： 离散力学 差分Hamilton系统 Lie对称性 Noether守恒量

The Lie symmetry and Noether conserved quantity of discrete difference variational Hamilton system

The Lie symmetry and Noether conserved quantity of discrete difference Hamilton system are investigated. Based on the extended mechanical variational principle of discrete time, the difference dynamical equations of Hamilton system are constructed. The invariance of difference equations of discrete system under infinitesimal transformation groups is defined to be Lie symmetry and the criterion for when discrete Noether conserved quantities may be obtained from Lie symmetries is also deduced. An example is discussed to show the applications of the results.