离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量

The Noether conserved quantity of Lie symmetry for discrete difference sequence Hamilton system with variable mass

本文研究离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量.构建了离散差分序列变质量Hamilton系统的差分动力学方程,给出了离散差分序列变质量Hamilton系统差分动力学方程在无限小变换群下的Lie对称性的确定方程和定义,得到了离散力学系统Lie对称性导致Noether守恒量的条件及形式,举例说明结果的应用.

In this paper the Lie symmetry and Noether conserved quantity of a discrete difference sequence Hamilton system with variable mass are studied. Firstly, the difference dynamical equations of the discrete difference sequence Hamilton system with variable mass are built. Secondly, the determining equations and the definition of Lie symmetry for difference dynamical equations of the discrete difference sequence Hamilton system under infinitesimal transformation groups are given. Thirdly, the forms and conditions of Noether conserved quantities to which Lie symmetries will lead in a discrete mechanical system are obtained. Finally, an example is given to illustrate the application of the results.