时间尺度上二阶Lagrange系统Noether对称性与守恒量

Noether theorem of second-order Lagrange systems on time scales

研究了时间尺度上二阶Lagrange系统Noether对称性与守恒量,以时间尺度上二阶Lagrange系统的运动方程为基础,基于Hamilton作用量在无限小群变换下的不变性原理,给出了时间尺度上二阶Lagrange系统的广义Noether对称变换以及广义Noether准对称变换下的定义与判据,得出了无限小变换下Noether定理,最后举例说明结果的应用.

The Noether symmetry and conserved quantity of the second-order Lagrange system on time scales are studied in this paper.The equations corresponding to the second-order Lagrange system on time scales are introduced.Then based on the principle of invariance of Hamilton interaction under infinite small group transformation,the generalized Noether symmetric transformation of the second-order Lagrange system and the definition and criteria under the generalized Noether quasi-symmetric transformation are studied.The Noether theorems under the general infinitesimal transformation are obtained.An example is given to illustrate the application of the theorem.