时间尺度上二阶Lagrange系统Mei对称性及守恒量

On Mei symmetry and conserved quantity of second-order Lagrange systems on time scales

研究时间尺度上二阶Lagrange系统的Mei对称性及守恒量.以时间尺度上二阶Lagrange系统的运动方程为基础,给出系统中的Lagrange方程在无限小变换下的Mei对称性及判定方程,并建立Mei对称性导致守恒量条件,最后举例说明结果的应用.

The Mei symmetry and conserved quantity of the second-order Lagrange system on time scales have been studied.Based on the motion equation of the second-order Lagrange system on time scales,the Mei symmetry of the second-order Lagrange system under infinitely small transformation has been explored.The definition of Mei symmetry and the decision equation of the second-order Lagrange system on time scales are obtained.And the conditions for the conserved quantity caused by Mei symmetry is established.An example is given to illustrate the application of the theorem.