时间尺度上奇异非保守Lagrange系统的Lie对称性和守恒量

Lie Symmetry and Conserved Quantity for Singular Non-conservative Lagrangian System on Time Scales

基于微分方程在无限小变换下的不变性,研究时间尺度上奇异非保守Lagrange系统的Lie对称性和守恒量.首先,在时间尺度上建立系统的运动微分方程;其次,基于时间尺度上微分方程在无限小变换下的不变性,建立Lie对称性的守恒量;最后举例说明结果的应用.

Based on the invariance of differential equation under infinitesimal transformat ion,we studied Lie symmetry and conserved quantity for a singular non-conservative Lagrangian system on time scales.First ly,we established the differential equation of motion on time scales.Secondly,based on the invariance of differential equations under infinitesimal trans formations on time scales,we established the conserved quantity of the Lie symm etry on time scale.Finally,we gave an example to illustrate the application of the result.