时间尺度上非保守系统的Lie对称性及其守恒量

Lie symmetry and conserved quantity for non-conservative systems on time scales

研究了时间尺度上非保守系统的Lie对称性及其守恒量.首先,基于时间尺度上微分方程在无限小变换下的不变性,导出了时间尺度上Lie对称性的确定方程;然后,建立了时间尺度上非保守系统的Lie对称性的结构方程,以及时间尺度上非保守系统的Lie对称性的Noether型守恒量;最后,举例说明其结果的应用.

In this paper, Lie symmetry and conserved quantity for non-conservative sys terns on time scales are studied. Firstly, based on the invariance of the differential equa tions on time scales under the infinitesimal transformations of groups, the determining equations of Lie symmetry on time scales are provided. Secondly, the structure equa tions of Lie symmetry for non-conservative systems on time scales are established, and formulation of the Noether conserved quantity is constructed. Finally, an example is presented to illustrate the application of the results.