含时滞的非保守系统动力学的Noether对称性

摘要

The Noether symmetries and the conserved quantities of dynamics for non-conservative systems with time delay are proposed and studied. Firstly, the Hamilton principle for non-conservative systems with time delay is established, and the Lagrange equations with time delay are obtained. Secondly, based upon the invariance of the Hamilton action with time delay under a group of infinites-imal transformations which depends on the generalized velocities, the generalized coordinates and the time, the Noether symmetric transformations and the Noether quasi-symmetric transformations of the system are defined and the criteria of the Noether symmetries are established. Finally, the relationship between the symmetries and the conserved quantities are studied, and the Noether theory of non-conservative systems with time delay is established At the end of the paper, some examples are given to illustrate the application of the results.%提出并研究含时滞的非保守系统动力学的Noether 对称性与守恒量。首先，建立含时滞的非保守系统的Hamilton原理，得到含时滞的Lagrange方程；其次，基于含时滞的Hamilton作用量在依赖于广义速度的无限小群变换下的不变性，定义系统的Noether对称变换和准对称变换，建立Noether对称性的判据；最后，研究对称性与守恒量之间的关系，建立含时滞的非保守系统的Noether理论。文末举例说明结果的应用。