Abstract:

Noether symmetries and their inverse problems of the nonholonomic systems with the fractional derivatives are studied. Based on the quasi-invariance of fractional Hamilton action under the infinitesimal transformations without the time and the general transcoordinates of time-reparametrization, the fractional Noether theorems are established for the nonholonomic constraint systems. Further, the fractional Noether inverse problems are firstly presented for the nonholonomic systems. An example is designed to illustrate the applications of the results.

Key words: fractional derivative, nonholonomic system, Noether symmetry, Noether inverse problem

摘要：

研究分数阶非完整系统的Noether 对称性及其逆问题。基于分数阶非完整系统的Hamilton 作用量关于广义坐标以及时间在无限小变换下的不变性, 提出系统的 Noether 定理, 并首次提出分数阶非完整动力学系统的逆问题。最后给出一个算例, 以说明结果的应用。

关键词: 分数阶导数, 非完整系统, Noether 对称性, Noether 逆问题