有多余坐标完整力学系统的形式不变性与非Noether守恒量

Form invariance and non-Noether conserved quantity for holonomic mechanical systems with remainder coordinates

研究有多余坐标完整力学系统的形式不变性与非Noether守恒量.首先,建立了系统的运动微分方程,给出了系统在仅依赖于广义坐标的无限小变换下的形式不变性和Lie对称性的定义和判据,讨论了形式不变性与Lie对称性的关系;其次,给出了形式不变性导致非Noether守恒量的条件及守恒量的形式;最后,举例说明结果的应用.

This paper studies the form invariance and the non-Noether conserved quantity of the holonomic mechanical systems with remainder coordinates. Firstly, the differential equations of motion of the systems are established. The definitions and criterions of the form invariance and the Lie symmetry of the systems under the infinitesimal transformations which only depend upon the generalized coordinates are given, and the relation between the form invariance and the Lie symmetry is discussed. Secondly, the condition under which the form invariance can lead up to a non-Noether conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.