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 of Holonomic Mechanical System

研究完整力学系统的由形式不变性导致的非Noether守恒量.建立系统的运动方程和形式不变性的判据方程.给出形式不变性为Lie对称性的充分必要条件.得到形式不变性导致非Noether守恒量的条件以及守恒量的形式.举例说明结果的应用.

NonNoether conserved quantity led by form invariance for holonomic systems is studied. Equations of motion and criterion equations of the form invariance are established. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the result.