非保守Nielsen方程的形式不变性导致的非Noether守恒量

研究非保守Nielsen方程由形式不变性直接导致的非Noether守恒量．函数对时间的全导数采 用沿运动轨道曲线的方式，给出非保守Nielsen方程的非点的形式不变性的定义和判据，并 研究其Noether守恒量．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，并 给出三种特殊情形的推论．举例说明结果的应用． 关键词： Nielsen方程 形式不变性 非Noether守恒量

A non-Noether conserved quantity constructed using form invariance for Nielsen equation of a non-conservative mechanical system

This paper deals with a non-Noether conserved quantity constructed directly by u sing the form invariance for the Nielsen equation of a non-conservative mechanic al system. The definition and the criterion of a non-point form invariance of th e equation, of which the Noether conserved quantity is studied, are established by relying on the total time derivative along the trajectory of the equation. T he condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced, and three corollar ies in special cases are presented. Two examples are finally given to illustrate the application of the results.