【摘要】 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.更多还原

【Abstract】 This paper deals with a non-Noether conserved quantity constructed directly by using the form invariance for the Nielsen equation of a non-conservative mechanical system. The definition and the criterion of a non-point form invariance of the equation, of which the Noether conserved quantity is studied, are established by relying on the total time derivative along the trajectory of the equation. The 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 corollaries in special cases are presented. Two examples are finally given to illustrate the application of the results.更多还原