广义力学中Lagrange方程的形式不变性

Form Invariance of Lagrange′s Equations in Generalized Mechanics

对称性方法是寻求守恒量的近代方法,形式不变性是一种新的对称性.研究广义力学中Lagrange方程在无限小变换下的形式不变性.给出形式不变性的定义和判据.建立形式不变性导致守恒量的条件,并举例说明结果的应用.

Symmetry method is a modern method in seeking conservation.A form invariance is a new symmetry.The aim of this paper is to study the form invariance of Lagrange′s equations in generalized mechanics under the infinitesimal transformations of groups.First,the definition and criterion of the invariance are given.Next,the condition under which the invariance can lead to a conserved quantity is established.Finally,we given an example to illustrate the application of the result.