经典力学中加速度相关的Lagrange函数

Acceleration-dependent Lagrangians in classical mechanics

研究了加速度线性相关的Lagrange函数,在加速度项系数对称的条件下,Lagrange方程保持为二阶微分方程;给出了从运动方程构造加速度相关的Lagrange函数的方法;研究同一系统的加速度相关和加速度无关的Lagrange函数之间的关系.举例说明结果的应用.

The linear acceleration-dependent Lagrangians are studied. Under the symmetric conditions of coefficients in acceleration terms, the Lagrange＇ s equations remain second-order differential equations. The approach to constructing an accelerationdependent Lagrangian from its equations of motion is presented. The relations between the acceleration-dependent Lagrangians and the acceleration independent ones of the same system are studied. Two examples are given to illustrate the application of the results.