Acceleration-dependent Lagrangians in classical mechanics
经典力学中加速度相关的Lagrange函数

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 acceleration-dependent 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.