阻尼运动的动力学逆问题和变分法逆问题

以阻尼运动为例,研究动力学逆问题和变分法逆问题的特征,以及两者之间的关联.首先,从该运动的运动规律导出几种对应的运动微分方程,即得到几种不同的作用于质点上的力,并讨论了这几种情况之间的联系和区别;其次,从其中两种运动微分方程出发,直接构造出相应的Lagrange函数和函数族;最后,指出了两种逆问题相组合产生的新结果.

Inverse problem of dynamics and inverse problem of variational calculus for damped motion

In this paper,a damped motion is taken as an illustrative example to study the characteristics of inverse problem of dynamics and inverse problem of variational calculus and the relation between the two. First, from a special equation of damped motion, four differential equations of motion, i.e. four different functions of force are obtained, the connections and the differences among them are discussed. Secondly, the corresponding Lagrangians and a family of Lagrangians are constructed directly from the two among the four above equations. Finally, new result of the combination of the two inverse problems is pointed.