Carathéodory变分方法与经典力学

The Variational Method of Carathéodory and Classical Mechanies

在勒让德变换存在的前提下，通过Caratheodory变分方法在经典力学中的应用，阐明这一较为近代的方法，并由此导出哈密顿一雅科比方程、哈密顿方程以及欧拉一拉格朗日方程．

On the premise that the Legendre transformation exists, we apply the variationalrnethod of Caratheodory to classical mechanies- In this way, we expound this modern methodand derive the Hamilton-Jacobi equations, Hamilton's equations of motion, and Euler-La-grange equations.