# 拉格朗日力学

## 自由度

${\displaystyle S=3N-m}$

## 拉格朗日量

${\displaystyle {\mathcal {L))(q_{1},\ q_{2},\ \dots ,\ q_{n};\ {\dot {q_{1))},\ {\dot {q_{2))},\ \dots ,\ {\dot {q_{n))},\ t)}$

${\displaystyle {\mathcal {L))=T-V}$

## 拉格朗日方程

${\displaystyle {\mathrm {d} \over \mathrm {d} t}{\partial {\mathcal {L)) \over \partial {\dot {q_{i))))-{\partial {\mathcal {L)) \over \partial q_{i))=Q_{i))$

## 拉格朗日力学的扩展

1948年，费曼发明了路径积分表述，将最小作用量原理扩展到量子力学。在该表述中，粒子穿过所有可能的始态和终态的所有路径；特定终态的概率是所有可能导向它的轨迹的概率之和。在经典力学的范围，路径积分表述简单的退化为哈密顿原理

## 参考文献

1. ^ Goldstein, H. Classical Mechanics 3rd. Addison-Wesley. 2001: 35.
2. ^ 陈世民. 理论力学简明教程. 高等教育出版社. : 185–186页. ISBN 978-7-04-023918-8.
• 梁昆淼：《力学》
• 朗道：《力学》

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