# 南部力学

## 单自由度情形

### 哈密顿力学

${\displaystyle {\dot {\xi _{1}}}={\frac {\partial H}{\partial \xi _{2}}},\qquad {\dot {\xi _{2}}}=-{\frac {\partial H}{\partial \xi _{1}}}.}$

${\displaystyle {\dot {\xi _{i}}}={\frac {\partial \left(\xi _{i},H\right)}{\partial \left(\xi _{1},\xi _{2}\right)}},\qquad i=1,2.}$

${\displaystyle \left[F,H\right]={\frac {\partial \left(F,H\right)}{\partial \left(\xi _{1},\xi _{2}\right)}}.}$

${\displaystyle {\dot {F}}={\frac {\partial F}{\partial t}}+\left[F,H\right].}$

### 南部力学

${\displaystyle {\dot {\xi _{i}}}={\frac {\partial \left(\xi _{i},H_{1},\cdots ,H_{n-1}\right)}{\partial \left(\xi _{1},\xi _{2},\cdots ,\xi _{n}\right)}},\qquad i=1,2,\cdots ,n.}$

${\displaystyle \left[F,H_{1},\cdots ,H_{n-1}\right]={\frac {\partial \left(F,H_{1},\cdots ,H_{n-1}\right)}{\partial \left(\xi _{1},\xi _{2},\cdots ,\xi _{n}\right)}}}$

${\displaystyle {\dot {F}}={\frac {\partial F}{\partial t}}+\left[F,H_{1},\cdots ,H_{n-1}\right].}$

## 南部力学与刚体力学的联系

${\displaystyle H_{1}={\frac {1}{2}}\sum _{i=1}^{3}L_{i}^{2},\qquad H_{2}={\frac {1}{2}}\sum _{i=1}^{3}{\frac {L_{i}^{2}}{I_{i}}}.}$

## 参考文献

1. Y . Nambu . Phys.Rev. . D7(1973)2405.
2. 张启仁 . 2002 . 经典力学 . 北京 : 科学出版社