# 辛標記

${\displaystyle {\dot {\mathbf {q} }}=~~{\frac {\partial {\mathcal {H}}}{\partial \mathbf {p} }}\,\!}$
${\displaystyle {\dot {\mathbf {p} }}=-{\frac {\partial {\mathcal {H}}}{\partial \mathbf {q} }}\,\!}$

${\displaystyle {\boldsymbol {\xi }}^{T}=[q_{1},\ q_{2},\ q_{3},\ \dots ,\ q_{N},\ p_{1},\ p_{2},\ p_{3},\ \dots ,\ p_{N}]\,\!}$

${\displaystyle {\boldsymbol {\Omega }}={\begin{bmatrix}\mathbf {0} &\mathbf {1} \\-\mathbf {1} &\mathbf {0} \end{bmatrix}}\,\!}$

${\displaystyle {\dot {\boldsymbol {\xi }}}={\boldsymbol {\Omega }}{\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {\xi }}}}\,\!}$

## 正則變換

${\displaystyle {\dot {\boldsymbol {\Xi }}}={\boldsymbol {\Omega }}\ {\frac {\partial {\mathcal {K}}}{\partial {\boldsymbol {\Xi }}}}\,\!}$

## 帕松括號

${\displaystyle {\big [}f,g{\big ]}_{\mathbf {q} ,\ \mathbf {p} }=\sum _{i=1}^{N}\left({\frac {\partial f}{\partial q_{i}}}{\frac {\partial g}{\partial p_{i}}}-{\frac {\partial f}{\partial p_{i}}}{\frac {\partial g}{\partial q_{i}}}\right)\,\!}$

${\displaystyle {\big [}f,g{\big ]}_{\boldsymbol {\xi }}=\left({\frac {\partial f}{\partial {\boldsymbol {\xi }}}}\right)^{T}{\boldsymbol {\Omega }}\ {\frac {\partial g}{\partial {\boldsymbol {\xi }}}}\,\!}$

## 參考文獻

1. ^ Goldstein, Herbert. Classical Mechanics 3rd. United States of America: Addison Wesley. 1980: pp. 343. ISBN 0201657023 （英语）.