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Display information for equation id:math.1326.28 on revision:1326

* Page found: Der Hamiltonsche kanonische Formalismus (eq math.1326.28)

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Die Hamiltonschen Gleichungen Eq: math.1948.2

Hash: ff7067b1a410d88b29ce8b5439d49327

TeX (original user input):

\begin{align}
  & L=L(q,\dot{q},t):dL=\frac{\partial L}{\partial q}dq+\frac{\partial L}{\partial \dot{q}}d\dot{q}+\frac{\partial L}{\partial t}dt \\ 
 & H=H(q,p,t):dH=\frac{\partial H}{\partial q}dq+\frac{\partial H}{\partial p}dp+\frac{\partial H}{\partial t}dt \\ 
 & H=\dot{q}p-L\Rightarrow dH=\dot{q}dp+pd\dot{q}-dL=\dot{q}dp+pd\dot{q}-\frac{\partial L}{\partial q}dq-\frac{\partial L}{\partial \dot{q}}d\dot{q}-\frac{\partial L}{\partial t}dt \\ 
\end{align}

TeX (checked):

{\begin{aligned}&L=L(q,{\dot {q}},t):dL={\frac {\partial L}{\partial q}}dq+{\frac {\partial L}{\partial {\dot {q}}}}d{\dot {q}}+{\frac {\partial L}{\partial t}}dt\\&H=H(q,p,t):dH={\frac {\partial H}{\partial q}}dq+{\frac {\partial H}{\partial p}}dp+{\frac {\partial H}{\partial t}}dt\\&H={\dot {q}}p-L\Rightarrow dH={\dot {q}}dp+pd{\dot {q}}-dL={\dot {q}}dp+pd{\dot {q}}-{\frac {\partial L}{\partial q}}dq-{\frac {\partial L}{\partial {\dot {q}}}}d{\dot {q}}-{\frac {\partial L}{\partial t}}dt\\\end{aligned}}

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\begin{aligned} L = L (q, \dot{q}, t) : d L = \frac{\partial L}{\partial q} d q + \frac{\partial L}{\partial \dot{q}} d \dot{q} + \frac{\partial L}{\partial t} d t \\ H = H (q, p, t) : d H = \frac{\partial H}{\partial q} d q + \frac{\partial H}{\partial p} d p + \frac{\partial H}{\partial t} d t \\ H = \dot{q} p - L \Rightarrow d H = \dot{q} d p + p d \dot{q} - d L = \dot{q} d p + p d \dot{q} - \frac{\partial L}{\partial q} d q - \frac{\partial L}{\partial \dot{q}} d \dot{q} - \frac{\partial L}{\partial t} d t \end{aligned}

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