This is a question, not a homework problem, as i am currently studying for my test on classical mechanics(adsbygoogle = window.adsbygoogle || []).push({});

suppose [tex] H = \sum_{i} \dot{q_{i}}(p,q,t) p_{i} - L(p,q,t) [/tex]

also i can prove that

[tex] dH = \sum_{i} (\dot{q_{i}}dp_{i} - \dot{p_{i}} dq_{i}) - \frac{\partial L}{\partial t} dt [/tex]

suppose [tex] \frac{\partial L}{\partial t} = \frac{\partial H}{\partial t} = 0 [/tex] then dH/dt = 0 i.e. H = E

now if i sub in to the equation above i get

[tex] dH = \sum_{i} (\dot{q_{i}}dp_{i} - \dot{p_{i}} dq_{i}) [/tex]

how would i transform the above dH into dH/dt formally?

Do i simply integrate by parts to get H and then differentiate wrt t??

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# The Hamiltonian

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