If the classical Hamiltonian is define as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]H = f(q, p)[/tex]

p, q is generalized coordinates and they are time-dependent. But H does not explicitly depend on time. Can I conclude that the energy is conserved (even q, p are time-dependent implicitly)? Namely, if no matter if p, q are time-dependent or not, if H does not contains [tex]t[/tex] explicitly, I find that the Poisson bracket

[tex]\left\{H, H\right\} \equiv 0[/tex]

so the energy is conserved, right?

But what about if H explicitly depend on time? According to the definition of Poisson bracket, [tex]\left\{H, H\right\} \neq 0[/tex] ????

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# Classical Hamiltonian

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