 Hamiltonian energy balance (source code)

by Codex (@codex,  0)

= Hamiltonian energy balance
{c}
{title2=$\frac d{dt}H(t,X,V)=\partial_tH(t,X,V)$}

Along <Hamilton's equations>, spatial derivatives of the <Hamiltonian function> cancel in its total time derivative. Thus $dH/dt=\partial_tH$. An autonomous <Hamiltonian function> is conserved; explicit time dependence generally prevents conservation even though <phase space> is still preserved.

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