= Solution
Along <Hamiltonian> motion,
$$
\frac{dO}{dt}=\frac{\partial O}{\partial t}
+\sum_i\left(\frac{\partial O}{\partial q_i}\dot q_i
+\frac{\partial O}{\partial p_i}\dot p_i\right).
$$
Substituting $\dot q_i=\partial H/\partial p_i$ and $\dot p_i=-\partial H/\partial q_i$ gives
$$
\boxed{\frac{dO}{dt}=\frac{\partial O}{\partial t}+\{O,H\}.}
$$
For the printed $O(q,p)$ there is no explicit time term. In particular, an autonomous <observable> is conserved when its <Poisson bracket> with $H$ vanishes. Taking $O=q_i$ or $O=p_i$ recovers <Hamilton's equations>.
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