Use this tag for questions related to Hamilton's equations.
Hamilton's equations are $$\dot q = \frac{\partial H}{\partial p} \qquad \dot p = -\frac{\partial H}{\partial p}$$ where $\dot p = dp /dt$, $\dot q = dq /dt$ is fluxion notation, and $H$ is the so-called Hamiltonian. Those equations frequently arise in problems of celestial mechanics.
The vector form of Hamilton's equations is $$\dot p = H_{p_i} (t, \mathbf q, \mathbf p) \qquad \dot q = -H_{q_i} (t, \mathbf q, \mathbf p).$$
Another formulation related to Hamilton's equation is $$p = \frac{\partial L}{\partial \dot q}$$ where $L$ is the so-called Lagrangian.
