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Hamilton's equations

Analogous to what the Euler-Lagrange equation is to Lagrangian mechanics, Hamilton's equations give the equations of motion from a given input Hamiltonian:

\frac{\partial H}{\partial q _{j}} = - \overset{p}{˙}_{j} \frac{\partial H}{\partial p _{j}} = \overset{q}{˙}_{j}

So once you have the Hamiltonian, you can write down this system of partial differential equations which can then be numerically solved.

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