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# Hamilton's equations

nosplit "Hamiltonian mechanics" words: 46
Analogous to what the Euler-Lagrange equation is to Lagrangian mechanics, Hamilton's equations give the equations of motion from a given input Hamiltonian: $$∂qj​∂H​=−p˙​j​∂pj​∂H​=q˙​j​ (15)$$ So once you have the Hamiltonian, you can write down this system of partial differential equations which can then be numerically solved.