For canonical coordinates and Hamiltonian ,
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Hamilton's equations by Ciro Santilli 40 Updated 2025-07-16
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Analogous to what the Euler-Lagrange equation is to Lagrangian mechanics, Hamilton's equations give the equations of motion from a given input Hamiltonian:
(1)
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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