Hamilton's Equations -- from Eric Weisstein's World of Physics

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Hamilton's Equations

A Hamiltonian system always has an even number of dimensions N, since and are defined as conjugate variables. Therefore, integrals specify a trajectory. Hamilton's equations are

for i = 1, ..., n, where are the generalized coordinates,

their conjugate momenta, L is the Lagrangian, and the Hamiltonian H is defined by

where Einstein summation Eric Weisstein's World of Math has been used.

Hamiltonian, Hamiltonian Mechanics