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

Mechanics

Hamiltonian Mechanics

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

			(1)
			(2)
			(3)

for i = 1, ..., n, where

are the generalized coordinates,

(4)

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

(5)

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

Hamiltonian, Hamiltonian Mechanics