The Hamiltonian of a system is defined as

(1)

where q is a generalized coordinate, p is a generalized momentum, L is the Lagrangian, and Einstein summation has been used. If L is a sum of functions homogeneous (i.e., no products of different degrees) in generalized velocities of degrees 0, 1, and 2 and the equations defining the generalized coordinates are not functions of time, then

(2)

where T is the kinetic energy, V is the potential energy, and E is the total energy of the system.

Hamiltonian Mechanics, Hamiltonian Operator, Kamiltonian