Astrophysics (Index)About

Hamiltonian

(Hamiltonian function)
(mathematical transform useful in mechanics)

Hamiltonian (or Hamiltonian function) is the name of a function used in Hamiltonian mechanics consisting of (in a closed system), the total energy of the system, consisting of kinetic energy plus potential energy. Hamiltonian mechanics can solve classical mechanical problems and was useful as a step toward statistical mechanics and quantum mechanics.

The Hamiltonian function, ℋ(q,p,t), of space coordinates q, momentum coordinates p and time t satisfies:

dp     ∂ℋ
—— = - ——
dtq

dq     ∂ℋ
—— = + ——
dtp

(These are derived from Newton's laws.) In a simple system, i.e., single particle traveling on a single dimension:

ℋ = T + V

where

    p²
T = ——
    2m

V = V(q)

(mathematics,mechanics,function)
Further reading:
http://en.wikipedia.org/wiki/Hamiltonian_mechanics

Referenced by pages:
Lie transform
perturbation theory

Index