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Hamiltonian

(Hamiltonian function)
(mathematical transform useful in mechanics)

Hamiltonian (or Hamiltonian function) is the name of a function used in Hamiltonian mechanics, consisting of the total energy of a closed system (one in which energy is not at the time being exchanged with the outside world): its kinetic energy plus its 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:
https://en.wikipedia.org/wiki/Hamiltonian_mechanics

Referenced by pages:
Lie transform
perturbation theory

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