Astrophysics (index)

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 or 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

In a simple system, i.e., single particle traveling on a single dimension:

ℋ = T + V

where

    p²
T = ——
    2m

V = V(q)
  • T - kinetic energy.
  • m - mass of particle.
  • V - potential energy.

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

Referenced by:
Lie Transform
Perturbation Theory

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