### 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
—— = - ——
*dt* ∂*q*
*dq* ∂ℋ
—— = + ——
*dt* ∂*p*

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

ℋ = *T* + *V*
where
*p*²
*T* = ——
2*m*
*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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