Hamiltonian mechanics

Hamiltonian mechanics is a mathematical way of understanding the way something  mechanical will behave. It was invented  in 1833 by Irish mathematician William Rowan Hamilton.

The value of the Hamiltonian is the total energy of the thing  being described. For a closed system, it is the sum of its  kinetic and potential energy. There will be  a set of differential equations known as the Hamilton equations which show how the thing changes through time. 

Hamiltonians can be used to describe such simple systems as a bouncing ball, a pendulum or an oscillating spring in which energy changes between  kinetic and  potential energy and back again over time. Hamiltonians can also be used to study the orbits of planets and in the behaviour of atoms using the principles of quantum mechanics.

Category:Classical mechanics