# Hamiltonian

The **Hamiltonian** ^{[1]}^{[2]} is given by

where are the generalised coordinates, are the canonical momentum,
and *L* is the Lagrangian.
Using the Hamiltonian function, the equations of motion can be expressed in the so-called
canonical form:

and

## References

- ↑ William Rowan Hamilton "On a General Method in Dynamics; By Which the Study of the Motions of All Free Systems of Attracting or Repelling Points is Reduced to the Search and Differentiation of One Central Relation, or Characteristic Function", Philosophical Transactions of the Royal Society of London
**124**pp. 247-308 (1834) - ↑ William Rowan Hamilton "Second Essay on a General Method in Dynamics", Philosophical Transactions of the Royal Society of London
**125**pp. 95-144 (1835)

- Related reading

- Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002) Chapter 8: The Hamiltonian Equations of Motion.