Lagrangian and Hamiltonian Mechanics

i thought that i had mastered mechanics but then i heard of langragian mechanics and hamiltonian mechanics.my question is what are they ... why do we need them how are they different from newtonian mechanics and i would very grateful if i can get some links....
- deepak (age 17)
northern lko ,india

Lagrangian and Hamiltonian mechanics are different mathematical formulations which give the same results as Newtonian mathematics. In some ways they can be more convenient, for example in problems where there is some constraint (such as a fixed surface on which an object travels) which is inconvenient to express in terms of forces. They also happen to be forms which are more convenient for the transition to quantum mechanics.

There are nice Wikipedia articles: and .

Mike W.

(published on 04/13/2009)