lagrangian mechanics vs hamiltonian mechanics

Dear student,

n Lagrangian mechanics, you are using what is called an action principle. For very subtle mathematical reasons, you know the action is minimized over the trajectory of the particle in a conservative force field. The Lagrangian action is L=T-U (T is kinetic energy, U is potential energy). Minimizing that action yields the Euler-Lagrange equations, a system of differential equations that describes the behavior of the particle.

In Hamiltonian mechanics, you use the Lagrangian (L, from the previous paragraph) to calculate the Hamiltonian. In systems where energy is conserved, the Hamiltonian is just the total energy (all forms of kinetic, all forms of potential, etc.... all added up). Then you use Hamilton's equations to give you a system of first order differential equations for quantities that are called generalized momentum and generalized position.

Regards

Sumit