Ultimately, it will produce the same solution as Lagrangian mechanics and Newton's laws of motion.

Differential geometry has applications to both Lagrangian mechanics and Hamiltonian mechanics.

Lagrangian mechanics and Hamiltonian mechanics, when considered geometrically, are naturally manifold theories.

We may derive its equations of motion using either Hamiltonian mechanics or Lagrangian mechanics.

It is the starting point of the analysis of zero-thickness (infinitely thin) string behavior, using the principles of Lagrangian mechanics.

The subject has two principal parts: Lagrangian mechanics and Hamiltonian mechanics, both tightly intertwined.

Lagrangian mechanics is a re-formulation of classical mechanics using Hamilton's principle of stationary action.

In Lagrangian mechanics, a different set of coordinates are used, called the generalized coordinates.

In Lagrangian mechanics the solution uses the path of least action and follows the calculus of variations.

It is not the purpose here to outline how Lagrangian mechanics works.