Lagrangian Mechanics is a very elegant formulation of classical mechanics which was published by Lagrange in 1788. This formulation has a handful of benefits over the earlier Newtonian formulation of mechanics. First, we can virtually ignore forces that constrain a system, i.e. to a plane or surface. Second, Lagrange's equations take the same form in any coordinate system. Further, from a more aesthetic standpoint, an entire physical system can be represented with one equation, the Lagrangian. I will briefly review Newtonian mechanics, then use the calculus of variations to develop the Euler-Lagrange equation, which is of great importance in both physics and differential geometry. I will then define the Lagrangian and give an example of a problem using both Newtonian and Lagrangian methods to exploit the elegance and convenience of the later formulation.
Prerequisites: Calculus. Introductory physics would be helpful, but not necessary.