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Classical Mechanics Fall 2011 Chapter 7: Lagrange's Equations

What is Lagrange's formulation of classical mechanics?
The notions of phase space, momentum and energy are introduced. This lecture introduces Lagrange's formulation of classical mechanics. That formulation is formal and elegant; it is based on the Least Action Principle. The concepts introduced here are central to all modern physics.
How can scalar potentials be used in Lagrangian mechanics?
Use of the concept of scalar potentials is a trivial and powerful way to incorporate conservative forces in Lagrangian mechanics. The Lagrange multipliers approach requires using the Euler-Lagrange equations for n + m n + m coordinates but determines both holonomic constraint forces and equations of motion simultaneously.
Why is Lagrange mechanics important?
As a consequence, Lagrange mechanics allows use of any set of independent generalized coordinates, which do not have to be orthogonal, and they can have very different units for different variables. The generalized coordinates can incorporate the correlations introduced by constraint forces.
How do you find the Lagrangian for a cylinder?
Write down the Lagrangian for a cylinder (mass m, radius R, and moment of inertia I ) that rolls without slipping straight down an inclined plane which is at an angle α from the horizontal. Use as your generalized coordinate the cylinder's distance x measured down the plane from its starting point.

What is Lagrange's formulation of classical mechanics?