Lagrangian, least action, Euler-Lagrange equations

Classical Mechanics (Fall, 2011)

Lecture Playlist

  1. State diagrams and the nature of physical laws

  2. Newton's law, phase space, momentum and energy

  3. Lagrangian, least action, Euler-Lagrange equations

  4. Symmetry and conservation laws

  5. The Hamiltonian

  6. Hamilton's equations

  7. Liouville s theorem

  8. Poisson brackets

  9. Electric and magnetic fields 1

  10. Electric and magnetic fields 2

October 10, 2011

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. The lecture ends with angular momentum and coordinate transforms.

Topics: 
  • Principle of Least Action (“stationary action”)
  • Equilibrium points of a function
  • Trajectories
  • Calculus of variations
  • Light in a refractive media and hanging chain catenary
  • Lagrangian and Action
  • Euler Lagrange equations of motion
  • Newton equations from the Lagrangian of a system of particles
  • Importance of the Lagrange formulation of physics
  • Lagrangian and coordinate changes
  • Rotating frame, centrifugal and Coriolis forces
  • Polar coordinates and angular momentum conservation
  • Lagrangian, conservation and cyclic coordinates
References