Newton's laws, principle of least action

Classical Mechanics (Fall, 2007)

Lecture Playlist

  1. State diagrams and the nature of physical laws

  2. Newton's laws, principle of least action

  3. Euler-Lagrange equations, symmetry and conservation laws

  4. Symmetry and conservation Laws

  5. Lagrangians and Hamiltonians

  6. Hamilton's equations

  7. Liouville’s theorem

  8. Motion in an electromagnetic field

  9. Poisson brackets formulation

October 22, 2007

Consider Newton's law relating force and acceleration. Define kinetic energy and potential energy. Derive conservation of energy for a system of particles. Define the Lagrangian and derive the Principle of Least Action starting from Newton's Law. Newton's Law is local, but the Principle of Least Action is global.

Topics: 
  • Force and acceleration
  • Newton's second law
  • Kinetic energy and potential energy
  • Momentum and Newton's 2nd law
  • Definition of the Lagrangian
  • Definition of the action
  • Principle of least action
  • Phase space
  • Newton's three laws
  • Conservation of energy and momentum for an isolated system of particles
References