Physics 419: Theoretical Mechanics

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Final Exam solutions now available in postscript and pdf.

Short Description

Classical mechanics, or dynamics, is the science of motion and it is fundamental to all of modern physics. In this course we will study some famous and amusing problems. We will recast Newton's mechanics in languages (Lagrangian and Hamiltonian) which are not only practical for many problems but allow the methods and ideas of mechanics to be extended into every corner of physics. Though foundational, dynamics is not petrified. The study of chaotic dynamics is a thriving research field today. Unfortunately, there is only so much time, and not everything which belongs to mechanics can be studied in this course. It will be possible to look at chaos only briefly. We will not study fluid and continuum mechanics, nor relativistic mechanics at all.

Short Outline

  1. Review of the Basic Principles: Newtonian mechanics for one or many particles
  2. Lagrangian Formulation of Classical Mechanics
  3. Linear Oscillators: one degree-of-freedom
  4. One Degree-of-Freedom Systems, Central Forces and the Kepler Problem
  5. Small Vibrations
  6. Hamiltonian dynamics
  7. Chaotic and nonchaotic motion
  8. Mechanics in Accelerated Reference Frames
  9. Rigid Body Dynamics