Physics 505 Classical Mechanics
Fall Semester 2009

 
Note: Below is a preliminary list of topics that may change during the course of the semesters. "Chapters" refer to class notes rather than to the text.

Chapter 1: Mechanics Preliminaries & basic concepts

  1. Mechanics of a particle & system of particles
  2. Constraints
  3. D'Alemberts principle & Lagrange's Equations
  4. Applications of Lagrangians

Chapter 2: Calculus of Variations

  1. Hamilton's principle
  2. Lagrange multipliers
  3. Conservation laws & symmetries: Noether's theorem
    1. Conservation of momentum
    2. Conservation of angular momentum
    3. Conservation of energy

Chapter 3: Central Force Problems

  1. Reduction to equivalent 1 body problem
  2. constants of motion (aka first integrals)
  3. orbits
    1. equations of orbits (including differential equation for orbits)
    2. shape of orbits (conic sections)
    3. turning points
    4. period (and frequency) of oscillation
  4. Kepler's problem
  5. scattering
    1. scattering angle
    2. impact parameter
    3. cross-section

Chapter 4: Rigid Bodies

  1. Mathematical Preliminaries
  2. Moments of inertia, principal moments of inertia & inertia tensor
  3. Lagrangian of rigid bodies (i.e., kinetic and potential energy expressions)
  4. Torque

Chapter 5: Small Oscillations

  1. equilibrium positions (stable vs. unstable)
  2. characteristic equations
  3. eigenfrequencies and polarization vectors

Chapter 6: Hamiltonians

  1. Relation between Lagrangian and Hamiltonian (obtaining H from L)
  2. Hamiltonian as a function of q, p (not q, dq/dt)
  3. Hamilton equations of motion

Chapter 7: Canonical transformations

Text

The official text for the course is Mechanics 3rd Edition, Course of Theoretical Physics Volume 1 by Landau and Lifshitz.
 
  Another popular text is Classical Mechanics 3rd Edition by Goldstein, Poole & Safko.
 
  Another book that I recently came across that also looks good is Classical Mechanics by John Michael Finn. This book intrigues me because it contains a more through mathematical treatment in the first few chapters.
 
  Choose whichever of these books you like best! The course notes tend to follow Goldstein in the beginning, while leaning more toward Landau and Lifshitz as the course progresses. The homework will be independent of text, and the notes should be reasonably self-contained. Goldstein tends to have longer, more colloquial explanations; L&L is concise and to the point. Choose whichever suits you (there has never been a consensus as to which students like better).
 

Problem Assignments and Exam Dates


  Problem Assignment 1 due 9/04/09 ( PDF )
  Problem Assignment 2 due 09/11/09 ( PDF )
  Problem Assignment 3 due 09/18/09 ( PDF )
  Exam 1 Sept. 25, 2009 Exam 1 Study Guide
  Problem Assignment 4 due 10/02/09 ( PDF )
  Problem Assignment 5 due 10/09/09 ( PDF )
  Problem Assignment 6 due 10/21/09 *WEDNESDAY* ( PDF )
  Problem Assignment 7 due 10/30/09 ( PDF )
  Problem Assignment 8 due 11/06/09 ( PDF )
  Exam 2 November 13, 2009 Exam 2 Study Guide
  Problem Assignment 9 due 11/25/09 *WEDNESDAY* ( PDF )
 
 
  Homework is due in class. If I receive it before I leave on the due date, there will be no penalty. I may leave before 5:00 PM, so it is your responsibility to make sure it is on time. If I receive it the next business day, there will be a 5 point penalty. Homework more that a week late will be assigned a zero.
 
  Homework due dates and exam dates are subject to change.

Grading

Problem Assignments 25%
Exam 1 25%
Exam 2 25%
Final Exam 25%