Class Notes:
Lecture Notes will be posted here.
- Class Intro
- Review of Newtonian Mechanics
(side note: Ronald Newburgh's article in Phy. Ed. 2001 on varying mass)
- Constraints and Generalized Coordinates, J&S 2.1.1, 2.1.2
- Class Review #2
- Here is a paper on the work energy theorem with variable mass.
- D'Alember Principle and Lagrange Equations
- Examples using Lagrange Equations
- Here is a link on Gauage Invariance from Scholarpedia.
- Calculus of Variations I
- Class Review #3
- Here is link to the "Primer on Index Notation by Prof. John Crimaldi from the University of Colorado Boulder.
- Calculus of Variations II
- Examples with Constraints
- Class Review #4
- Conservation Laws and Symmetry
- Brief Introduction to Dynamical Systems
- A good introductory text for dynamical system is, Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, by Steven Strogatz from Cornell University.
- Class Review #5
- Central Force I
- Central Force II
- Kepler Problems I
- Review notes from Lecture #6
- Here is the article by S. Dutta and S. Ray from Jadavpur University on the bead on a rotating circular hoop problem.
- Kepler Problems II
- RKP Zia et al., "Making Sense of the Legendre Transform", Am. J. Phys., 77, 614 (2009)
- Review notes from Lecture #7
- Hamiltonian
Formalism (Introduction)
- Review notes from Lecture #8
- Canonical Transformation I
- Review notes from Lecture #9
- Canonical Transformation II
- Hamilton-Jacobi Equation
- W.P. Schleich et al., "Schrodinger equation revisited", PNAS, 110, 5374 (2012)This is one of the more recent papers in revisiting the connection between the Hamiltonian Jacobi equation and QM.
- Review notes from Lecture #10
- Small Oscillations
- Small Oscillations Example
- Review notes from Lecture #11
- Rigid Body Motion Introduction
- Review notes from Lecture #12
- Motion in Rotating Reference Frames
- Moments of Inertia
- Review notes from Lecture #13
- Euler's Equations for Rigid Bodies
- Review notes from Lecture #14
- More on Motion of Rigid Bodies