PHYS3002

Classical Mechanics Segment

Lecturer: Bob Dewar
Department of Theoretical Physics
Room 427, Olipant Building (Bldg. 60)
Tel. 6125 2949, Fax 6125 4676

This is the home page for a short course of about a dozen lectures offered in Third Year in the Department of Physics at The Australian National University.

Some previous exams: Exam2001.pdf, Exam2000.pdf, Exam99.pdf, Exam98.pdf

Current course: Second Semester 2006, 9am Tuesdays, Thursdays and Fridays in PSYC G8 till August 11.

Slides from lecture (to print from Acrobat try CMD-P on a Mac or CTL-P on a PC):

Lecture 1, Tuesday July 17 2006 (PDF)

Useful links:

Version 1.51 of lecture notes (20 May 2001: 813 KByte pdf file, 2.3 MByte Postscript file*)
* you will probably need to have the Type 1 Postscript Computer Modern fonts installed in your system to read or print this postscript file (PDF file is OK because it embeds these fonts).

Maple example worksheets mentioned in notes:

(These are the source of the workbooks printouts in Chapter 5: ANSWERS TO PROBLEMS. To view and run using xmaple, you can download a copy of the worksheet file by clicking on one of the links below and saving the source to your home directory):

• Problems in Chapters 2.8.2 and 3.5.2: Anharmonic oscillator
• Problem in Chapter 4.7.2: Difference approximation to harmonic oscillator equation of motion
• Poincare examples discussed in Lecture 12

Historical sketches

• Leonhard Euler (1707-1783)
• Joseph-Louis Lagrange (1736-1813)
• Sir William Rowan Hamilton (1805-1865)
• Amalie Emmy Noether (1882-1935)

Nonlinear Dynamics Links

• Physics Summer School at ANU January 2002 : DYNAMICSUMMER (after getting the CTP home page, click on CTP Summer Schools in the Information menu on the left, then click on the link at the top of the main panel on the right)
• Visualization projects (Honours or 3rd Year Special Topics)
  • 4-D symplectic maps
  • Singularity theory
• Mac Application available for download
  The Macintosh application MiniFlux used in the last lecture to discuss the Standard Map is available by anonymous ftp from the directory /pub/software/MiniFlux/ on nctp.anu.edu.au or by using the link below. The version for a PowerPC Mac is MiniFlux_PPC_9+1+1+1.bin, which uses a nine-mode trial function to construct approximate KAM curves. If you need a version for a 68000 series Mac with arithmetic coprocessor, contact Robert Dewar.
  • MiniFlux_PPC_9+1+1+1.bin
• Web site for Brian Davies' Exploring Chaos book (1 D dissipative dynamical systems - with Java applets providing interactive graphics)

Course description

Classical mechanics is the abstraction and generalisation of Newton's laws of motion undertaken, historically, by Lagrange and Hamilton. Hamiltonian and Lagrangian approaches form the starting points for modern quantum mechanics and quantum field theory. Furthermore, the purely classical theory itself has had a strong revival in recent decades due to the upsurge of interest in nonlinear dynamics and chaos due to new mathematical results (such as KAM theory) and new applications to physical systems such as plasmas and lasers, greatly aided by the development of easy-to-use computer simulation and visualisation techniques.

The course will introduce the two main approaches to classical mechanics:
1. the variational formulation (variational calculus, Hamilton's Principle, Euler--Lagrange equations), and
2. the phase space formulation (Hamilton's equations, Poisson brackets, canonical transformations, action-angle variables).

Applications of the formalism to physical problems will be mentioned as appropriate and an exploratory approach using computational physics techniques will be encouraged.

Created on 25 February 1999. Last modified on 17 July 2006.
Please send any comments to Robert Dewar.