Classical Mechanics a Computational Approach

Taken from MIT.

MASSACHVSETTS INSTITVTE OF TECHNOLOGY

	Joint Subject Offering: 6.946J, 8.351J, 12.620J, 12.008
	Classical Mechanics:
	A Computational Approach
	href="http://swiss.csail.mit.edu/users/wisdom/"
	Jack Wisdom,
	href="http://groups.csail.mit.edu/mac/users/gjs/"
	Gerald Jay Sussman
	We will study the fundamental principles of classical mechanics, with
	a modern emphasis on the qualitative structure of phase space. We
	will use computational ideas to formulate the principles of mechanics
	precisely. Expression in a computational framework encourages clear
	thinking and active exploration.
	We will consider the following topics: The Lagrangian formulation.
	Action, variational principles, and equations of motion. Hamilton's
	principle. Conserved quantities. Rigid bodies and tops. Hamiltonian
	formulation and canonical equations. Surfaces of section. Chaos.
	Canonical transformations and generating functions. Liouville's
	theorem and Poincaré integral invariants. Poincaré-Birkhoff and
	KAM theorems. Invariant curves and cantori. Nonlinear resonances.
	Resonance overlap and transition to chaos. Properties of chaotic
	motion.
	Ideas will be illustrated and supported with physical examples. We
	will make extensive use of computing to capture methods, for
	simulation, and for symbolic analysis.
	This subject awards H-LEVEL Graduate Credit, however the subject
	is appropriate for undergraduates who have taken the prerequisites.
	Undergraduates are welcome.
	Prerequisites: 8.01, 18.03, programming experience
	Lectures: MWF at 11 AM in room 54-317.
	Computer Lab: Wednesday evenings, 7--10 PM, Room 14-0637.
	Units: 3-3-6
	href="http://mitpress.mit.edu/book-home.tcl?isbn=0262194554"
	MIT Press Mechanics Book
	href="http://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/index.html"
	Mechanics Book (HTML)
	href="http://groups.csail.mit.edu/mac/users/gjs/6946/errata.txt"
	Errata for Mechanics Book
	href="http://mitpress.mit.edu/sicp/full-text/book/book.html"
	Structure and Interpretation of Computer Programs (HTML)
	href="http://groups.csail.mit.edu/mac/users/gjs/6946/red-tape.pdf"
	Red Tape Memo
	href="http://groups.csail.mit.edu/mac/users/gjs/6946/assignments.html"
	Assignments
	href="http://groups.csail.mit.edu/mac/users/gjs/6946/beginner.ps"
	Beginner notes
	href="http://groups.csail.mit.edu/mac/users/gjs/6946/refman.ps"
	Scmutils manual
	href="http://groups.csail.mit.edu/mac/users/gjs/6946/graphing.ps"
	Graphing notes
	href="calculus.pdf"
	Supplementary notes on Differential Geometry
	href="calculus" Experimental Software for Differential Geometry
	href="poincare-lecture.pdf" Notes on the Poincare equations lecture
	href="poincare.pdf" Notes on the Poincare equations
	href="henon_anim.gif" Animation of motion of islands in Henon map (Courtesy of Alex Schwendner)
	We will provide access to computers that run our software.
	If you want to install the software on your personal computers
	see href="http://groups.csail.mit.edu/mac/users/gjs/6946/linux-install.htm"   here.