From: sramjee@hss.hns.com
Date: Mon Aug 28 2000 - 01:13:06 PDT
"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 Poincar
é 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"
"Structure and Interpretation of Classical Mechanics" - a draft version is
available at:
http://www-swiss.ai.mit.edu/~gjs/6946/book.pdf
I wish I had this kinda book with me when I did those olde classical mech
courses in the early eighties... And, I thought everything that Jerry had
to say
to the world was over with SICP! What a relief! :-)
__ramjee.
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