Syllabus for Math 8520 --- Spring 2004
Classical mechanics has always been a source of interesting dynamics problems.
Many ideas in dynamical systems theory (and the rest of mathematics, for that matter) were first
developed in an attempt to understand the Newtonian n-body problem or the motion of a rigid body.
I will try to present the theory in a modern style and illustrate it with concrete
examples. Topics will include as many of the following as time permits:
|Newtonian and Lagrangian mechanics, calculus of variations|
|Hamiltonian mechanics, symplectic structures, Liouville's theorem|
|Symmetry, Noether's theorem, reduction|
|Equilibrium points, Birkhoff normal form|
|Nonintegrability and chaos|
Mathematical Methods of Classical Mechanics (2nd edition)
, by V.I. Arnold. This is one of the two classic mathematics texts
in the subject, the other being "Foundations of Mechanics", by Abraham and Marsden.
Which one you prefer can be viewed as a test of your mathematical tastes --- intuitive or
formal. They actually complement one another nicely. In any case Arnold's book is a
source of inspiration for anyone interested in mechanics. I will try to maintain its spirit.
|"Foundations of Mechanics", by Abraham and Marsden|
|"Introduction to Mechanics and Symmetry", by Marsden and Ratiu|
|"Math. Aspects of Classical and Celestial Mechanics", by Arnold, Koslov and Neistadt|
|"Lectures onCelestial Mechanics", by Siegel and Moser|