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
Integrable systems
Equilibrium points, Birkhoff normal form
KAM theorem
Nonintegrability and chaos
Variational methods


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.


Homework 100 %

Reserve Books:

"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

Mathematica Notebooks:

Lissajous Figures
Central Force Plots