PHY 411: Classical Mechanics & Chaotic Dynamics
(Fall 2023)
Instructor: Alice Quillen, Bausch and Lomb Hall 424, Phone:275-9625, Email:alice.quillen at rochester.edu
There is no TA, TI or grader.
Lectures:
MW 2:00-3:15pm in Gavett 310
Note: First lecture is Wednesday Aug 30 2023 at 2:00pm;
we will have an organizational meeting!
Overview:
Topics covered will include:
Lagrangian and Hamiltonian dynamics, canonical transformations, Hamilton-Jacobi equations, chaotic dynamics, periodic orbits, stable and unstable orbits, resonances in celestial mechanics, resonance capture, resonance overlap criterion, bifurcations, Julia and Fatou sets, convergence of Newton's Iteration, KAM theory, non-holonomic mechanics,
discrete dynamical systems, infinite dimensional Hamiltonian models,
classical field theory.
Quantum ergodicity and Quantum chaos. Wigner/Weyl transformations and ways to quantize classical systems.
The quantized rotor kicked rotor.
We will explore these topics analytically and possibly numerically (in python).
Prerequisite:
A good knowledge of classical mechanics. PHY235 is more than enough.
Undergraduates are very welcome to join this class (including for the entire class
not just the first 8 weeks).
Course requirements:
- About 6 problem sets
- 1 project
Grading: problem sets 60%, projects 40%, no exams.
Webite:
http://astro.pas.rochester.edu/~aquillen/phy411/
Lecture notes and problem sets will be posted on this website, not on blackboard.
Policies:
Collaboration is encouraged. However, you should write your own solutions to problems and write your own reports.
Reading material:
I will be sharing research papers and chapters of some books electronically.
The link for these is available on blackboard. If you are auditing or are not yet enrolled in the class, send me an email and I will share the link.
I will be happy to share literature with the class that students find interesting!
References:
- Mathematical Methods of Classical Mechanics , by V. I. Arnold, QA805 .A6813 1989
- Nonlinear Dynamics and Chaos, with Applications to physics, biology, chemistry,
and engineering by Steven H. Strogatz Q172.5.C45 S767 1994
- A first course in Discrete Dynamical Systems
by Richard A. Holmgren QA614.8 .H65 1994
- The Transition to Chaos, Conservative Classical and Quantum Systems
by Linda Reichl
- Stability and Chaos in Celestial Mechanics by Allesandra Celleti
- Advanced Mechanics, From Euler's Determinism to Arnold's Chaos by S. G. Rajeev
- The Chaos Book