Physics 210 (Fall 2011): Graduate Classical Mechanics

Course information

Instructor: Stefano Profumo
Office: ISB, Room 325
Phone Number: 831-459-3039
Office Hours: Wednesday 2PM - 3:30PM, or by appointment
E-mail: profumo AT scipp.ucsc.edu

Click here to download the syllabus in PDF format

Class Hours

Lecture Times: Mondays, 3:15PM - 5:10PM (incl. 10' break); Wednesdays 3:00PM - 4:55PM (incl. 10' break)
Lecture Location: ISB 231

Course description

This course is a graduate-level introduction to the theoretical techniques of classical mechanics.

Emphasis will be given in particular to those principles and mathematical constructions relevant to modern physics (including quantum mechanics and general relativity), as well as to more classical physical applications.

A list of topics that will be covered in this course includes:

Variational Principles
Lagrangian Formulation
Applications: the Central Force Problem, the Motion of Rigid Bodies, Small Oscillations
Hamiltonian Formulation
Canonical Transformations
Hamilton-Jacobi Theory and Action-Angle Variables
Classical Chaos

Required Textbook

Classical Mechanics, 3rd edition by Goldstein, Poole, and Safko

Other Textbooks

Mathematical Methods of Classical Mechanics by Arnold
Analytical Mechanics by Fasano and Marmi
The Elements of Mechanics by Gallavotti
Theoretical Mechanics by Neal Moore
Classical Mechanics by Barger and Olsson
Mechanics by Landau and Lifshitz

Note: the Relevant Library Sections are QA805 and QC125

Course Outline

Lect.	~ Date	Topic	Reading (Goldstein+P+S)
1	9/26	Preliminary remarks; Lagrangian formalism	1.1-1.4
2	9/28	Lagrangian methods: examples; Hamilton's principle	1.5-1.6; 2.1
3	10/3	Calculus of variations; Hamilton's principle with constraints	2.2-2.5
4	10/5	Symmetries and conservation laws	2.6-2.7
5	10/10	Central force problem; Closed orbits; Virial theorem	3.1-3.7
6	10/12	Scattering in a central force field	3.10-3.11
7	10/17	Lenz vector; Three-body problem; Numerical methods	3.9; 3.12
8	10/19	Coordinate transformations; Euler angles	4.1-4.5
9	10/24	Infinitesimal and finite rotations; Coriolis effect	4.6-4.10
10	10/31	Inertia tensor; Rigid-body motion	5.1-5.6
11	11/2	Small oscillations and related examples	6.1-6.4
12	11/7	Legendre transformation and Hamilton equations of motion	8.1-8.2; 8.4
13	11/9	Principle of least action; Canonical transformations	8.5-8.6; 9.1-9.2
14	11/14	Canonical transformations: examples; Poisson brackets	9.3-9.7
15	11/16	Symmetry groups; Liouville's theorem; Hamilton-Jacobi theory	9.8-9.9; 10.1-10.2
16	11/21	Hamilton Jacobi theory and applications	10.3-10.6
17	11/23	Classical chaos; Attractors	11.1-11.3
18	11/28	Poincare' maps	11.4-11.5
19	11/30	Bifurcations; Logistic equation; Fractals	11.6-11.9

Course Grading and Requirements

There will be four homework sets, handed out on the following dates:

HW#1: handed out on 10/10, due on 10/17
HW#2: handed out on 10/24, due on 10/31
HW#3: handed out on 11/14, due on 11/21
HW#4: handed out on 11/30, due on 12/8

Each one of the homework sets will count 10% towards the final evaluation. There will be one midterm exam, scheduled for Friday October 28, under ``quals'' conditions, which will count 20%. The remaining 40% will be based on your performance in the final exam, also to be held under "quals conditions", scheduled for Thursday, December 8, 12:00--3:00 P.M..

Homework exercises

Homework Set number (PDF) Due Date

HW Set #1 phys210_HW01.pdf Monday 10/17

HW Set #1 - sol. to #2 HW1_sol2.pdf

HW Set #2 phys210_HW02.pdf Monday 10/31

HW Set #3 phys210_HW03.pdf Monday 11/21

HW Set #3 - sol. to #1 HW3_sol1.pdf

HW Set #3 - sol. to #3 HW3_sol3.pdf

HW Set #4 phys210_HW04.pdf Thursday 12/8

Final Solutions phys210_final_solutions.pdf Thursday 12/8

Homework Set number	(PDF)	Due Date
HW Set #1	phys210_HW01.pdf	Monday 10/17
HW Set #1 - sol. to #2	HW1_sol2.pdf
HW Set #2	phys210_HW02.pdf	Monday 10/31
HW Set #3	phys210_HW03.pdf	Monday 11/21
HW Set #3 - sol. to #1	HW3_sol1.pdf
HW Set #3 - sol. to #3	HW3_sol3.pdf
HW Set #4	phys210_HW04.pdf	Thursday 12/8
Final Solutions	phys210_final_solutions.pdf	Thursday 12/8

Links to Classical Chaos Resources

Galileo's Corner

La filosofia e' scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si puo' intendere se prima non s'impara a intender la lingua, e conoscer i caratteri, ne' quali e' scritto. Egli e' scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezzi e' impossibile a intenderne umanamente parola; senza questi e' un aggirarsi vanamente per un oscuro laberinto. (Galileo Galilei, Il Saggiatore, 1623)

Philosophy (Knowledge) is written in that great book which ever lies before our eyes (I call it the Universe), but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word; without knowledge of those, it's a useless wandering in a dark labyrinth.