\ UCSC Physics 210 "Graduate Classical Mechanics" (Fall 2016)
UC Santa CruzUC Santa Cruz Department of Physics
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Physics 210 (Fall 2016): Graduate Classical Mechanics

Course information

Instructor: Stefano Profumo
Office: ISB, Room 325
Phone Number: 831-459-3039
Office Hours: Thursday 12:30PM - 1:30PM, or by appointment
E-mail: profumo AT ucsc.edu

Click here to download the syllabus in PDF format

Class Hours

Lecture Times: Wednesdays and Fridays, 3:20 PM - 4:55 PM
Lecture Location: ISB 235

new!!! The following classes are canceled: W Sept 28, F Sep 30, F Oct 14, F Nov 18, F Dec 2. Lectures are rescheduled for M Oct 3, M Oct 10, M Oct 17, M Oct 24, M Nov 21, ISB 235, 9:45 -11:20 AM.

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:

Recommended Textbook

Other Textbooks

Note: the Relevant Library Sections are QA805 and QC125

Course Outline

Lect. Topic Reading (Goldstein+P+S; *: Soper)
1 Preliminary remarks; Lagrangian formalism 1.1-1.4
2 Lagrangian methods: examples; Hamilton's principle 1.5-1.6; 2.1
3 Calculus of variations; Hamilton's principle with constraints 2.2-2.5
4 Symmetries and conservation laws 2.6-2.7
5 Central force problem; Closed orbits; Virial theorem 3.1-3.7
6 Scattering in a central force field 3.10-3.11
7 Lenz vector; Three-body problem; Numerical methods 3.9; 3.12
8 Coordinate transformations; Euler angles 4.1-4.5
9 Infinitesimal and finite rotations; Coriolis effect 4.6-4.10
10 Inertia tensor; Rigid-body motion 5.1-5.6
11 Small oscillations and related examples 6.1-6.4
12 Legendre transformation and Hamilton equations of motion 8.1-8.2; 8.4
13 Principle of least action; Canonical transformations 8.5-8.6; 9.1-9.2
14 Canonical transformations: examples; Poisson brackets 9.3-9.7
15 Symmetry groups; Liouville's theorem; Hamilton-Jacobi theory 9.8-9.9; 10.1-10.2
16 Hamilton Jacobi theory and applications 10.3-10.6
17 Fields and transformation laws; stationary action and fields 1*, 2*
18 Classical field theory; the electromagnetic field 3*, 8*
19 Further general properties of Field Theories 9*
19 Course Review

Course Grading and Requirements

There will be four homework sets. Each one of the homework sets will count 10% towards the final evaluation. There will be one midterm exam, scheduled for Wednesday November 9, 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", in December.

Homework exercises

Homework Set number (PDF) Due Date Solutions
HW Set #1 phys210_HW01.pdf Friday 10/14 HW1_solutions.pdf
HW Set #2 phys210_HW02.pdf Friday 10/28 HW2 Solutions (by John Tamanas)
Midterm phys210_midterm.pdf Wednesday 11/9 Midterm Solutions
HW Set #3 phys210_HW03.pdf Monday November 21 phys210_HW3_sol.pdf and Hanwen's solutions
HW Set #4 phys210_HW04.pdf Thursday December 8, 11AM, ISB 235 (final exam) Hanwen's solutions
Final phys210_final.pdf Thursday December 8 Final Solutions

A proof of Bertrand's Theorem
A proof of Chasles' theorem
An alternate proof of Chasles' theorem

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.