Caltech California Institute of Technology

Caltech Division of Physics, Mathematics and Astronomy

Physics 106a - Topics in Classical Physics, Sep-Dec 2018.

Physics 106a is a 10-week intermediate course in the application of basic principles of classical physics to a wide variety of subjects.
The first half of Ph106b will continue with classical physics and special relativity. The second half, continuing through Ph106c, will cover topics in Electromagnetism.

This website is: (pdf)


Please watch this space for announcements regarding Ph 106a; things like rescheduling of lectures, typos in assignments, etc. It is your responsibility to keep up to date with the course information.

Ph 2 ab or Ph 12 abc, Ma 2.

Tuesdays and Thursdays, 10:30-11:55, 103 Downs.
Any changes will be announced well in advance. Please arrive on time!

Instructor: Prof. Alan J. Weinstein
Office: 354A West Bridge; Mail Code: 100-36; Phone: x2166; E-mail: ajw AT

Teaching assistants:

Textbook for Phys 106a:
Analytical Mechanics by L.N. Hand and J.D. Finch, Cambridge University Press (1998) (on amazon).

Much of the structure, pacing, notation, etc. is taken from this text. It is far from perfect: it doesn't have a review of elementary Newtonian mechanics; it has typos; many people think the explanations are often unclear. Looking at other texts can always help.

Recommended texts: On reserve at Fairchild Library. Use these texts for alternate explanations or for additional problems or examples.
  • Classical Mechanics by Goldstein, Poole, and Safko (3rd edition): This is a classic textbook (I was taught the subject using an earlier edition, back in the 70s).
  • Classical Mechanics by John Taylor: a nice book, with more review of the basics than Hand and Finch, but slightly less advanced than the level of the class; it will need supplementing with other reading in a few places.
  • Mechanics by Landau and Lifshitz: classic but terse.
  • Classical Dynamics of Particles and Systems by Thornton and Marion: not as advanced as class text, and does not cover all the material, but good supplement if you find the jump from earlier classes to Ph106 too large.

Approximately 50% problem sets, 15% midterm, 35% final exam.

Problem Sets:

Midterm and final exams during appropriate weeks of the term (5th and 10th). Both will be take-home and "limited" open-book (only the text and class notes allowed); see Honor Code section below. The final exam will be comprehensive.


Honor Code and Collaboration policy:

I greatly appreciate student feedback; feedback prior to the end-of-term TQFR evaluations lets me modify the class to fit your needs. If you want to send an anonymous comment about the course to me, click here.
I also welcome any comments in person, by email to ajw AT, by campus mail, whatever you like.

Lecture schedule and reading, fall term:

Week (Tuesday) Tuesday Lecture Thursday Lecture Assignment
(by Friday PM)
October 2
1. Review of Newtonian Mechanics
Reading: Notes; HF §1.1; T Chs. 1,3,4; GPS §1.1-2
Your favorite elementary mechanics text
2. Variational Approach
Reading: Notes; HF §2.1-5; T Ch6, §7.1-2
Assignment 1,
due next Friday.
October 9
3. The Lagrangian
Reading: Notes
4. Constraints, Virtual Work...
Reading: Notes; HF §2.6-9; T §7.3-9
Assignment 2
A1 Solutions
October 16
5. Variational Approach with Constraints
Reading: Notes; HF §2.6-9; T §7.3-10
6. Equilibria and Oscillations I
Reading: Notes; HF Ch 3; T Ch 7
Assignment 3
A2 Solutions
October 23
7. Equilibria and Oscillations II
Reading: Notes; HF §4.1-6; T §8.1-6
8. Central Forces: Bound States
Reading: Notes; HF §4.7; T §8.7, Ch 14
Midterm Exam
A3 Solutions
October 30
9. Central Forces: Scattering States
Reading: Notes; HF §5.1-5; T §13.1-6
10. Hamiltonian Dynamics I
Reading: Notes; HF §5.6-8, Appendices; T §13.7
Assignment 4
Midterm Solutions
November 6
11. Hamiltonian Dynamics II
Reading: Notes; HF Ch 6 §1-3,5, Appendix
12: Canonical Transformations
Reading: Notes; HF Ch 6 §4,5
Assignment 5
A4 Solutions
November 13
13. Hamiltonian-Jacobi Theory
Reading: Notes; HF §7.1-4
14. Rotations
Reading: Notes; HF §7.7-10; T Ch 9
Assignment 6
A5 Solutions
November 20
15. Rotating Frames
Reading: Notes; HF §8.1-4,12, App A,B; T §10.1-8
No class: Thanksgiving
No Assignment
November 27
16. Dynamics of Rigid Bodies I
Reading: Notes; HF §8.6-8,10-11, App C; T §10.9-10
17. Dynamics of Rigid Bodies II
Reading: Notes; Euler Disk movie, paper
Assignment 7
A6 Solutions
December 4
18. Dynamics of Rigid Bodies: Examples
Reading: Notes; HF Ch 9; T Ch 11.
19. Normal Modes
Reading: Notes; Notebook; HF §9.7; T §16.1-11
Final exam
A7 Solutions
December 11
No class. Optional reading:
20. Normal Modes, continuum limit
Reading: Notes; HF Ch 9; T Ch 11.
Chladni plate movies: square, Violin
No class
Final Exam Solutions

Acknowledgements: Most of the lecture notes and problem sets / solutions for this class were developed by Prof. Michael Cross. Many thanks to him!

Last Updated: Oct 5, 2018
Alan Weinstein/ajw AT