Caltech California Institute of Technology

Caltech Division of Physics, Mathematics and Astronomy

Physics 106b - Topics in Classical Physics, Jan-Mar 2018.

Physics 106b is a 10-week intermediate course in the application of basic principles of classical physics to a wide variety of subjects.
The first half (taught by Prof. Weinstein) will continue the study of Classical Mechanics started in Ph 106a, including special relativity, parametric resonance, Hamiltonian Chaos, Dissipative Systems.
The second half (taught by Prof. Golwala) will begin the study of Electromagnetism, to be continued in Ph106c: boundary-value problems, multipole expansions, and various applications of electromagnetic theory.

This website is:
The website for Ph106a (Fall 2017) is:
The website for the second half of Ph 106b (Winter 2017) and Ph106c is:


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

Ph106a. Ph 2 ab or Ph 12 abc, Ma 2.

Tuesdays and Thursdays, 10:30-11:55, 107 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
I do not have regular office hours; email me!

Teaching assistants:

Textbook for Phys 106b:
Analytical Mechanics by L.N. Hand and J.D. Finch, Cambridge University Press (1998) (on amazon).
In the first half of Ph106b I will largely be following the chapters 10-12 of Hand and Finch, with some additions, subtractions, and reorderings.
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 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.
  • 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).
  • 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.
  • Spacetime Physics by Taylor and Wheeler.
  • Nonlinear Dynamics And Chaos by Strogatz.

See the Announcement section above for how Ph106b is being divided up.

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
January 2
No Lecture. Happy New Year!
Reading: HF §12.1-5; T §15.1-7
1. Relativity I: Introduction, Lorentz transform
Reading: Notes; HF §12.1-5, T§15.1-7
No assignment
(TA: )
January 9
2. Relativity II: Geometric approach, 4-vectors
Reading: Notes; HF §12.11-12; T §15.7-11
3. Relativity III: Mechanics
Reading: Notes; HF §12.6-10,12.14-18; T §15.12-16
Assignment 1
January 16
4. Relativity IV: Relativistic force, Lagrangians, E&M
Reading: Notes; HF §12.13, T §15.17-18
5. Relativity V: Geometry of Relativity, Lorentz transforms
Reading: Notes; HF §12.11-12.18
Assignment 2
A1 Solutions
January 23
6. Nonlinear oscillators, perturbation theory
Reading: Notes; Supplement; Duffing.nb; HF Ch. 10
7. Hamiltonian Chaos I
Reading: Notes; Sims: see below; HF §6.6-7, §11.1-4
Assignment 3
A2 Solutions
January 30
8. Hamiltonian Chaos II
Reading: Notes; HF §11.5-9,11.13
9. Dissipative Dynamical Systems
Reading: Notes; Sims: see below; HF §11.10-12; T Ch 12
Midterm Exam
A3 Solutions
Midterm Solutions
February 6
11. Electromagnetism
12. Electromagnetism

Chaos demos:

  • DoublePendulumModes.nb Mathematica notebook
  • Double pendulum, html-based, from myphysicslab
  • Double Pendulum With Poincare Map Model, java-based, from Open Source Physics
  • Some example Poincare maps from the above model, pdf
  • Double pendulum, html-based, from
  • Double Pendulum Exercises, from Chris Meyers, Cornell
  • "Dynamics of a double pendulum with distributed mass", pdf
  • First draft of an ipython notebook for the Kicked Rotor Standard Iterative Map
  • ipython notebook for the Damped Driven Pendulum Iterative Map

    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: Feb 3, 2018
    Alan Weinstein/ajw AT