Physics 105 - Analytic Mechanics

[shortcut to the homework assignments]

Basic Info

Spring 2003, Tue and Thu, 8:00 - 9:30 a.m., 385 LeConte Hall

Instructor: Petr Horava (email:
Office: 441 Birge (office hours: Thu 10:00 -12:00 noon; usually, you can also find me there on Tue, 10:00 -12:00 noon); 50-5056E LBNL (usually on Mon, Wed, Fri)

Discussion sections: Mon 3 - 4 p.m. 395 LeConte (this is the section originally scheduled for Tue 10 - 11 a.m. 105 Dwinelle), Thu 4 - 5 p.m. B51 Hildebrand
GSI: Keshav Dani
Office: 281 Le Conte, 642-5647 (office hours: Mon 10:00 - 11:00 a.m.)

New/Important Info

NEW (5/21): The final grades have been submitted to bearfacts. All homeworks (including the really late ones) have been graded, and can be collected in front of 441 Birge.

NEW (5/20): The final exam has been graded, you can stop by in 441 Birge to discuss your final exam results (the median score was 16 out of 30). The final grades for the course will be posted on bearfacts on May 21. A few grading rules: If your total performance in this course was 66% or better, you get a straight A; if it was higher than 85%, you get an A+. 30% is the cutoff for a passing grade.

NEW (5/20): All homeworks (with the exception of those coming in after May 13) have been graded. You can pick up all your hw assignments in 441 Birge.

NEW (5/13): list of most important concepts from Chapters 1 - 9 of Hand-Finch can be found here.

The Final Exam took place on Saturday, May 17, 4:30 - 7:30 p.m., in Room 329 LeConte.

Homeworks and Grading Policy

[link to the homework assignments]

Homeworks will be assigned every Thursday (in the form of a pdf file posted on this web site around noon each Thursday), and will be due in 8 days on Friday by 12noon in Keshav's homework box (located in the breezeway between Le Conte and Birge Halls, and labeled "Physics 105, Horava, Spring 2003"). Contrary to some early information, our official grading system is on the scale of 0-10 per problem, with each homework assignment typically containing 5 problems and therefore worth the total of 50 points per assignment. HW I was originally graded on the 0-2 scale; your scores for HW I have now been renormalized to the new 0-10 scale by multiplying the original HW I scores by five.

The penalty for late homework assignments is 25% off for homework that is less than a week late and 50% off for homework that is more than a week late; in addition, there is an absolute cutoff (=0 points afterwards) when the official solution appears on this web site (usually two weeks after the assignment is due).

50% of the final grade will be based on homework assignments,
20% will be based on the single mid-term exam (administered in class at some point before the spring break), and
30% will be based on the final exam.

We will decide on the offical breakdown of percentage versus grade later this semester, and post the official rules in due time (see above).

Textbook Information

[An approximate syllabus, to be refined, can be found here.]

The primary required text that I will be using for the course is

L.N. Hand and J.D. Finch, "Analytical Mechanics" (Cambridge, 1998)
ISBN: 0 521 57572 9 paperback (0 521 57327 0 hardcover)

This text is based on a similarly advanced undergraduate course taught in recent years at Cornell. This book indeed reflects very closely the logic of Analytic Mechanics as I see it. Why didn't you see this text on the original list of required books for the course? Originally, the course was scheduled to be taught by Kam-Biu Luk, who chose

J.B. Marion and S.T. Thornton, "Classical Dynamics of Particles and Systems"(4th Edition, Harcourt Brace, 1995)

as the required text for the course, and

H. Goldstein, "Classical Mechanics" (2nd Edition, Addison-Wesley, 1980)

as recommended. As a compromise, I will use Marion-Thornton as a complementary text throughout the semester, primarily for solved problems and for homework assignments. I leave it up to the individual students to decide whether they should really buy the book. (And I apologize for the late notice!) We will try to make sure that the homework assignments are available to the students via the web site even if they decide not to buy Marion-Thornton.
Goldstein is a classic text that is always a good book to have in your library. If you compare the Table of Contents of Golstein you will find out that its logic is actually quite close to that of Hand-Finch. On the other hand, Goldstein was written in the 50's and it shows...

There are several other textbooks that deserve an honorary mention, and you may want to take a look at them depending on your interests. Let me mention a few:

L.D. Landau and E.M. Lifshitz, "Mechanics" (3rd Edition, Butterworth-Heinemann, 1981)
This is an excellent, very dense and very no-nonsense summary of basic principles of analytic (="theoretical") mechanics. It is also Volume 1 of the famous Landau-Lifshitz encyclopedic series on theoretical physics, demonstrating the unique position of analytic mechanics as the most fundamental building block of all of modern theoretical physics.

J.V. Jose and E.J. Saletan, "Classical Dynamics. A Contemporary Approach" (Cambridge, 1998)
As I will claim repeatedly during this course, the natural language of analytic mechanics is that of modern differential geometry. However, many of the classic textbooks (Goldstein, Landau-Lifshitz, etc) don't really do a good job with the more geometric aspects of mechanics. Jose-Salentan is meant to remedy that problem, and you can think of it as a sort of modern version of Goldstein, with emphasis on geometrical methods and modern geometrical thinking.

R. Talman, "Geometric Mechanics" (John Wiley and Sons, 2000)
Another book stressing the modern geometric aspects of mechanics.

If you are very mathematically oriented, there are also two classic books on the formal geometric aspects of mechanics,
R. Abraham and J.E. Marsden, "Foundations of Mechanics" (Benjamin/Cummins, 1978), and
R. Hermann, "Differential Geometry and the Calculus of Variations" (Academic Pres, 1968).
They are both excellent (although slightly outdated) but I wouldn't recomment them to people who are not serious about abstract differential geometry.

In addition, if you read French or Russian, there is an excellent little book about mathematical aspects of Analytic Mechanics,
C. Godbillon, "Geometrie Differentielle et Mecanique Analytique" (Hermann, Paris, 1969).
(This book was also translated in the 1970's into Russian and published by one of the main Soviet publishing houses in Moscow.)

A really entertaining advanced presentation of mathematical aspects of mechanics can also be found in the modern classic written by Arnold,
V.I. Arnold, "Mathematical Methods of Classical Mechanics" (Springer, 1989).
Of course, this is an English translation of the Russian original, as published originally by Nauka in Moscow in 1989.