SI2360 Analytical Mechanics and Classical Field Theory 7.5 hp

WRITTEN EXAMINATION 2009-05-19, 14-19, FB53-55

In addition there is an oral examination after the written exam.

In 2009 the course will not be lectured at KTH. Instead we recommend the Stockholm University course FK8001 with start Monday Jan 19 at 10.15 in FB41: follow this link for information. Alternatively you can study the course as a reading course using last years course material. In any case you need to contact Mats and register for the course.

The rest of the page refers to the course given in 2008:

Oral examination
To set up a time for the required oral examination send me an email. It takes about 30 minutes and focuses on theory questions from the lecture notes.

Information

First lecture Spring 2008: Wednesday Jan 23, 13:00-15:00, in room FB51 in AlbaNova. Welcome!
Course homepage: http://courses.theophys.kth.se/SI2360
Course homepage 2007: http://courses.theophys.kth.se/5A1383
Credits: 7.5 ECTS points.
Course format: The course consists of 15 lectures (30 h). There will be no exercise classes. Selected problems and solutions will be provided and discussed at the lectures.
Language: English
Updates: News, updated information, and course material is posted on the web page. Check regularly!
Course material download page Username=student. The password is provided at the lectures.

Aims

After the course you should be able to:

Formulate mechanics problems using the formalisms of analytical mechanics.
Solve mechanics problems using the methods introduced in the course.
Formulate the connection between classical mechanics and quantum mechanics.

Content

This is an advanced course on classical physics, including mechanics and classical field theory. The course develops basic theoretical skills and understanding that form a necessary preparation to many modern developments of theoretical physics. In particular it gives the background to appreciate the transtion to quantum mechanics. The aim is to give a good working knowledge of the formalisms of Lagrange and Hamilton and their applications in classical (i.e. non-quantized) non-relativistic and relativistic systems. The course should be useful to all theoretically interested students in physics and other related areas.

Topics

Review of elementary Newtonian mechanics: Newton's laws, Galilei transformations, conservation laws, accelerated reference systems, etc.
Principles of canonical mechanics: Lagrange and Hamilton formalism, canonical transformations, Hamilton-Jacobi equations, etc.
The mechanics of rigid bodies
Relativistic mechanics
Continuous systems: introduction to classical field theory
many examples

Prerequisites

Introductory mechanics and engineering mathematics courses.

Course literature

There is no course book, but the following material is recommended:

Tong: David Tong, Lectures on Classical Dynamics
FW: A. L. Fetter and J. D. Walecka, Theoretical Mechanics of Particles and Continua, McGraw-Hill 1980. Effective introduction to analytical mechanics and classical field theory.
LL: E. M. Lifshitz, L. D. Landau, Mechanics (Course of Theoretical Physics), Butterworth-Heinemann (1982). A classic.
G: H. Goldstein, C. P. Poole, and J. L. Safko, Classical Mechanics, 3rd ed., Addison-Wesley (2002). A classic textbook.
A: V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer (1997). Advanced more mathematical presentation.
JS: J. V. Jose´ and E. J. Saletan, Classical Dynamics - A Contemporary Approach, Cambridge (2002). Modern textbook with several examples.
S: F. Scheck, Mechanics. From Newton's laws to deterministic chaos. Springer (1999).

Lectures

Prof Mats Wallin, Room A4:1078 in AlbaNova, Email: , Phone: 08-5537 8715

Course requirements and examination

Written examination: May 29, in room FB53, time 8.00-13.00

Written August Examination Friday 29/8 time 8.00-13.00 in classroom FB51.

1. Volunatry homework will be given throughout the course, that gives bonus points on the written examination.
2. A written examination will take place in the end of May.
3. An oral examination on theory questions.
Rules for homework:
Homework sets are posted on the download page.
Some collaboration is allowed, but you must solve, formulate and write your solutions individually.

Time and place

Time: Wednesdays at 13.15-15.00
Place: FB51

Lecture plan

LECTURE	CONTENT	LITERATURE (Reference+chapter number)
1. Jan 23	Newtonian mechanics	FW 1
2. Jan 30	Kepler problem	FW 1
3. Feb 6	Lagrangian dynamics	FW 3
4. Feb 13	Lagrangian dynamics	FW 3
5. Feb 20	Hamiltonian dynamics	FW 6
6. March 5	Hamiltonian dynamics	FW 6
7. March 26	Small oscillations	FW 4
8. April 2	Rigid bodies	FW 5
9. April 9	The spinning top	FW 5
10. April 16	Canonical transformations	FW 6, G 9
11. April 23	Hamilton-Jacobi theory, transition to quantum mechanics	FW 6, G 10
12. April 30	Classical field theory	JS 9
13. May 7	Classical field theory	JS 9
14. May 13	Fluid dynamics	JS 9

Mats Wallin