## Graduate course *Classical Mechanics*

A graduate course in classical mechanics will be
given by the Division of Mechanics during late spring
and early autumn 2011, as detailed below. *Note:*This course has now finished. There are as yet no plans for when it will be given next time.

## Teacher

Lars Johansson## Course start

April 11 2011 at 13.15 in A35.## Lecture plan

### Rigid body dynamics

*Literature:*
Principia Scholium, Axioms.

*Literature:* Baruh 2.3, 2.4, 7.3.

*Literature:* Baruh 2.5, 2.6, 7.4.

*Literature:* Baruh 2.7, 2.8.

*Literature:* Baruh 3.2, 3.3, 8.5.

*Literature:* Baruh 6.3, 6.4, 6.5, 8.2, 8.3.

*Literature:* Baruh 7.5.

*Literature:* Baruh 7.7.

### Analytical mechanics

*Literature:* Baruh derives Lagrange's
equations from Hamilton's principle in chapter 4. We will do it
the other way around, but study sec. 4.2-4.3 on constraints for
this lecture.

*Literature:* Baruh 8.9, 8.10.

*Literature:* Baruh 7.9, 5.8.

*Literature:* Lecture notes.

*Literature:* Baruh 5.8, 5.11.

*Literature:* Baruh 4.4, 4.5, 4.7, 4.9.

*Literature:* Baruh 5.13.

*Literature:* Baruh 8.11.

## Course contents

*Rigid body dynamics:*Newton's equations of motion, Coriolis' equation, The strap-down equations, The equations of motion for a system of particles and for a rigid body, The moment of momentum, The Euler angles, The Euler parameters.

*Analytical mechanics:*
Lagrange's equations of motion, Classical calculus of variations,
Hamilton's principle, Principle of virtual work, Jourdain's
principle.

## Organization

About 20 lectures of 2 hours.## Course credits

9 hp.## Examination

*First part*Three computer assignments in rigid body dynamics, marked with a maximum of 3, 4 and 5 points respectively.

*Second part* Written exam in analytical mechanics.
Three questions marked with a maximum of 4 points each.

A minimum score of 5 points for each part *or*
12 points total with at least 3 points for each part is required.

## Literature

Literature selection is somewhat difficult; there is a wealth of literature, but many authors are much concerned either with laying the foundations for quantum mechanics or with the "multi" aspects of multi-body dynamics.It is suggested to select one of the following alternatives:

- Haim Baruh
*Analytical Dynamics*. Unique in its coverage but sometimes difficult to read. Out of print, but reasonably easy to find at internet bookshops. This is the main alternative. - Herbert Goldstein
*Classical Mechanics*, chapters 1, 2, 4, 5, 8.1, 8.2, combined with Francis C. Moon*Applied Dynamics*, chapters 4, 5. - Careful note-taking at lectures combined with supplementary
material. The following list of suggested supplementary reading
will hopefully grow longer:
- Read chapters 3, 4, and app. A of prof. Durham's flight dynamics book. (As an alternative, go to prof. Nikravesh' course homepage. Select "Reading Assignments" and read the material for lessons 7, 8, 9 and 10. Then, select "Textbook" and read chapters 6 and 15.)
- Hui Cheng & K.C. Gupta, An Historical Note on Finite Rotations,
*Journal of Applied Mechanics*, 56 (1989) 139-145. - Go to prof. Hanno Essen's
course homepage and download
*The Theory of Lagrange's Method*. Read chapters 1-19. (As an alternative, go to the library and find any book that covers Lagrange's equations and Hamiltons's equations.) - A writeup on the calculus of variations by prof. Alan Cairns is found here.
- T.R. Kane & C.F. Wang, On the Derivation of Equations
of Motion,
*J. Soc. Indust. Appl. Math.*, 13 (1965) 487-492.