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

1:st lecture 11/4 at 13.15 in A35: Newton's laws of motion, inertial systems. Literature: Principia Scholium, Axioms.

2:nd lecture 18/4 at 13.15 in A36: geometric vectors, Eulers' theorem. Literature: Baruh 2.3, 2.4, 7.3.

3:rd lecture 27/4 at 13.15 in A37: Coriolis' equation, strap-down equations. Literature: Baruh 2.5, 2.6, 7.4.

4:th lecture 5/5 at 13.15 in A35: Particle motion relative to rotating earth. Literature: Baruh 2.7, 2.8.

5:th lecture 9/5 at 13.15 in IKP3: Equations of motion for a particle system and for a rigid body. Literature: Baruh 3.2, 3.3, 8.5.

6:th lecture 19/5 at 13.15 in A34: The inertia tensor. Literature: Baruh 6.3, 6.4, 6.5, 8.2, 8.3.

7:th lecture 23/5 at 13.15 in A37: The euler angles. Literature: Baruh 7.5.

8:th lecture 27/5 at 10.15 in A33: The euler parameters. Literature: Baruh 7.7.

1:st problem solving demonstration: 16/6 at 13.15 in A32: Kinematics.

2:nd problem solving demonstration: 17/6 at 10.15 in A35: Kinetics.

Analytical mechanics

1:st lecture 5/9 at 13.15 in A36: Lagrange's equations from Newton's second law. 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.

2:nd lecture 13/9 at 10.15 in IKP3: Lagrange's equations for rigid bodies. Literature: Baruh 8.9, 8.10.

3:rd lecture 28/9 at 8.15 in A36: The rolling constraint, generalized momentum, Jacobi's integral. Literature: Baruh 7.9, 5.8.

4:th lecture 5/10 at 8.15 in A36: Classical calculus of variations, Hamilton's principle. Literature: Lecture notes.

5:th lecture 18/10 at 8.15 in A37: Hamilton's equations of motion. Literature: Baruh 5.8, 5.11.

1:st problem solving demonstration 20/10 at 13.15 in A37.

6:th lecture 3/11 at 15.15 in IKP3: Principle of virtual work. Literature: Baruh 4.4, 4.5, 4.7, 4.9.

7:th lecture 9/11 at 10.15 in A37: Jourdain's principle. Literature: Baruh 5.13.

8:th lecture 17/11 at 10.15 in A33: Jourdain's principle. Literature: Baruh 8.11.

2:nd problem solving demonstration 2/12 at 10.15 in A36.

2:nd problem solving demonstration.

Exam paper on the analytical mechanics part of the course 16/3. Instructions.

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:

  1. 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.

  2. Herbert Goldstein Classical Mechanics, chapters 1, 2, 4, 5, 8.1, 8.2, combined with Francis C. Moon Applied Dynamics, chapters 4, 5.

  3. 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.