Graduate course Classical MechanicsA 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.
Course startApril 11 2011 at 13.15 in A35.
Rigid body dynamics
Course contentsRigid 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.
OrganizationAbout 20 lectures of 2 hours.
Course credits9 hp.
ExaminationFirst 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.
LiteratureLiterature 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.