Advanced Mechanics (PHYS*3400)
Code and section: PHYS*3400*01
Term: Fall 2016
Instructor: Paul Garrett
This course covers rotational dynamics, Lagrangian mechanics and Hamiltonian mechanics. Topics include a formal treatment of rotations, rigid-body rotations and Eulers equations, generalized coordinates, least action principles, Poisson brackets, Liouville's theorem, Hamilton-Jacobi theory. If time permits, an introduction to differential geometry and tensor calculus will be given.
|Tuesday, Thursday||10:00 am – 11:20 am||MCKN 230|
Wednesday, December 14, 7:00 pm – 9:00 pm
- Review of rotation matrices and their derivatives
- Tensors and the Inertia tensor
- Euler’s equations
- Generalized coordinates
- d’Alembert’s principle and virtual displacements
- Lagrangian formulism
- Constraint forces
- Calculations of variations
- Least action principle
- Hamiltonian mechanics
- Phase space and Liouville’s theorem
- Canonical transformations
- Hamilton-Jacobi theory
- Applications of the action
The lecture notes will be posted on Courselink. In addition, an excellent set of course notes used by Prof. E. Poisson is available. The text from Mechanics I and II, John R. Taylor “Classical Mechanics” will also be very useful.
The following texts are excellent additional references:
- Herbert Goldstein, Charles P. Poole, and John L. Safko, Classical Mechanics (3rd Edition) (Addison Wesley, 2002; ISBN 0201657023; QA 805.G6)
- Walter Greiner, Classical Mechanics: Systems of Particles and Hamiltonian Dynamics (Springer, 2003; ISBN 0-387-95128-8)
- Walter Greiner, Classical Mechanics: Point Particles and Relativity (Springer, 2004; ISBN 0-387-95586-0)
- Harold J W Müller-Kirsten, Classical Mechanics and Relativity (World Scientific, 2008; ISBN-10: 981-283-252-1)
- Cornelius Lanczos, The Variational Principles of Mechanics (4th Edition) (Dover Publications, 1986; ISBN 0486650677; QA 845.L3)
- Keith R. Symon, Mechanics (3'rd Edition) (Addison-Wesley, 1971; ISBN 0-201-07392-7)
|Midterm: Time and location TBD||25%|
The assignments for this course that will be handed out and submitted in class. No assignments will be accepted after the posting of the solutions on the course webpage. Submitted assignment solutions must show calculational details, be legible, and written with a logical flow. Marks on assignments will rapidly trend to zero if not presented well.
(Not) Working With Other Students
All work submitted for grading in this course must be each individual student's own work. While students are encouraged to share thoughts and ideas, it is not acceptable to share assignment solutions. The assignments are not group projects. It is important that you do not show your final written solutions to other students.
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When You Cannot Meet a Course Requirement
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The last date to drop one-semester courses, without academic penalty, is Friday, Nov. 4, 2016. For regulations and procedures for Dropping Courses, see the Undergraduate Calendar.
Copies of out-of-class assignments
Keep paper and/or other reliable back-up copies of all assignments and midterm exam: you may be asked to resubmit work at any time.
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