Brock Calendar entry:
Advanced treatment of the mechanics of particles and of rigid bodies; Lagrangian and Hamiltonian methods; Poisson brackets, applications to the theory of small oscillators and central force motions, elements of chaotic motions.
Prerequisites: PHYS 2P20, MATH 2P03, 2P08 and 3P06
There is no required textbook for the course. The main source of information
will be the lecture notes. The students are encouraged to consult numerous textbooks
available in the library.
Some suggested books are:
- Analytical Mechanics by Grant R. Fowles and George L. Cassidy
- Classical Mechanics by Tai L. Chow John Wiley & Sons, Inc. (This is a good book, but happens to have many typos.
You need to watch out for them. On the other hand, being mindful of the typos will probably keep you more engaged with the material than otherwise.)
- Classical Mechanics (5th edition) by Tom W.B. Kibble and Frank H. Berkshire, Imperial College Press (2004).
- Classical Mechanics by Herbert Goldstein
- Classical Mechanics- A Modern Perspective by Vernon D. Barger and Martin G. Olsson
- Classical Mechanics by John R. Taylor
My lectures will draw from the first two books, among several other sources.
Topics covered in the course:
Lagrangian and Hamiltonian dynamics: Generalized coordinates. Lagrange equations. Generalized momenta. Hamiltonian function. Hamiltonian equations of motion. Hamilton's principle of Least Action.
Poisson Barckets and equations of motion, Constants of Motion, Unfolding theorem of Poisson Barckets
Oscillations: Damped oscillations. Forced oscillations, resonance. Parametric resonance.
Dynamics in two and three dimensions: Central force. Newton's universal law of gravitation. Gravitation forces and potentials. Planetary motion. Scattering.
Non-inertial (accelerating) frames, Corilois force and applications of this concept.
Rigid body motion: Planar motion. Moment of inertia. Angular momentum and kinetic energy. Motion in three dimensions. Moment of inertia tensor. Euler's equations of motion. Free symmetrical top.
Selected problems from Calculus of Variation.
Note: The above list is tentative. We may not have the time to cover some topics, while others may be
added. The examination will be only on the material actually covered in the lectures.
1 midterm test(closed book): 25%;
final exam (closed book): 40%
A minimum of 50% in the final exam is needed to pass the course
Late assignments will not be accepted unless approved by the instructor