Course Code : AMAT 32353
Title : Mechanics III
Pre-requisites : AMAT 21272
Learning Outcomes:
Upon successful completion of this course, the student will be able to
- describe Eularian angles and apply in symmetrical tops
- solve and explain the problems small oscillation and normal modes
- explain the D’Alambert’s principal 4. explain the Hamilton principal and derive Hamilton’s equation of motion
- demonstrate the ability to apply Poisson and Lagrangian brackets and their properties
- understand and apply the Canonical transformation and determine generating functions
- compare Hamilton’s equations of motion in Poisson brackets.
Course Content:
Rigid body kinematics: Eularian angles, Motion of a symmetrical top, small oscillations and Normal modes, D’Alambert’s principal.
Hamiltonian formalism of mechanics: Hamilton’s principle and Hamilton’s equations of motion, Poisson and Lagrangian brackets and their properties, Hamilton’s equations of motion in Poisson brackets.
Canonical transformations: Canonical transformation and generating functions
Method of Teaching and Learning : A combination of lectures and tutorial discussions.
Assessment: Based on tutorials, tests and end of course examination.
Recommended Reading:
1. Rao, A.V. (2011). Dynamics of Particles and Rigid Bodies: A Systematic approach, Cambridge University Press.
2. Chorlton, F. (2nd Ed., 2019). Textbook of Dynamics, D. Van Nostrand.
3. Gignoux C & Silvestre-Brac, B. (2014). Solved Problems in Lagrangian and Hamiltonian Mechanics, Springer Netherlands.
4. Kelley, J.D. & Leventhal, J.J. (2016). Problems in Classical and Quantum Mechanics: Extracting the Underlying Concepts. Springer.
5. Strauch, D. (2009). Classical Mechanics, An Introduction, Springer.
6. Goldstein, H., Poole, C. P. & Safko, J. (3rd Ed., 2011). Classical Mechanics, Pearson.
7. Mondal, C.R. (2005). Classical Mechanics, Prentice Hall of India. 8. Ramsey, A.S. (1975). Dynamics, Parts I & II, Cambridge University Press.