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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.
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