AMAT 32353: Mechanics III

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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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