Theoretical Mechanics

This course focuses on analytical aspects of classical mechanics and is targeted towards the audience who are interested in pursuing research in Physics. Various formulations of mechanics, like the Lagrangian formulation, the Hamiltonian formulation, the Poisson bracket formulation will be taught in the course. The course also introduces the mechanics of continuous systems and fields.
INTENDED AUDIENCE: First year of MSc or 2nd and 3rd year of BE/BTech in Engg PhysicsPREREQUISITES: Introduction to Newtonian Mechanics is desired.

COURSE LAYOUT

Week 1: Motion and Constraints, Generalized Coordinates, D’Alembert’s Principle of Virtual WorkWeek 2: Variational Calculus, Hamilton’s Principle, Lagrangian Formulation.Week 3: Application of Lagrangian Formulation, Configuration Space and Phase Space.Week 4: Hamilton’s Equations of MotionWeek 5: Cannonical Transformations, Cannonical invariants, Symplectic Approach to CT.Week 6: Poisson Bracket Formulation, Symmetry groups of Mechanical Systems, Liouville’s TheoremWeek 7: Hamilton Jacobi Theory, Hamilton’s Principal Fucntion, Action-Angle variables.Week 8: Lagrangian and Hamiltonian Formulation for Continuous Systems and Fields.
Week 9: CanonicalTransformations
Week 10:Poisson Bracket Formulation
Week 11:Hamilton-jacobi Theory
Week 12:Chaos