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.
Week 1: Motion and Constraints, Generalized Coordinates, D’Alembert’s Principle of Virtual Work
Week 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 Motion
Week 5: Cannonical Transformations, Cannonical invariants, Symplectic Approach to CT.
Week 6: Poisson Bracket Formulation, Symmetry groups of Mechanical Systems, Liouville’s Theorem
Week 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.