Theoretical Mechanics

This course has been designed based on the syllabus of a typical master's level at universities. It primarily 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 includes the applications of these formulations to central force problems, rigid body motion and small oscillations.INTENDED AUDIENCE: First year of MSc or 2nd and 3rd year of BE/BTech in Engg PhysicsPREREQUISITES: Introduction to Newtonian Mechanics is desired.

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: Applications of Lagrangian Mechanics, Phase Space.Week 4:Central Forces, Orbits, Kepler Motion. Week 5: Central Forces, Scattering.Week 6: Rigid Body Kinematics, Euler Angles, Rotating Frames.Week 7:Rigid Body Dynamics, Euler Equations. Week 8: Small Oscillations.
Week 9: Phase Space, Hamilton’s Equations of Motion.
Week 10:Cannonical Transformations, Cannonical invariants, Symplectic Approach to CT.
Week 11:Poisson Bracket Formulation, Symmetry groups of Mechanical Systems, Liouville’s Theorem.
Week 12:Hamilton Jacobi Theory, Hamilton’s Principal Fucntion, Action-Angle variables.