Course Content

Course Content:

• Unit I: Lagrangian Mechanics (7 Lectures) [PD]

Configuration space and constraints, Generalised coordinates, Hamilton’s principle, Lagrangian Mechanics with examples, cyclic coordinates and conservation laws.

• Unit II: Hamiltonian Mechanics (4 Lectures) [AS]

Hamiltonian Mechanics and phase space description, Liouville’s theorem.

• Unit III: Central Force Problem (6 Lectures) [PD]

Motions in central field. Equivalence one dimensional problem, Laplace-Runge-Lenz vector.

• Unit IV: Rigid Body (6 Lectures)[PD]

Kinematics of rigid bodies, Degrees of freedom, Moment of inertia tensor, principal axis, Euler angles, Cayley-Klein parameters, symmetric top.

• Unit V: Small Oscillations (4 Lectures) [AS]

Small oscillations, eigenvalue problem.

• Unit VI: Canonical Transformations (6 Lectures) [AS]

Canonical transformations, Poisson Bracket, Poisson equation of motion, Action angle variables and Hamilton-Jacobi Theory.

• Unit VII: Chaos (6 Lectures) [AS]

Fixed point and stability, Linear stability analysis, Saddle Node and Pitchfork bifurcation, Lorenz Map.

*In bracket, we mention the approximate number of lectures required on each topic.