Course Contents:
Lagrangian formulation: Degrees of freedom, constraints, generalized coordinates and velocities, Lagrangian, Euler-Lagrange equation, examples. Symmetries and conservation laws: Conservation of momentum, angular momentum and energy, virial theorem Central force motion: Kepler problem, Scattering in a central potential, Rutherford formula.
Small oscillations: Perturbations away from equilibrium, stability analysis, normal modes and normal coordinates, examples (molecular dynamics).
Rigid body motion: Motion in non-inertial frames, Coriolis force, degrees of freedom of a rigid body, moment of inertia tensor, principal axes, Euler angles and Euler equations of motion, example (symmetric top).
Hamiltonian formalism: Legendre transforms, generalized momenta, Hamiltonian, Hamilton's equations, phase space and phase trajectories, examples, conservative versus dissipative systems (simple examples). Canonical transformations: Poisson brackets, Louiville's theorem, Generating functions, Action-angle variables Elements of time-independent perturbation theory, introduction to non-integrable systems.
Special relativity: Postulates of relativity, Lorentz transformations, length contraction and time dilation, Doppler effect,velocity addition law, four-vector notation.
Text Books:
1. S. T. Thornton and J. B. Marion, Classical Dynamics of Particles and Systems (Cengage Learning, Singapore, 2004).
2. A. P. French, Special Relativity (W. W. Norton, New York, 1968).
- Teacher: prasanta PRASANTA KUMAR TRIPATHY