M.Sc. Physics (l Semester)
Paper II : CLASSICAL MECHANICS
Unit-I(Lagrangian mechanics )
Newtonian mechanics of one and many particle systems, Conservation laws, Constraints and their classification, principle of virhral work, D'Alembert's principle and Lagmnge's equation of motion, Applications: Iinear harmonic oscillator, simple pendulum, compound pendulum, L-C Circuit, Lagrangian for a Charged Particle Moving in an Electromagnetic field.
Unit-II (Hamilton's mechanics )
Deduction of Hamilton's principle from D'Alemberts principle, modified Hamilton's principle, Hamilton's principle and Lagrange's equations, generalized momentum and cyclic coordinates, Hamilton function H and conservation ofenergy, Hamilton's equation (Hamilton's canonical equations of motion), Simple application of the Hamilton principle- linear harmonic oscillator, simple pendulum, A-variation, principle of least action. Equations of canonical transformation, (Generating functions), examples of canonical transformations for a harmonic oscillator.
Unit-111(Poisson's bracket and Hamilton Jacobi method)
Introduction to Poisson's bracket notation, equations of motion in Poisson bracket form, fundamentals of Poisson's bracket notation, angular momentum and Poisson brackets, Jacobi's identity. Hamilton - Jacobi equation of Hamilton's principal function' The Harmonic oscillator problem as an example of the Hamilton - Jacobi Method, Hamilton -Jacobi equation for Hamilton's characteristic function, Action - angle variables'
Unit-IV (Dynamics of a rigid bodY)
The Euler angles-hrst rotation, second rotation and third rotation' angular momentum and inertia tensor, principal axes and principal moments of inertia' rotational kinetic energy of a rigid body, Euler's equations of motion of a rigid body' torque-free motion ofa rigid body.
Unit-V (Special th€ory of rehtivity) Introductiontospecialtheoryofrelativity,Galileantransformations,principleof relativity, transformation of force from one inertial system to another' covariance of the physicai laws, principle of relativity and speed of light' Lorentz transformations' consequences of Lorentz transformations, aberration of light from stars' relativistic Doppler's effect.