Classical mechanics

Course Outline

Review of Newtonian Mechanics:

Frame of reference, orthogonal transformations, angular velocity and angular acceleration, Newton’s laws of motion, Galilean transformation, conservation laws, systems of particles, motion under a constant force, motions under variable force, time-varying mass system.

The Lagrange Formulation of Mechanics and Hamilton Dynamics:

Generalized co-ordinates and constraints, D’Alembert’s principle and Lagrange’s Equations, Hamilton’s principle, integrals of motion, non-conservative system and generalized potential, Lagrange’s multiplier method, the Hamiltonian of a dynamical system, canonical equations, canonical transformations, Poisson brackets, phase space and Liouville’s theorem.

Central Force Motion:

The two-body problem, effective potential and classification of orbits, Kepler’s laws, stability of circular orbits, hyperbolic orbits and Rutherford scattering, center of mass co-ordinate system, scattering cross-sections. Motion in Non-Inertial Systems: Accelerated translational co-ordinate system, dynamics in rotating co-ordinate system, motion of a particle near the surface of the earth.

The Motion of Rigid Bodies:

The Euler angles, rotational kinetic energy and angular momentum, the inertia tensor, Euler equations of motion, motion of a torque-free symmetrical top, stability of rotational motion.

Special Relativity:

Michelson-Morley Experiment, Einstein's Postulates of Relativity, Lorentz Transformation, Geometry of Space and Time, Addition of Velocities, Kinetic Energy of Relativistic Particles, Mass Energy Relation, Momentum of Relativistic Particles, Orthogonal Transformation in three Dimensions, Lorentz Transformation as Orthogonal Transformation

Recommended books

1. Herbert Goldstein, Charles Poole, John Safko “Classical Mechanics”, PEARSON, 3rd Edition.
2. Stephen T. Thornton, Jerry B. Marion “Classical dynamics of particles and systems”, Thomson, Brooks/Cole, 5th Edition (2004).
3. T. Kibble and F. Berkshire, “Classical Mechanics”, World Scientific, 5th edition 2004.
4. T. L. Chow, “Classical Mechanics”, John Wiley, 1995.