Course Details
Subject {L-T-P / C} : PH4003 : Classical Mechanics { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Ananta Charan Pradhan
Syllabus
PH403: Classical Mechanics (3-1-0)
The Kinematics of rigid body motion : Co-ordinates of rigid body, orthogonal transformation, properties of transformation matrix, Euler angles, Cayley-Klein parameters, Euler's theorem in motion of rigid body, infinitesimal rotations, rate of change of vectors, Coriolis effects.
Rigid body equation of motion : Angular momentum & kinetic energy of motion about a point, inertial tensor and moment of inertia, principal axis transformation and eigenvalue values of inertia tensor, Euler equation of motion, torque free motion of rigid body, heavy symmetrical top with one point fixed, Gyroscope.
Small Oscillations : Formulation, eigenvalue equation and principal axis transformation, free vibration and normal co-ordinates, forced vibration and effect of dissipation, sub-harmonic and super harmonics.
Special theory relativity: Basic postulates of special theory of relativity, Lorenz transformation, velocity addition, relativistic kinematics of collisions and many particle systems, Lagrangian, Hamiltonian formulations in relativistic mechanics, illustrations (1D harmonic oscillator, hyperbolic motion of particle, motion of a charged particle), covariant formulation Lagrangian.
Canonical Transformation: The equation of canonical transformation, Poisson brackets and other canonical invariant, infinitesimal canonical transformation, conservation theorem in Poisson bracket formulations, angular momentum Poisson bracket relations.
Hamilton-Jacobi theory: Hamilton-Jacobi equation for Hamilton-principle & Hamilton's characteristic functions, separation of variables in H. J. equations, cyclic coordinates, action angle variables for one degree freedom, action angle variables for completely separable systems.
Course Objectives
- To gain deeper understanding of classical mechanics using Lagrangian and Hamiltonian formalism.
- To learn advance skills and capabilities for formulating and solving problems relating to complicated mechanical systems.
- To study of the motion of non-quantum mechanical, low-energy particles.
Course Outcomes
Students will get to know <br />1. Solving of equations of motion for complicated mechanical systems using the Lagrangian and Hamiltonian formulation and other advanced formalism (Hamiltonian Jacobi method, Action angle variables, brackets, etc.). 2. About motion and kinematics of rigid body and small oscillations and advanced version of special theory of relativity.
Essential Reading
- Herbert Goldstein, Charles P. Poole, and John Safko, Classical Mechanics, Pearson Education , 3rd Edition
- L. D. Landau and E. M. Lifshitz, Mechanics: Course of Theoretical Physics - Vol. 1, Elsvier , 3rd Edition
Supplementary Reading
- Leonard Susskind and George Hrabovsky, Classical Mechanics: The Theoretical Minimum, Penguin Publisher , 2014
- J. C. Upadhaya, Classical Mechanics, Himalaya Publication , Latest publication