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Subject Code: 09020102

 S. No. Topic Learning Objective Teaching guidelines Methodology Time (Hrs) 1 LAGRANGIAN FORMULATION &HAMILTON’S PRINCIPLES Mechanics of a system of particles constraints of motion, generalized coordinates D’Alembert’s Principle Lagrange’s velocity dependent forces (gyroscopic) dissipation function Application of Lagrangian formulation, Hamilton principle, Lagrange’s equation from Hamilton principle extension to non-holonomic systems To acquaint the student with the mathematical concepts and techniques in regard to various problems of classical mechanics for a mature understanding of physical theories and concepts. To cover the mechanics of a system of particles constraints of motion, generalized coordinates, D’Alembert’s Principle, Lagrange’s velocity dependent forces (gyroscopic), dissipation function, Application of Lagrangian formulation, Hamilton principle and Lagrange’s equation from Hamilton principle. Lecture. Seminar. Discussion/Interaction with Students. Assignment. Discussion on Assignment.         Evaluation of Assignment. 10 2 RIGID BODY MOTION Reduction to equivalent one body problem the equation of motion and first integrals the equivalent one dimensional problem classification of orbits the differential equation for orbits. Kepler’s problem (inverse square law), scattering in central force field The Euler’s angles, rate of change of a vector Coriolis force and its applications. To attempt to analyse/understand/predict the behavior of rigid bodies. To cover Reduction to equivalent one body problem the equation of motion and first integrals the equivalent one dimensional problem classification of orbits the differential equation for orbits. Kepler’s problem (inverse square law) and scattering in central force field. Lecture. Seminar. Discussion/Interaction with Students. Assignment. Discussion on Assignment.         Evaluation of Assignment. 10 3 SMALL OSCILLATIONS & HAMILTON EQUATION Euler equation of motion Torque free motion of rigid body, motion of a symmetrical top, Eigen value equation, Free vibrations, Normal coordinates vibration of Tri-atomic Molecule, Legendre Transformation Hamilton’s equations of motion, Hamilton’s equations from variation principle, Principle of least action. To acquire working knowledge of the methods of Hamiltonian Dynamics. Students are also expected to become familiar with the specific topics of central force, rigid body and small oscillations. To cover Euler equation of motion, Torque free motion of rigid body, motion of a symmetrical top, Eigen value equation, Free vibrations, Normal coordinates, vibration of Tri-atomic Molecule, Legendre Transformation, Hamilton’s equations of motion,  Hamilton’s equations from variation principle, Principle of least action. Lecture. Seminar. Discussion/Interaction with Students. Assignment. Discussion on Assignment.         Evaluation of Assignment. 10 4 CANONICAL TRANSFORMATION AND HAMILTON-JACOBI THEORY Canonical transformation and its examples Poisson’s brackets Equation of motion Angular momentum, Poisson’s Brackets relations, infinitesimal canonical transformation, Conservation Theorems., Hamilton-Jacobi equation Hamilton’s principal function, Harmonic Oscillator problem Detailed knowledge of canonical transformation and Hamilton-Jacobi equation will help students greatly in their future study of graduate level quantum mechanics. To cover canonical transformation and its examples, Poisson’s brackets, Equation of motion, Angular momentum, Poisson’s Brackets relations, infinitesimal canonical transformation, Conservation Theorems, Hamilton-Jacobi equation  , Hamilton’s principal function and Harmonic Oscillator problem. Lecture. Seminar. Discussion/Interaction with Students. Assignment. Discussion on Assignment.         Evaluation of Assignment. 10