Syllabus
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Course Code: EP-702 Course Name: Classical Mechanics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Survey of Elementary Principles and Lagrangian Formulation Newtonian mechanics: mechanics of one and many particle systems; conservation laws, motion with variable Mass-The rocket Problem, constraints, their classification; virtual displacement, virtual work, D' Alembert's principle, Lagrange's equations; velocity dependent potential, Rayleigh Function, Invariance of Lagrangian Under Galilean Transformation, dissipative forces, generalized coordinates and momenta; integrals of motion; symmetries of space and time and their connection with conservation laws- conservation of Energy, Conservation of Linear Momentum, conservation of angular Momentum. |
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| 2 | Moving coordinate systems and Motion in a central force field Rotating frames; inertial forces; terrestrial applications of Coriolis force, Central force: definition and characteristics; two body problem- Reduction to the equivalent one body problem; conservation theorem-First Integral of motion, virial theorem, closure and stability of circular orbits; general analysis of orbits; Kepler's laws, Kepler’s equations and the Kepler Problem ; the Laplace-Runge-Lenz vector, Centre of Mass and Laboratory Coordinate systems, cross section, Rutherford scattering. |
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| 3 | Hamiltonian Formalism Legendre transformation, Hamiltonian equations of motion; the physical significance of the Hamiltonian-H; Cyclic/ignorable coordinates; Canonical transformation; generating functions; Poisson bracket & properties of Poisson bracket, integrals of motion, Poisson’s theorem, invariance of Poisson Bracket under canonical Transformation, Lagrange’s Brackets, Infinitesimal Contact Transformation; angular momentum and Poisson bracket relations; Liouville’s theorem and its applications. |
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| 4 | Variational Principle, Equation of motion and Hamilton-Jacobi Equation Principle of least action; derivation of equations of motion; variation and end points; Hamilton's principle and characteristic functions; Hamilton-Jacobi equation, harmonic oscillator problem as an example of Hamilton Jacobi Method. Small Oscillations Small oscillations; stable and unstable equilibrium, normal modes and coordinates. |
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