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2019-CM @ HCU :: Lessons

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This course was very similar to a course given in summer of  2018 See  2018 CM@HCU
The course was be covered in nine parts. The syllabus for different parts is as follows.

Part-1 From Newton to Euler Lagrange EOM

        Review of Newtonian Mechanics
        Euler Lagrange Equations
        Energy Conservation, Cyclic coordinates
        Reducing Solution to Quadratures        

Part-2 Action Principle 

        Hamilton's Principle
         Noether's Theorem; Examples

Part-3 Small Oscillations

        Small Oscillations in One Dimension
        An Exmaple in Two Dimension
        Normal coordinates and Normal Modes of Vibration
        Lagrangian Formalism; Examples

Part-4 Hamiltonian Form of Dynamics

        Hamiltonian Form of Dynamics; Poisson Brackets;
        Variational Principle in Phase Space

Part-5  Spherically symmetric potentials in three dimensions

         General Properties of Motion
         Solving Equation of Motion
         Keplar Problem, Bounded Orbits
         Unbounded orbits

Part-6  Scattering

        FLux, Scattering, Total Cross Section, Differential Cross Section
        Cross Section for Waves;
        Why call it Cross Section?
        Computing Cross Section
        Lab and Center of Mass Frames

Part-7 Non-Inertial Frames

        Galiliean Transformations;
        Accelerated Frames
        Rotation Group;
        Motion in a Rotating Frame
        Centrifugal and Coriolis Forces;

Part-8 Canonical Transformations

        Action Principle in Phase Space;
        Canonical Transformations and Poisson Brackets;
        Four Types of Generators
        Infinitesimal Canonical Transformations

Part-9 Hamilton Jacobi Theory

Hamilton Jacobi Equation
Hamilton's Principal Function
Jacobi's Complete Integral

 More lessons will be made available in due courseourse



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