||Message]
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;
Examples
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
