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2018-CM @ UoHyd :: Lessons

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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 Hamiltonian Form of Dynamics

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

Part-4 Small Oscillations

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

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        


   Click on Tab   Attached File(s)     to go to download link for  full set of Lecture Notes           

Lessons for other parts will follow soon.            


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