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        

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Lessons for other parts will follow soon.            


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