PROOFS PROGRAMME

Classical Mechanics (2018)

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Classical Mechanics-I
A course given at University of Hyderabad
Summer Semester May14 - July10 (2018)

Part-I From Newton to Euler and Lagrange

  1. Review of Newtonian Mechanics
  2. Euler Lagrange Equations
  3. Energy Conservation, Cyclic Coordinates

Part-II Action Principle

  1. Hamilton's Principle
  2. Noether's Theorem
  3. Examples

Part-III Hamiltonian Form of Dynamics

  1. Hamiltonian Equations of Motion
  2. Poisson Brackets, EOM in Poisson Bracket Form
  3. Variational Principle in Phase Space

Part-IV Spherically Symmetric Potentials

  1. General Properties of Motion
  2. Solving Equations of Motion
  3. Keplar problem, bounded orbits
  4. Unbounded orbits

Part-V Scattering

  1. BasicDefinitions
  2. Scattering of Waves
  3. Why  callit cross setion?
  4. Computing cross section
  5. Lab and center of mass frames

Part-VI Small Oscillations

  1. Oscillations in One Dimension
  2. A Simple Example in Two Dimensions
  3. Normal Frequencies and Norma lModes of Vibration
  4. Several Degreesof Freedom
  5. Examples

Part-VII Galilean Transoformations, Noninertial Frames,

  1. Galiliean Transformations
  2. Accelerated Linear Motion
  3. Rotation Group
  4. Motion in a Rotating Frame;
  5. Centrifugal and Coriolis Forces

Part-IX Canonical Transformations

  1. Variatonal Principle in Phase Space
  2. Canonical Transformations;
  3. Properties of Canonical Transfomations
  4. Infinitesimal Canonical Transformations

Part-X Hamilton Jacobi Theory

  1. Hamilton's Principal Function
  2. Jacobi's Complete Integral
  3. Time Independent Hamilton Jacobi Equation
  4. Solution of Separation of Variables
  5. Examples

 

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