Classical Mechanics (2018) :: Course given at University of Hyderabad

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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

Assignment, Quiz, Test and Examination Papers

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