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2019-CM-I @ CMI :: Lessons

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  1.  Unit-A Vectors, Summation Convention
    Preliminaries: Kronecker delta and Levi-Civita symbol;
    Einstein summation convention;
    123 notation for vector components.
    Dot and cross products of two vectors and vector identities.

  2. Unit-B Group of Rotations in Three Dimensions
    Newton's Laws; Inertial and non-inertial frames;
    Galilean transformations;
    Rotation of coordinate axes;
    The rotation group
    \(O(3)\)..

  3. Unit-C Motion in Accelerated Frames
    Frames with constant acceleration;
    EOM in Rotating frames;
    Centrfugal force; Coriolis force; Examples

  4. Unit-D General Properties of Motion in One Dimension
    Transformation of momentum, kinetic energy, angular momentum under Galilean transformations;
    Separation of center of mass in dynamical variables.

  5. Unit-E Kinematics of Rigid Body Motion
    Angular velocity of a rigid body;
    Moment of Inertia tensor;
    Kinetic energy and Angular Momentum of rigid body;
    Euler's equations of motion in rotating frames;
    Examples of rigid body motion.

  6. Unit-G Rigid Body Dynamics-I
    Limitations of Newtonian Mechanics;
    Euler Lagrange equation of motion;
    Energy conservation;
    Canonical Momentum and Hamiltonian;
    Cyclic coordinates;
    Solution by quadratures;

  7.  Unit-H Action Principle (New Uploaded on 30-11-2019)
    Hamilton's Action Principle;
    Noether's theorem and conservation laws;
    Symmetries and conservation laws;
    Hamilton's equations; Poisson bracket form of equations of motion.

  8. Unit-I Rigid Body Dynamics-II  ( Moved  from Unit H 30-11-2019)
    Lagrangian for a rigid body with one point fixed;
    Motion of a heavy symmetrical top (Analytical approach);
    Qualitative discussion  using graphical analysis;
    Sleepinp top.

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  • This  collection has a variety of archived  teaching resources.
  • Contributed by friends colleagues and by some of my teachers at different institutions. 
  • Resources of  selected courses given by me at different  institutions.
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This is  proofs archive. This  collection  is planned to have :

(A)  Set of resources used for courses offered at different institutions  and made available by teachers, friends and colleagues acknowledged for their love, passion and excellence in teaching.

(B) Selected scanned resources  for found useful for  different  courses in  more than one  area of Physics and more ...

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