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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

  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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