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Lecture Details :
Special Topics in Classical Mechanics by Prof. P.C. Deshmukh,Department of Physics,IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Course Description :
Essentially, foundations of ‘classical mechanics’ would include a comprehensive introduction to Newtonian, Lagrangian and Hamiltonian Mechaincs, and include an introduction to mechanics of a system of particles, fluid mechanics, introduction to ‘chaos’, to the special theory of relativity and also to electrodynamics.
The course is designed as the first course students would take after high school, and the scope of some of the advanced topics that are introduced is therefore restricted. A comfortable introduction, adequately rigorous but not overly involved, to advanced applications is attempted. In this course, we emphasize that ‘observation’ and ‘measurements’ play a fundamental role in Physics.
We introduce mathematical methods as and where needed, but keep the focus on physical principles. The course aims, even as it will provide a rigorous introduction to the foundations of classical mechanics, at discovering the romance in physics, beauty in its simplicity, and rigor in its formulation.
content:
Equations of Motion. Principle of Causality and Newton’s I & II Laws. Interpretation of Newton’s 3rd Law as ‘conservation of momentum’ and its determination from translational symmetry. Alternative formulation of Mechanics via ‘Principle of Variation’. Determination of Physical Laws from Symmetry Principles, Symmetry and Conservation Laws. Lagrangian/Hamiltonain formulation. Application to SHO.
Oscillations. Small oscillations. SHM. Electromechanical analogues exhibiting SHM. Damped harmonic oscillator, types of damping. Driven and damped & driven harmonic oscillator. Resonance, Quality Factor. Waves.
Polar coordinate systems.
Kepler Problem. Laplace-Runge-Lenz vector, ‘Dynamical’ symmetry. Relationship between ‘Conservation principle’ and ‘Symmetry’.
Inertial and non-inertial reference frames. Pseudo forces.
Galilean & Lorentz transformations. Special Theory of Relativity.
Physical examples of fields. Potential energy function. Gradient, Directional Derivative, Divergence of a vector field.
Gauss’ Law; Equation of Continuity. Hydrodynamics and Electrodynamics illustrations.
Fluid Flow, Bernoulli’s Principle. Equation of motion for fluid flow. Definition of curl, vorticity, Irrotational flow and circulation. Steady flow. Bernoulli’s principle, some illustrations. Applications of Gauss’ divergence theorem and Stokes’ theorem in fluid dynamics.
Classical Electrodynamics and the special theory of relativity. Introduction to Maxwell’s equations.
‘Chaos’, bifurcation, strange attractors, fractals, self-similarity, Mandelbrot sets.
Other Resources :
Syllabus | Citation |
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