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.
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