Special Topics in Classical Mechanics

Overview

Equations of Motion. Principle of Causality and Newtons I & II Laws. Interpretation of Newtons 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, Bernoullis Principle. Equation of motion for fluid flow. Definition of curl, vorticity, Irrotational flow and circulation. Steady flow. Bernoullis principle, some illustrations. Applications of Gauss divergence theorem and Stokes theorem in fluid dynamics - Classical Electrodynamics and the special theory of relativity. Introduction to Maxwells equations - Chaos, bifurcation, strange attractors, fractals, self-similarity, Mandelbrot sets.