Special Topics in Classical Mechanics

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2 STUDENTS

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.

Course Curriculum

Course Overview Details 1:18:2
Equations of Motion Details 51:33
Equations of Motion(ii) Details 1:5:42
Equations of Motion(iii) Details 58:6
Equations of Motion(iv) Details 1:38
Equations of Motion(v) Details 1:8:15
Oscillators, Resonances, Waves(i) Details 1:6:46
Oscillators, Resonances, Waves(ii) Details 54:36
Oscillators, Resonances, Waves(iii) Details 50:33
Oscillators, Resonances, Waves(iv) Details 53:22
Polar Coordinates(i) Details 44:23
Polar Coordinates(iI) Details 1:3:40
Dynamical Symmetry in the Kepler Problem(i) Details 56:46
Dynamical Symmetry in the Kepler Problem(ii) Details 55:3
Real Effects of Pseudo-Forces Details 52:7
Real Effects of Pseudo-Forces(ii) Details 50:57
Real Effects of Pseudo-Forces(iii) Details 1:24:2
Real Effects of Pseudo-Forces(iv) Details 59:29
Special Theory of Relativity(i) Details 57:27
Special Theory of Relativity(ii) Details 1:19:1
Special Theory of Relativity(iii) Details 1:14:28
Special Theory of Relativity(iv) Details 59:32
Potentials Gradients Fields(i) Details 1:1:11
Potentials Gradients Fields(ii) Details 56:49
Potentials Gradients Fields(iii) Details 58:47
Gauss Law Eq of continuity(i) Details 59:57
Gauss Law Eq of continuity(ii) Details 41:50
Gauss Law Eq of continuity(iii) Details 1:21:44
Fluid Flow Bernoulli Principle (i) Details 1:2:4
Fluid Flow Bernoulli Principle (ii) Details 1:25:30
Classical Electrodynamics (i) Details 1:2:3
Classical Electrodynamics (ii) Details 1:2:37
Classical Electrodynamics (iii) Details 57:54
Chaotic Dynamical Systems (i) Details 55:40
Chaotic Dynamical Systems (ii) Details 57:28
Chaotic Dynamical Systems (iii) Details 52:52
Chaotic Dynamical Systems (iv) Details 51:35
Chaotic Dynamical Systems (v) Details 46:38
The Scope and Limitations of Classical Mechanics Details 51:13

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