infocobuild

Special Topics in Classical Mechanics

Special Topics in Classical Mechanics. Instructor: Professor P.C. Deshmukh, Department of Physics, IIT Madras. This course has grown out of the first course in Physics taught to engineering students at IIT-Madras. However, the contents are expanded to include the interests of students of basic sciences and a strong emphasis on the foundations of classical mechanics is aimed at.

Essentially, foundations of 'classical mechanics' would include a comprehensive introduction to Newtonian, Lagrangian and Hamiltonian Mechanics, 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. (from nptel.ac.in)

Course Overview


Lecture 01 - Course Overview
Lecture 02 - Equations of Motion; Galileo's Experiments; Principle of Causality and Newton's Laws
Lecture 03 - Equations of Motion (ii): Newton's Third Law
Lecture 04 - Equations of Motion (iii): Principle of Least Action
Lecture 05 - Equations of Motion (iv): Lagrange's Equation, Hamilton's Principle Function
Lecture 06 - Equations of Motion (v): Applications of Lagrange's/Hamilton's Equations
Lecture 07 - Oscillators, Resonances, Waves (i)
Lecture 08 - Oscillators, Resonances, Waves (ii): Damped Harmonic Oscillator
Lecture 09 - Oscillators, Resonances, Waves (iii): Forced Oscillations
Lecture 10 - Oscillators, Resonances, Waves (iv): Aspects of Resonances and Waves
Lecture 11 - Polar Coordinates (i)
Lecture 12 - Polar Coordinates (ii)
Lecture 13 - Dynamical Symmetry in the Kepler Problem (i)
Lecture 14 - Dynamical Symmetry in the Kepler Problem (ii)
Lecture 15 - Real Effects of Pseudo-Forces: Inertial and Noninertial Reference Frames
Lecture 16 - Real Effects of Pseudo-Forces (ii): Noninertial Frame of Reference
Lecture 17 - Real Effects of Pseudo-Forces (iii): Noninertial Frame of Reference
Lecture 18 - Real Effects of Pseudo-Forces (iv): The Foucault Pendulum; The Coriolis Effect
Lecture 19 - Special Theory of Relativity (i): Introduction
Lecture 20 - Special Theory of Relativity (ii): Length Contraction and Time Dilation
Lecture 21 - Special Theory of Relativity (iii): Twin Paradox
Lecture 22 - Special Theory of Relativity (iv): Conclusion
Lecture 23 - Potentials, Gradients, Fields (i): Potentials, Vector Fields, Directional Derivative
Lecture 24 - Potentials, Gradients, Fields (ii): Directional Derivative (cont.), Gradients
Lecture 25 - Potentials, Gradients, Fields (iii): Connections between Potential Gradients and Fields
Lecture 26 - Gauss' Law: Equation of Continuity (i)
Lecture 27 - Gauss' Law: Equation of Continuity (ii): Gauss' Divergence Theorem
Lecture 28 - Gauss' Law: Equation of Continuity (iii): Application Examples
Lecture 29 - Fluid Flow, Bernoulli's Principle (i)
Lecture 30 - Fluid Flow, Bernoulli's Principle (ii)
Lecture 31 - Classical Electrodynamics (i): Gauss' Law
Lecture 32 - Classical Electrodynamics (ii): Maxwell's Equations
Lecture 33 - Classical Electrodynamics (iii): The Special Theory of Relativity
Lecture 34 - Classical Electrodynamics (iv): The Special Theory of Relativity
Lecture 35 - Chaotic Dynamical Systems (i): Complex Behavior of Simple Systems
Lecture 36 - Chaotic Dynamical Systems (ii): Bifurcations, Chaos
Lecture 37 - Chaotic Dynamical Systems (iii): Chaos, Fractal Dimensions
Lecture 38 - Chaotic Dynamical Systems (iv): Fractal Dimensions/ Mandelbrot Sets
Lecture 39 - Chaotic Dynamical Systems (v): Mandelbrot Sets
Lecture 40 - The Scope and Limitations of Classical Mechanics

Related Links
Special Topics in Classical Mechanics
Instructor: Professor P.C. Deshmukh, Department of Physics, IIT Madras. Syllabus. This course has grown out of the first course in Physics taught to engineering students at IIT-Madras.