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Introduction to Classical Mechanics. Instructor: Prof. Anurag Tripathi, Department of Physics, IIT Hyderabad.
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Description
This is an introductory course on Classical Mechanics covering topics: Generalised coordinates, d'Alembert's Principle, Euler Lagrange equation of motion and its applications; Hamilton's Principle. Conservation laws; Small oscillations: Free Oscillations, Damped oscillations; Forced Oscillations, Resonance, Normal Coordinates; Central force problem, reduction to 1 body problem, Equation of motion and first integrals (from nptel.ac.in)
Course content
- Lecture 01 – Introduction, Symmetries of Space and Time Unlimited
- Lecture 02 – Generalized Coordinates and Degrees of Freedom Unlimited
- Lecture 03 – Virtual Work Unlimited
- Lecture 04 – Virtual Work (Rigid Body) Unlimited
- Lecture 05 – d’Alembert Principle Unlimited
- Lecture 06 – Euler Lagrange Equation for a Holonomic System Unlimited
- Lecture 07 – Euler Lagrange Equations: Examples Unlimited
- Lecture 08 – Euler Lagrange Equations: Examples (cont.) Unlimited
- Lecture 09 – Properties of Lagrangian Unlimited
- Lecture 10 – Kinetic Term in Generalized Coordinates Unlimited
- Lecture 11 – Cyclic Coordinates Unlimited
- Lecture 12 – Conservation Laws – Conservation of Energy Unlimited
- Lecture 13 – Energy Function, Jacobi’s Integral Unlimited
- Lecture 14 – Momentum Conservation Unlimited
- Lecture 15 – Matrices and All That Unlimited
- Lecture 16 – Matrices, Forms, and All That Unlimited
- Lecture 17 – Principal Axis Transformation Unlimited
- Lecture 18 – Small Oscillations Unlimited
- Lecture 19 – Oscillations, Normal Coordinates Unlimited
- Lecture 20 – Oscillations, Triatomic Molecule Unlimited
- Lecture 21 – Triatomic Molecule Normal Coordinates Unlimited
- Lecture 22 – Coupled Pendulums, Normal Modes Unlimited
- Lecture 23 – Coupled Pendulums, Beats Unlimited
- Lecture 24 – Oscillations, General Solution Unlimited
- Lecture 25 – Forced Oscillations Unlimited
- Lecture 26 – Damped Oscillations Unlimited
- Lecture 27 – Forced Damped Oscillations Unlimited
- Lecture 28 – One Dimensional Systems Unlimited
- Lecture 29 – Two-body Problem Unlimited
- Lecture 30 – Two-body Problem: Kepler’s Second Law Unlimited
- Lecture 31 – Two-body Problem: Kepler’s Problem Unlimited
- Lecture 32 – Two-body Problem: Conic Sections in Polar Coordinates Unlimited
- Lecture 33 – Two-body Problem: Ellipse in Polar Coordinates Unlimited
- Lecture 34 – Orbits in Kepler Problem Unlimited
- Lecture 35 – Apsidal Distances, Eccentricity of Orbits Unlimited
- Lecture 36 – Kepler’s Third Law; Laplace-Runge-Lenz Vector Unlimited
- Lecture 37 – Rigid Body: Degrees of Freedom Unlimited
- Lecture 38 – Rigid Body: Transformation Matrix Unlimited
- Lecture 39 – Rigid Body: Euler Angles Unlimited
- Lecture 40 – Rigid Body: Parameterization using Euler Angles Unlimited
- Lecture 41 – Rigid Body: Euler’s Theorem Unlimited
- Lecture 42 – General Motion of a Rigid Body Unlimited
- Lecture 43 – Moment of Inertia Tensor Unlimited
- Lecture 44 – Principal Moments Unlimited
- Lecture 45 – Lagrangian of a Rigid Body Unlimited
- Lecture 46 – Motion of a Free Symmetric Top Unlimited
- Lecture 47 – Angular Velocity using Euler Angles Unlimited
- Lecture 48 – Lagrangian of a Heavy Symmetric Top Unlimited
- Lecture 49 – First Integrals of a Heavy Symmetric Top Unlimited
- Lecture 50 – Nutation and Precision of a Heavy Symmetric Top Unlimited
- Lecture 51 – Sleeping Top Unlimited
- Lecture 52 – Rotating Frames, Euler Equations Unlimited
- Lecture 53 – Calculus of Variations: Functionals Unlimited
- Lecture 54 – Method of Lagrange Multipliers Unlimited
- Lecture 55 – Calculus of Variations: Condition for Extremum Unlimited
- Lecture 56 – Calculus of Variations: Several Variables Unlimited
- Lecture 57 – Cartesian Tensors Unlimited
- Lecture 58 – Hamiltonian Mechanics: Hamilton’s Equations of Motion Unlimited
- Lecture 59 – Hamiltonian Mechanics: Liouville’s Theorem Unlimited
- Lecture 60 – Hamiltonian Mechanics: Poisson Bracket Unlimited
- Lecture 61 – Hamiltonian Mechanics: Canonical Coordinates Unlimited
- Lecture 62 – Hamiltonian Mechanics: Generating Function of Canonical Transformations Unlimited
- Lecture 63 – Hamiltonian Mechanics: Generating Functions of the 4 Kinds Unlimited
- Lecture 64 – Examples of Generating Functions Unlimited
- Lecture 65 – Harmonic Oscillator (Canonical Transformations) Unlimited
- Lecture 66 – Invariance of Poisson Brackets Unlimited
- Lecture 67 – Normal Modes of Triatomic Molecule using Mathematica Unlimited
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