Introduction to Classical Mechanics
Introduction to Classical Mechanics. Instructor: Prof. Anurag Tripathi, Department of Physics, IIT Hyderabad. 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 )

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