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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 02 - Generalized Coordinates and Degrees of Freedom

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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