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Theoretical Mechanics

Theoretical Mechanics. Instructor: Prof. Charudatt Kadolkar, Department of Physics, IIT Guwahati. This course focuses on analytical aspects of classical mechanics and is targeted towards the audience who are interested in pursuing research in Physics. Various formulations of mechanics, like the Lagrangian formulation, the Hamiltonian formulation, the Poisson bracket formulation will be taught in the course. The course also introduces the mechanics of continuous systems and fields. (from nptel.ac.in)

Lecture 37 - Action-Angle Variables


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Lecture 01 - Introduction
Lecture 02 - Generalized Coordinates, Configuration Space
Lecture 03 - Principle of Virtual Work
Lecture 04 - D'Alembert's Principle
Lecture 05 - Lagrange's Equations
Lecture 06 - Hamilton's Principle
Lecture 07 - Variational Calculus, Lagrange's Equations
Lecture 08 - Conservation Laws and Symmetries
Lecture 09 - Velocity Dependent Potentials, Non-holonomic Constraints
Lecture 10 - An Example: Hoop on a Ramp
Lecture 11 - Phase Space
Lecture 12 - Central Force Problem, Constants of Motion
Lecture 13 - Classification of Orbits
Lecture 14 - Determining Orbits
Lecture 15 - Kepler Problem
Lecture 16 - Runge-Lenz Vector, Virial Theorem
Lecture 17 - Scattering
Lecture 18 - Scattering (cont.)
Lecture 19 - Rigid Bodies and Generalized Coordinates
Lecture 20 - Rotations and Euler Angles
Lecture 21 - Rotating Frames
Lecture 22 - Instantaneous Angular Velocity
Lecture 23 - Moment of Inertia Tensor
Lecture 24 - Euler Equations
Lecture 25 - Heavy Symmetric Top
Lecture 26 - Legendre Transforms
Lecture 27 - Hamilton's Equations
Lecture 28 - Conservation Laws, Routh's Procedure
Lecture 29 - An Example: Bead on Spinning Ring
Lecture 30 - Canonical Transformations
Lecture 31 - Symplectic Condition
Lecture 32 - Canonical Invariants, Harmonic Oscillator
Lecture 33 - Poisson Bracket Formulation
Lecture 34 - Infinitesimal Canonical Transformations
Lecture 35 - Symmetry Groups of Mechanical Systems
Lecture 36 - Hamilton Jacobi Theory
Lecture 37 - Action-Angle Variables
Lecture 38 - Separation of Variables and Examples
Lecture 39 - Small Oscillations
Lecture 40 - Coupled Oscillators
Lecture 41 - General Formalism
Lecture 42 - Double Pendulum