Overview

COURSE OUTLINE: This introductory course on Classical Mechanics covers the following topics: Euler Lagrange Equations, Small Oscillations, Central Force Problem, Rigid Body Motion.

ABOUT INSTRUCTOR: Dr. Anurag Tripathi is an Assistant Professor in the Department of Physics at IIT Hyderabad since 2015 and his area of research is Theoretical High Energy Physics.

Syllabus

Introduction to Classical Mechanics - Course Introduction.
Classical Mechanics: L1: Introduction. Symmetries of space and time..
Cassical Mechanics: L2: Generalized coordinates and degrees of freedom.
Classical Mechanics: L3: Virtual Work.
Classical Mechanics: L4: Virtual Work (rigid body).
Classical Mechanics: L5: d'Alembert Principle.
Classical Mechanics: L6: Euler Lagrange Equation for a holonomic system.
Classical Mechanics: L7: Euler Lagrange Equations. Examples.
Classical Mechanics: L8: Euler Lagrange Equations. Examples continued.
Classical Mechanics: L9: Properties of Lagrangian.
Classical Mechanics: L10: Kinetic term in generalized coordinates.
Classical Mechanics: L11: Cyclic coordinates.
Classical Mechanics: L12: Conservation laws -Conservation of Energy.
Classical Mechanics: L13: Energy Function, Jacobi's Integral.
Classical Mechanics: L14: Momemtum conservation.
Classical Mechanics: L15: Matrices and all that.
Classical Mechanics: L16: Matrices, Forms, and all that.
Classical Mechanics: L17: Principal axis transformation.
Classical Mechanics: L18: Small Oscilaltions.
Classical Mechanics: L19: Oscillations, Normal Coordinates.
Classical Mechanics: L20: Oscillations, Triatomic molecule.
Classical Mechanics: L21: Triatomic molecule normal coordinates.
Classical Mechanics: L22: Coupled pendulums, normal modes.
Classical Mechanics: L23: Coupled pendulums, Beats.
Classical Mechanics: L24: Oscillations, General solution.
Classical Mechanics: L25: Forced oscillations.
Classical Mechanics: L26: Damped oscillations.
Classical Mechanics: L27: Forced Damped oscillations.
Classical Mechanics: L28: one dimensional systems.
Classical Mechanics: L29: Two-body problem.
Classical Mechanics: L30: Two-body problem, Kepler's second law.
Classical Mecahnics: L31: Two-body problem, Kepler problem.
"Classical Mecahnics: L31: Two-body problem, Conic Sections in Polar Coordinates".
Classical Mechanics: Two-body problem, Ellipse in polar coordinates.
Orbits in Kepler Problem.
Apsidal distances, eccentricity of orbits.
Kepler's Third law; Laplace-Runge-Lenz vector.
Rigid Body, degrees of freedom.
Rigid Body, Transfromation matrix.
Rigid Body, Euler Angles.
Parameterization using Euler Angles.
Rigid Body, Euler's Theorem.
General motion of a rigid body.
Moment of Inertial Tensor.
Principal Moments.
Langrangian of a rigid body.
Motion of a free symmetric top.
Angular velocity using Euler angles.
Lagrangian of a heavy symmetric top.
Classical Mechanics: First integrals of a heavy symmetric top.
Classical Mechanics: Nutation and Precission of a heavy symmetric top.
Sleeping Top.
Rotating Frames. Euler Equations.
Calculus of Variations: Functionals.
Method of Lagrange Multipliers.
Calculus of Variations: Condition for extremum.
Calculus of Variations: Several variables.
Cartesian Tensors.
Hamiltonian Mechanics: Hamilton's equations of motion.
Hamiltonian Mechanics: Liouville's theorem.
Hamiltonian Mechanics: Poisson Bracket.
Hamiltonian Mechanics: Canonical Coordinates.
Hamiltonian Mechanics: Generating Function of Canonical Transformations.
Hamiltonian Mechanics: Generating functions of the 4 kinds.
Examples of Generating Functions.
Harmonic Oscillator (Canonical Transformations).
Invariance of Poisson Brackets.
Normal modes of triatomic molecule using Mathematica.