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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.
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.
NPTEL-NOC IITM
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