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Theoretical Mechanics the complete guide in 2020

  • Course level: Beginner
  • Categories C-Science
  • Last Update 24/06/2021

Description

Theoretical Mechanics the complete guide in 2020.

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.

INTENDED AUDIENCE: First year of MSc or 2nd and 3rd year of BE/BTech in Engg Physics

What Will I Learn?

  • Week 1: Motion and Constraints, Generalized Coordinates, D’Alembert’s Principle of Virtual Work
  • Week 2: Variational Calculus, Hamilton’s Principle, Lagrangian Formulation.
  • Week 3: Application of Lagrangian Formulation, Configuration Space and Phase Space.
  • Week 4: Hamilton’s Equations of Motion
  • Week 5: Cannonical Transformations, Cannonical invariants, Symplectic Approach to CT.
  • Week 6: Poisson Bracket Formulation, Symmetry groups of Mechanical Systems, Liouville’s Theorem
  • Week 7: Hamilton Jacobi Theory, Hamilton’s Principal Function, Action-Angle variables.
  • Week 8: Lagrangian and Hamiltonian Formulation for Continuous Systems and Fields.
  • Week 9: CanonicalTransformations
  • Week 10:Poisson Bracket Formulation
  • Week 11:Hamilton-Jacobi Theory
  • Week 12:Chaos

Topics for this course

43 Lessons

Theoretical Mechanics

Theoretical Mechanics [Introduction Video]3:03
Lec 01: Introduction, Constraints44:45
Lec 02 : Generalized Coordinates, Configuration Space59:55
Lec 03 : Principle of Virtual Work00:00:00
Lec 04 : D’Alembert’s Principle00:00:00
Lec 05 : Lagrange’s Equations00:00:00
Lec 6: Hamilton’s Principle00:00:00
Lec 7: Variational Calculus, Lagrange’s Equations00:00:00
Lec 8: Conservation Laws and Symmetries00:00:00
Lec 9: Velocity Dependent Potentials, Non-holonomic Constraints00:00:00
Lec 10: An Example: Hoop on a ramp00:00:00
Lec 11: Phase Space00:00:00
Lec 12: Central Force Problem, Constants of Motion00:00:00
Lec 13: Classification of Orbits00:00:00
Lec 14: Determining Orbits00:00:00
Lec 15: Kepler Problem00:00:00
Lec 16: Runge-Lenz Vector, Virial Theorem00:00:00
Lec 17: Scattering – I00:00:00
Lec 18: Scattering -II00:00:00
Lec 19: Rigid Bodies and Generalised Coordinates00:00:00
Lec 20: Rotations and Euler Angles00:00:00
Lec 21: Rotating Frames00:00:00
Lec 22: Instantaneous Angular Velocity00:00:00
Lec 23: Moment of Inertia Tensor00:00:00
Lec 24: Euler Equations00:00:00
Lec 25: Heavy Symmetric Top00:00:00
Lec 26: Legendre Transforms00:00:00
Lec 27: Hamilton’s Equations00:00:00
Lec 28: Conservation Laws, Routh’s procedure00:00:00
Lec 29: An Example:Bead on Spinning Ring00:00:00
Lec 30: Canonical Transformations00:00:00
Lec 31: Symplectic Condition00:00:00
Lec 32: Canonical Invariants, Harmonic Oscillator00:00:00
Lec 33: Poisson Bracket Formulation00:00:00
Lec 34: Infinitesimal Canonical Transformations00:00:00
Lec 35: Symmetry Groups of Mechanical Systems00:00:00
Lec 36: Hamilton Jacobi Theory00:00:00
Lec 37: Action-Angle Variables00:00:00
Lec 38: Separation of Variables and Examples00:00:00
Lec 39: Small Oscillations00:00:00
Lec 40: Coupled Oscillators00:00:00
Lec 41: General Formalism00:00:00
Lec 42: Double Pendulum00:00:00
Theoretical Mechanics
Free

Enrolment validity: Lifetime

Requirements

  • Introduction to Newtonian Mechanics is desired.