Theoretical Mechanics the complete guide in 2020

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About Course

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 You 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

Course Content

Theoretical Mechanics

  • Theoretical Mechanics [Introduction Video]
    03:03
  • Lec 01: Introduction, Constraints
    44:45
  • Lec 02 : Generalized Coordinates, Configuration Space
    59:55
  • Lec 03 : Principle of Virtual Work
    00:00
  • Lec 04 : D’Alembert’s Principle
    00:00
  • Lec 05 : Lagrange’s Equations
    00:00
  • Lec 6: Hamilton’s Principle
    00:00
  • Lec 7: Variational Calculus, Lagrange’s Equations
    00:00
  • Lec 8: Conservation Laws and Symmetries
    00:00
  • Lec 9: Velocity Dependent Potentials, Non-holonomic Constraints
    00:00
  • Lec 10: An Example: Hoop on a ramp
    00:00
  • Lec 11: Phase Space
    00:00
  • Lec 12: Central Force Problem, Constants of Motion
    00:00
  • Lec 13: Classification of Orbits
    00:00
  • Lec 14: Determining Orbits
    00:00
  • Lec 15: Kepler Problem
    00:00
  • Lec 16: Runge-Lenz Vector, Virial Theorem
    00:00
  • Lec 17: Scattering – I
    00:00
  • Lec 18: Scattering -II
    00:00
  • Lec 19: Rigid Bodies and Generalised Coordinates
    00:00
  • Lec 20: Rotations and Euler Angles
    00:00
  • Lec 21: Rotating Frames
    00:00
  • Lec 22: Instantaneous Angular Velocity
    00:00
  • Lec 23: Moment of Inertia Tensor
    00:00
  • Lec 24: Euler Equations
    00:00
  • Lec 25: Heavy Symmetric Top
    00:00
  • Lec 26: Legendre Transforms
    00:00
  • Lec 27: Hamilton’s Equations
    00:00
  • Lec 28: Conservation Laws, Routh’s procedure
    00:00
  • Lec 29: An Example:Bead on Spinning Ring
    00:00
  • Lec 30: Canonical Transformations
    00:00
  • Lec 31: Symplectic Condition
    00:00
  • Lec 32: Canonical Invariants, Harmonic Oscillator
    00:00
  • Lec 33: Poisson Bracket Formulation
    00:00
  • Lec 34: Infinitesimal Canonical Transformations
    00:00
  • Lec 35: Symmetry Groups of Mechanical Systems
    00:00
  • Lec 36: Hamilton Jacobi Theory
    00:00
  • Lec 37: Action-Angle Variables
    00:00
  • Lec 38: Separation of Variables and Examples
    00:00
  • Lec 39: Small Oscillations
    00:00
  • Lec 40: Coupled Oscillators
    00:00
  • Lec 41: General Formalism
    00:00
  • Lec 42: Double Pendulum
    00:00

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