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Advanced Classical Mechanics
Rating: 4.0 out of 5(3 ratings)
10 students

Advanced Classical Mechanics

Features and Specifications of Updated Classical Mechanics
Last updated 1/2025
English

What you'll learn

  • This content - Advanced Classical Mechanics basically covers Lagrangian and Hamiltonian Dynamics and their applications to analyze several classical systems.
  • Here the discussion starts with particle motion under central force where the force is conservative and always acts in radial sense. The path will be planner.
  • The best application of Central force problem is to the motion of Planet around sun and the motion of a satellite around the planet through energy conservation.
  • After that in this content, the constrained motion is discussed here where the motion of the particle or system of particles is restricted by a few conditions.

Course content

1 section30 lectures5h 26m total length
  • Introduction3:11
  • 1. Central Force and Characteristics20:53
  • 2. Equation of Orbit under Central Force17:49
  • 3. Energy Conversion under Central Force18:56
  • 4. Eliptic Orbit of a Planet17:15
  • 5. Total Energy of Planet19:44
  • 6. Orbit of Satellite19:49
  • 7. Types of Orbit of Satellite Motion22:24
  • 8. Runge Lenz Vector in Central Force17:34
  • 9. Motion along Cardioid13:37
  • 10. Concept of Constrained Motion21:41
  • 11. Idea About Constrained Motion12:52
  • 12. Concept of Force of Constraint4:51
  • 13. D'Alambert's Principle5:28
  • 14. Degree of Freedom and Generalised Coordinate10:46
  • 15. Generalised Velocity and Acceleration6:19
  • 16. Idea of Generalized Momentum11:23
  • 17. Idea of Generalized Force4:49
  • 18. General Derivation of Lagrange's Equation of Motion7:23
  • 19. Cyclic or Ignorable Coordinates4:49
  • 20. Conversion of Lagrange's Equation of First Kind to Lagrange's Equation3:15
  • 21. Lagrange's Equation of Second Kind9:32
  • 22. Lagrange's Equation of First Kind for Conservative System4:44
  • 23. Lagrange's Equation from D'Alambert's Principle8:32
  • 24. Application of Lagrangian Mechanics to Oscillation of Simple Pendulum4:40
  • 25. Application of Lagrangian Mechanics to Oscillation of Compound Pendulum5:14
  • 26. Application of Lagrangian Dynamics to Spherical Pendulum7:38
  • 27. Application of Lagrangian Dynamics to Single Atwood's Machine6:17
  • 28. Application of Lagrangian Mechanics to Particle Motion7:16
  • 29. Hamilton's Variational Principle7:27

Requirements

  • This content of Advances Classical Mechanics is basically a total discussion on Motion under central force, Constrained motion and the Lagrangian and Hamiltonian dynamics.

Description

In this content - Advanced Classical Mechanics, we have started our discussion with particle motion under central force. This central force is a conservative irrotational force which always acts along the radial sense and it may be attractive or repulsive. Under action of this central force, the motion of the particle will become confined in a plane and the orbit of the particle must lie in two dimension. The motion will be restricted with energy and angular momentum conservation and here the best application of such central force problem is on the motion of planet and satellite.

After that we have discussed the features of constrained motion where the motion is restricted by at least one or more than one condition or restriction. For such constrained motion, the corresponding constraint will be hold by the force of constraint which is itself no work force. Here a several conservative holonomic systems are made analyzed in this constrained motion.

On the other hand, in this content, we have discussed the basic concept of Calculus of Variation as given by Euler and the concept is fully applied to the second generation of Classical Mechanics, known as Lagrangian Dynamics through the concept of Lagrangian of a holonomic conservative system by proper use of generalized coordinates and other generalized parameters.  Lagrange's equation of both 1st and 2nd kind are made developed in several way and then is applied to several conservative holonomic system.

At the end of this content, the Hamiltonian of the system is made defined through Legendre dual transformation and after that Hamilton's canonical equations of Hamiltonian dynamics which is specifically 3rd generation of Classical Mechanics are obtained from basic characteristics of Hamiltonian and finally these canonical equations are made applied for analyzing several conservative systems. 

Who this course is for:

  • This content is surely an advancement of basic classical mechanics and it enriches the knowledge on classical dynamics.