B10
Course Coordinator: 
Mahesh Bandi
Analytical Mechanics
Description: 

Mastery of the concepts and techniques of analytical mechanics is essential to a deep understanding of physics. This course begins with basic principles and proceeds to the Newtonian equations of motion and laws of conservation. We use the Lagrange formalism to describe particle motion in multiple modes, before covering the equations of Euler and Hamilton, and canonical transformations. The calculus of variation is used to develop Maupertuis’s principle and the Hamilton-Jacobi equations, providing a starting point for the consideration of waves in later courses. This course is taught from the unifying principles of symmetry and least action.

Aim: 
Covers the fundamental theories of classical mechanics, and provides a firm grounding for later studies of fluid dynamics and quantum physics.
Detailed Syllabus: 
  1. The Principle of Least Action
  2. Equations of Motion: Galileo and Lagrange
  3. Equations of Motion: Newton
  4. Conservation Laws: Energy, Momentum, and Angular Momentum
  5. Integration of Equations of Motion
  6. Breakup, Collision, and Scattering of Particles
  7. Harmonic Oscillations: Free, Forced, and Damped Oscillations, Resonance
  8. Rigid Body Dynamics: Angular Velocity, Inertia Tensor, Angular Momentum
  9. Equations of Motion for Rigid Body
  10. Euler's Equations
  11. Dynamics of Rigid Bodies in Contact
  12. Hamilton's Equations
  13. Maupertuis' Principle
  14. Canonical Transformations and Liouville's Theorem
  15. Hamilton-Jacobi Equations
Course Type: 
Elective
Credits: 
2
Assessment: 
Homework Assignments, 20%. Midterm written tests, 2 x 25%; Final written test, 30%.
Text Book: 
Mechanics, 4 edn, by Landau and Lifshitz (1976) Butterworth-Heinemann
Classical Mechanics, 3 edn, by Goldstein, Poole, and Safko (2001) Addison Wesley
Reference Book: 
The Variational Principles of Mechanics, 4 edn, Cornelius Lancoz (1970) Dover
The Feynman Lectures on Physics including Feynman's Tips on Physics: The Definitive and Extended Edition, 2 edn, by RP Feynman with Robert B. Leighton et al., editors (2005) Addison Wesley