Advanced Classical Mechanics - Core (PHY204.5)

Venue: Chern Lecture Hall

Class Timings: Mondays & Wednesdays from 9:45 AM - 11:15 AM

First Meeting: 7 August 2024

Course Description: A quick recap of Newtonian dynamics, Lagrangian formulation, Noether's theorem, Central force problems, Linear oscillations, Rigid body dynamics,  Hamiltonian formulation, Symplectic geometry, Poisson brackets, Canonical transformations, Hamilton-Jacobi methods, Action-angle variables, Integrability, Chaos, and Nonlinear-dynamics, Classical field theory

Course Syllabus:
1. Central force problems (2-body and 3-body problems): 
2. Lagrangian and Hamiltonian formulation of classical mechanics; 
3. Poisson brackets and symplectic structure; Hamilton Jacobi theory 
4. Rigid body motion 
5. Small oscillations 
6. Dynamical systems, fixed point analysis 
7. Integrability, Chaos, and Nonlinear-dynamics

References: 

1. Classical Dynamics: A Contemporary Approach, J V Jose and E J Saletan (1998)
2. Mathematical Methods of Classical Mechanics (2 ed), V I Arnold (1989)
3. A Student’s Guide to Analytical Mechanics, J L Bohn (2018)
4. No-Nonsense Classical Mechanics, J Schwichtenberg (2020)
5. Mechanics (3 ed), L D Landau and E M Lifshitz (1982)

Course Outcome: 

1. Have a clear understanding of the basic principles of Newtonian mechanics and applications to two body, rigid body and small oscillation problems. 
2. Understanding of the  Lagrangian and Hamiltonian formulations
   
3. Get an exposure to a few advanced topics (this is about 20% of the syllabus and includes topics such as three-body problems, Chaos, Integrability etc.)
   
4. Develop analytical and numerical problem-solving skills.