Class Timings: Tuesdays and Thursdays from 1:45 PM - 3:15 PM
First Meeting: 12th August 2025 (Tuesday)
Topics:
1) Recap:
- Recap of Newton's laws and their consequences
- System of point masses, Rigid Bodies
- Classical driven-dissipative systems
2) Lagrangian Formulation:
- Principle of least action
- Noether's Theorem, Symmetries
- Small Oscillations, Applications
3) Rigid body motion:
- Euler Angles
- Tops
4) Hamiltonian formulation:
- Liouville's Theorem
- Action-Angle variables
- Hamilton-Jacobi Equations
5) Classical Integrable Models and Field Theory:
- Lax Pairs
- Toda Model
- Calogero Family of Models
- Integrable Field Theories
- Integrable Partial Differential Equations and applications in physics
- Chaos
Books:
1) Landau Lifshitz course on theoretical physics: Vol 1: Classical Mechanics
2) Classical Mechanics by Herbert Goldstein, Charles P. Poole, John L. Safko
3) Analytical Mechanics by Louis N. Hand, Janet D. Finch
4) Classical integrable finite-dimensional systems related to Lie algebras, M.A. Olshanetsky, A.M.Perelomov, Physics
Reports, Volume 71, Issue 5, May 1981, Pages 313-400
Course Outcome:
- Have a clear understanding of the basic principles of Newtonian mechanics and applications to two body, rigid body
and small oscillation problems. - Understanding of the Lagrangian and Hamiltonian formulations
- Get an exposure to a few advanced topics (this is about 20% of the syllabus and includes topics such as Chaos, Integrability etc.)
- Develop analytical and numerical problem-solving skills.
- Teacher: Manas Kulkarni