Classical Mechanics (2025)

Administrivia

Time: Tu, Th at 530pm; Tutorial on Fridays at 530pm

Venue: AG69 + Zoom (link on Moodle page) ; Tutorials in AG80

First lecture: 26 Aug

Credit policy: Tutorials (30%) + Midterm (30%) + Endterm (40%)

Instructor: Basudeb Dasgupta

Tutors: Aditya Dwivedi and Aaghaz Mahajan

Course Webpage: Moodle [TIFR only]

Lecture Notes: Link in Moodle [TIFR only]

Course Contents

1. Recap of Newtonian Mechanics and Fundamentals

2. Lagrangian Mechanics

3. Rigid Bodies, Central force, Scattering, and Oscillations

4. Hamiltonian Mechanics

References

1. Goldstein (or later editions): Classic text. Still hard to beat.

2. Landau and Lifshitz Vol.1: Slim but packed. Best treatment of oscillations.

3. Rana and Joag: Has a very good discussion throughout, and has excellent examples on biomechanics, Can be used as an alternative to Goldstein.

4. Jose and Saletan: If you'd like the language of differential geometry, it is a nice self-study book.

5. Arnol'd: More advanced. Useful for specific topics.

6. Lecture notes by David Tong (Cambridge): Very accessible. The new "Theoretical Minimum".

Problem Sets

PS1 (Newtonian Mechanics and Fundamentals): assigned on 02/09 on Moodle

PS2 (Variational Calculus and Lagrangian Mechanics): assigned on 18/09 on Moodle

PS3 (Central Force, Oscillations, Rigid Body): assigned on 1/11 on Moodle

PS4 (Hamiltonian Mechanics): assigned on 11/11 on Moodle

Exams

1. Midterm on 16 Oct (4-7pm) 

2. Endterm on 11 Dec  (9am-1pm)

Lecture Summaries

 Lecture 1 (26 Aug)

• Newton's miracle

• F=ma in noninertial frames

• Counting DoFs

• Integrating out DoFs

Lecture 2 (2 Sep)

• Why Classical Mechanics?

• Newton's 2nd and 1st Laws

• Conservation of P, L, E, & role of conservative forces

• Many particles : Conservation of P, L, E, & role of 3rd Law (weak and strong form) and conservative forces

• What about 3-body forces? Stronger form of 3rd Law needed?

Lecture 3 (9 Sep)

• How to count DoFs?

• Constraints: Types, Examples (Rolling without Slipping)

Lecture 4 (11 Sep)

• From Static Eqbm to D'Alembert's Principle: Virtual Displacement and Virtual Work, eliminating (conservative) constraint forces

• Generalized Coordinates to eliminate constraints

• Euler-Lagrange Eqns.

• Generalized/Velocity-dep Potential

Lecture 5 (16 Sep)

• Symmetry, Lagrangian, Action

• E-L equations

Lecture 6 (18 Sep)

• Properties of E-L equations

• Symmetries and Conservation Laws (Noether's Thm.)

Lecture 7 (23 Sep)

• Examples of Conservation Laws

• Simple examples

Lecture 8 (25 Sep)

• 1d potential problems

• Turning points

• Time period of oscillations

• Inverse problem of computing V(x), given T(E)

• Geodesic equation

Lecture 9 (7 Oct)

• Central Force: 2 bodies -> 1 body

• Conserved qtys

• 1d effective potential

• Binet equation for general F(r); Conics for Kepler

• Perturbations and stability of circular orbits for F(r)

Lecture 10 (9 Oct) 

• Commensurability and Bertrand's theorem

• Rosette orbits

• Runge-Lenz-Laplace vector

• Scattering in central potential

Lecture 11 (11 Oct)

• Why harmonic potential is generic at minima of V(x)

• Normal modes for multi-d oscillators

• Forced-Damped

Midterm Exam (16 Oct)

Lecture 12 (17 Oct)

• Anharmonic + Poincare-Lindstedt Perturbation Theory

• Parametric resonance

• Effective potential in a fast-oscillating field

Lecture 13 (28 Oct)

• Rigid Body Theory

Lecture 14 (30 Oct)

• Free Tops: Spin, Precession, Nutation

• Free Precession

• Intermediate Axis Thm.

Lecture 15 (4 Nov)

• Euler equations

• Wobble of a Disk

• Poinsot Construction

• Heavy Top

Lecture 16 (6 Nov): 

• Legendre Transform

• Hamilton's Eqn.

Lecture 17 (11 Nov)

• Poisson Brackets

• Similarity to Quantum Mechanical Commutators 

Lecture 18 (13 Nov): Class cancelled

Lecture 19 (18 Nov)

• Canonical Transformations

• Symmetries generated by CTs

Lecture 20 (20 Nov) 

• Generating functions for CTs

Lecture 21 (25 Nov)

• Action-Angle variables

Lecture 22 (27 Nov) 

• Comments on: Bohr-Sommerfeld condition

• Hannay's Angle (Geometric Phases)

Lecture 23 (2 Dec)

• Hamilton-Jacobi Theory

Lecture 24 (4 Dec)

• Road to Quantum Mechanics

Endterm Exam (11 Dec)