The limits of my language define the limits of my world. – Ludwig Wittgenstein
Venue: Physics Auditorium, Department of Physics
Time: Tuesdays & Thursdays 1130-1300
Required textbooks:
- (RJ) Classical Mechanics, Rana and Joag, McGraw Hill
- (LL) Mechanics, Landau and Lifshitz, Elsevier, 3e
Required and Optional readings will be assigned before the class. You should finish reading the “required reading” before the class. If you have any specific questions, post them on the MS Teams page the night before the class.
MS Teams Link (Requires IISc login)
| Class ID | Class date (DDMMYY) | Topic | Reading | Other resources |
|---|---|---|---|---|
| 1 | 01-08-24 | Review of Newtonian Mechanics; Constraints; Lagrange's Eqn of 1st Kind; Principle of Virtual Work; | Required: RJ: I.5, I.6, 1.0-1.7 Optional: RJ I.1-I.4 | |
| 2 | 08-08-24 | Degrees of Freedom; Generalized coordinates; Lagrangian; Lagrange's Equation; Hamilton's least action principle; Derivation of EL equation | Required: RJ: 2.1-2.4, 6.1, 6.2, 6.4 Optional: 2.0, 6.3 | |
| 3 | 13-08-24 | Generalized Dynamic Variables; Symmetry and Conservation Laws; Derivation of Newton's laws. | Required: RJ: 2.9-2.15 Supplementary: LL Ch II, Section 6-9 | |
| 4 | 20-08-24 | Lagrangian in various coordinate systems; Properties of T and E; Gyroscopic forces and generalized potential; | Required: RJ: 2.5-2.8, 2.16 | |
| 5 | 22-08-24 | Solution of EoM in 1D; Mechanical Similarity; Virial Theorem; 2-body Central force problem; | Required: RJ: 4.1-4.2, 4.6.1, 4.7 Required: LL: Ch II Section 10 | |
| 6 | 27-08-24 | Equation of orbits; Condition for closure of orbits; Kepler's problem; Deriving Newton's law of gravitation from Kepler's laws; Tides | Required: RJ: 4.3-4.5, 4.6.1, 4.7, 4.14 | |
| 7 | 29-08-24 | Scattering in central force fields; Scattering Cross Section; Impact parameter; Small oscillation introduction; Fourier transform; | Required: RJ 4.15 LL: Chapter IV Section 17-20 | V. Balakrishnan's lectures on Fourier Transform : Fourier Transform I Fourier Transform II Fourier Transform III |
| 8 | 03-09-24 | Forced oscillation; Resonance; Energy spectral density; Normal modes; Characteristic Equation; Spring-Mass systems | Required: LL Ch V Section 21-23 | |
| 9 | 05-09-24 | Damped Oscillation; Motion in a rapidly oscillating field; Introduction to Rigid Body Dynamics; | Required: LL Ch V 25-26, 30 | |
| 10 | 10-09-24 | Space frame and body frames; Invariance of the angular velocity; Kinetic energy; Moment of inertia tensor | Required: RJ 12.1, 12.3, 12.5-12.7 | |
| 11 | 12-09-24 | Doubt clearing session; Angular momentum | Required: RJ 12.4, 12.8, 12.9 | |
| 12 | 17-09-24 | Rigid body kinetics; Direction cosine; Euler angles; Euler theorem; Charles theorem | Required: Goldstein Ch 4. Note: Goldstein has the best discussion on RB kinetics. I found the discussion in RJ and LL inadequate. | |
| 13 | 19-09-24 | Mid-term exam | ||
| 14 | 24-09-24 | Space frame to body frame; Coriolis force; Euler's equation; Symmetric top; | Required: RJ: 3.1-3.4, 12.10-12.14, 12.18 Optional: Goldstein: Ch 4 | |
| 15 | 26-09-24 | Hamiltonian; Hamilton's equations; Phase space; Configuration space; State space; Poisson Bracket | Required: RJ 5.1-5.3, 5.5, 6.5, 9.1-9.4 | |
| 16 | 01-10-24 | Hamilton's principal function; Noether's theorem; Canonical transformation; | Required: RJ 6.7-6.8, 8.1-8.5 | |
| 17 | 03-10-24 | Properties of the Poisson Bracket; Liouville's theorem | Required: RJ 8.6-8.7, 9.5-9.8 | |
| 18 | 15-10-24 | Nonlinear Dynamics Intro; Flows in 1D | NLD-1 | |
| 19 | 17-10-24 | Class cancelled. | ||
| 19 | 22-10-24 | Numerical Methods 101; Bifurcation in 1D flows. | NLD-2 | |
| 20 | 23-10-24 | Bifurcation in 1D; Synchronization | NLD-3 Firefly Model | |
| 21 | 24-10-24 | Linear Systems; 2D Flow; Classification of 2D fixed points. | NLD-4 | |
| 22 | 29-10-24 | Perils of Linear Stability Analysis; Limit cycle; Hopf bifurcations; Index theory. | NLD-5 | |
| 23 | 05-11-24 | Index theory contd; How to rule out limit cycles; Nullclines; Poincare-Bendixson Theorem | NLD-6 | |
| 24 | 07-11-24 | Lorenz Equation; Chaos; Strange attractor; Discrete maps; Period doubling route to chaos; Fractals | NLD-7 | |
| 25 | 12-11-24 | |||
| 26 | 14-11-24 |