Handwritten lecture notes from V. Balakrishnan's classical mechanics course, transcribed from the original notebook scans. The course covers dynamical symmetry and Hamiltonian mechanics before moving into chaos/nonlinear dynamics and, in its later lectures, equilibrium statistical mechanics and thermodynamics.

Video lectures: Classical Mechanics by Prof. Balakrishnan (YouTube playlist).

The scanned notebook covers Lec 13 through Lec 29 (Lec 18-19 are not present in the scans), split into four pages of four lectures each:

1. Lec 13-16 -- Noether's theorem, dynamical symmetry, canonical transformations, symplectic matrices, \(SU(2)\)/\(SU(N)\), the Kepler problem and the Laplace-Runge-Lenz vector, the bead-on-a-rotating-hoop problem, and randomness in phase space (ergodicity, mixing, Liapunov exponents).
2. Lec 17-22 -- one-dimensional maps, Baker's map, Arnold's cat map, the Gauss (continued-fraction) map, then the transition into classical statistical mechanics: microstates/macrostates, the postulate of equal a priori probabilities, the microcanonical ensemble, and the binomial/Poisson/Gaussian distributions.
3. Lec 23-26 -- temperature and entropy from \(\Omega(E)\), thermodynamic potentials and Legendre transforms, response functions, and the van der Waals gas.
4. Lec 27-29 -- phase transitions, the classical ideal gas partition function, and paramagnetism/Curie's law.

The same material, typeset in LaTeX with all diagrams redrawn, is also available as two PDFs (split roughly at the point the lectures turn from mechanics to statistical mechanics):

• Classical Mechanics and Dynamical Systems -- PDF (Lec 13-19)
• Thermodynamics and Statistical Mechanics -- PDF (Lec 20-29)

Acknowledgements:

All these html and tex files are created by use of Anthropic's Claude AI using sonnet 5 with max usage.

For any discrepancies, please refer to the original lectures on youtube or my handwritten notes.