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.

This is an independent re-transcription of the same scans, done from scratch with Claude Opus 5, with every diagram redrawn in TikZ. The earlier version is at Classical Mechanics and Dynamical Systems (Sonnet 5).

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, and Lec 26 is noted in the notebook itself as being written up in a separate mathematics notebook. A later notebook covers Mod 13, Lec 34-36. Split into five pages:

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, the connection with thermodynamics via the partition function, and the van der Waals gas.
4. Lec 27-29 -- phase transitions, Maxwell's equal-area construction, the classical ideal gas partition function, paramagnetism/Curie's law, Weiss molecular field theory and critical exponents.
5. Mod 13, Lec 34-36 -- the rotation group: rotations of the coordinate axes, orthogonality of rotation matrices, proper and improper rotations, generators of infinitesimal rotations in 3-D, the Lie algebra of the generators, \(SU(2)\) and its 2-to-1 map onto \(SO(3)\), the parameter space of \(SO(3)\), and homotopy groups.

The same material, typeset in LaTeX as a single document with all diagrams redrawn:

• Classical Mechanics and Dynamical Systems -- PDF (Lec 13-29, 34-36)

• Analytic Functions of a Complex Variable

Acknowledgements:

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

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