Mathematical Methods of Classical Mechanics
by Vladimir I. Arnold · Vladimir I. Arnold
Graduate text recasting Newtonian, Lagrangian and Hamiltonian mechanics in the language of differential geometry: manifolds, symplectic forms, canonical transformations and perturbation theory. Readers come to understand classical mechanics as geometry of phase space and can follow modern work in dynamical systems.
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Free graduate-level online textbook led by Predrag Cvitanović at Georgia Tech, with accompanying video lectures. It develops periodic-orbit theory and cycle expansions, teaching readers to compute averages, escape rates and spectra of chaotic deterministic and quantum systems from their unstable periodic orbits.
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Scholarpedia - Hamiltonian Systems
Peer-reviewed encyclopedia article by James Meiss covering Hamilton's equations, symplectic structure, canonical transformations, integrability, action-angle variables, and the onset of chaos through KAM theory. Readers gain a compact map of the theory of Hamiltonian dynamics and its main results.