2003/10/31 by Thomas F. Jordan · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Canonical coordinates #Covariant Hamiltonian field theory #Hamiltonian (control theory) #Hamiltonian mechanics #Hamiltonian system #Homotopy and Cohomology in Algebraic Topology #Integrable system #Nonlinear Waves and Solitons #Poisson bracket #Superintegrable Hamiltonian system #physics.class-ph #physics.ed-ph
paper · pdf · doi:10.1119/1.1737394
published as Am. J. Phys. 72, 1095 (2004) · 15 pages, 2 figures, submitted to American Journal of Physics, refereed, revised, recommended for publication by referee
arxiv created 2003/12/09 · openalex publication_date 2004/07/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Easy steps through essential Hamiltonian dynamics are outlined, from necessary definitions of Poisson brackets and canonical transformations, to a quick proof that Hamiltonian evolution is made by canonical transformations, the quickest proof of Liouville’s theorem, and on to the Poincaré-Cartan integral invariants and completely integrable dynamics, making room and providing tools for more recent developments.