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Belford, R. Linn Burkhardt, Paul 2015-09-25T22:13:11Z 2015-09-25T22:13:11Z 10000-01-01 2004 2004 Symplectic integrators are well known for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. There is a general operator splitting method for developing explicit symplectic integration algorithms to any arbitrary even order for separable Hamiltonians where the position and momentum coordinates are uncoupled. Explicit symplectic integrators for general Hamiltonians are more difficult to obtain, but can be developed by a composition of symplectic maps if the Hamiltonian can be split into exactly integrable parts. No general technique exists for splitting any Hamiltonian of general form. Many three body problems in classical mechanics can be effectively investigated in symmetrized, hyperspherical polar coordinates, but the Hamiltonian expressed in these coordinates is non-separable. In molecular dynamics, the hyperspherical coordinates facilitate the validation and visualization of potential energy surfaces and for quantum reactive scattering problems, the coordinates eliminate the need for adjusting the wavefunction between product and reactant channels. An explicit symplectic integrator for hyperspherical coordinates has not yet been devised. This dissertation presents an explicit, multi-map symmetrized composition method symplectic integrator for three-body Hamiltonians in symmetrized, hyperspherical polar coordinates, specifically for classical trajectory studies in the plane. Made available in DSpace on 2015-09-25T22:13:11Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3153258.pdf: 10198369 bytes, checksum: 967da41b0aaa58ec7ccca5ada0ca30f3 (MD5) Previous issue date: 2004 Embargo set by: Seth Robbins for item 85427 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 277 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004. http://hdl.handle.net/2142/84146 (MiAaPQ)AAI3153258 eng Chemistry, Physical Explicit, Multi-Map Symplectic Integrator for Three -Body Classical Trajectory Studies in Hyperspherical Coordinates text Chemistry Chemistry University of Illinois at Urbana-Champaign Dissertation Ph.D.