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The equations of classical spin-orbit motion can be extended to a Hamiltoniansystem in 9-dimensional phase space by introducing a coupled spin-orbit Poissonbracket and a Hamiltonian function. After this extension and by establishingconnections between initial and extended systems it becomes possible to applythe methods of the theory of Hamiltonian systems to the study of polarizedparticle beam dynamics in circular accelerators and storage rings. Some ofthose methods have been implemented in the computer code FORGET-ME-NOT.Comment: 103 pages. Latex. No figure

Hamiltonian methods for the study of polarized proton beam dynamics in accelerators and storage rings