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Inflation of Hamiltonian System: The Spinning Top in Projective Space

By Holger R. Dullin


We present a method to enlarge the phase space of a canonical Hamiltonian System in order to remove coordinate singularities arising from a nontrivial topology of the configuration space. This "inflation" preserves the canonical structure of the system and generates new constants of motion that realize the constraints. As a first illustrative example the spherical pendulum is inflated by embedding the sphere S 2 in the three dimensional Euclidean space. The main application which motivated this work is the derivation of a canonical singularity free Hamiltonian for the general spinning top. The configuration space SO(3) is diffeomorphic to the real projective space RP 3 which is embedded in four dimensions using homogenous coordinates. The procedure can be generalized to SO(n). 1 Introduction One of the pillars of classical mechanics is the process of deriving equations of motion via the Lagrangian L. It starts with some "generalized coordinates" on the configuration space Q as des..

Year: 1996
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