Inflation of Hamiltonian System: The Spinning Top in Projective Space
نویسنده
چکیده
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 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 which is embedded in four dimensions using homogenous coordinates. The procedure can be generalized to SO(n).
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Innation of Hamiltonian System: the Spinning Top in Projective Space
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 connguration space. This \innation" preserves the canonical structure of the system and generates new constants of motion that realize the constraints. As a rst illustrative example the spherical pendulum is innated by embedding t...
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