Innation 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 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 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 connguration space SO(3) is diieomorphic to the real projective space RP 3 which is embedded in four dimensions using homogenous coordinates. The procedure can be generalized to SO(n).
منابع مشابه
Inflation 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 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 embedd...
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