Motion On the Sphere: Integrability and Families of Orbits |
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Authors: | Despina Voyatzi Simos Ichtiaroglou |
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Institution: | (1) Physics Department, University of Thessaloniki, Thessaloniki, 54124, Greece |
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Abstract: | We study the problem of the motion of a unit mass on the unit sphere
and examine the relation between integrability and certain monoparametric families of orbits. In particular we show that
if the potential is compatible with a family of meridians, it is integrable with an integral linear in the velocities, while
a family of parallels guarantees integrability with an integral quadratic in the velocities. |
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Keywords: | motion on the sphere integrability inverse problem |
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