Motion On the Sphere: Integrability and Families of Orbits

Details Motion On the Sphere: Integrability and Families of Orbits Motion On the Sphere: Integrability and Families of Orbits

Sep 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cemda..93..331v&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 93, Issue 1-4, pp. 331-342

Astronomy and Astrophysics

Astronomy

6

Motion On The Sphere, Integrability, Inverse Problem

Scientific paper

We study the problem of the motion of a unit mass on the unit sphere {mathbb S}^2 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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