The two-body problem of a pseudo-rigid body and a rigid sphere

Details The two-body problem of a pseudo-rigid body and a rigid sphere The two-body problem of a pseudo-rigid body and a rigid sphere

Feb 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012cemda.112..169k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 112, Issue 2, pp.169-190

Astronomy and Astrophysics

Astronomy

Full Two-Body Problem, Symmetry Reduction, Pseudo-Rigid/Affine Bodies, Riemann Theorem

Scientific paper

In this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational and "re-labelling" symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann's theorem on pseudo-rigid bodies has an extension to this system for planar relative equilibria.

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