Abstract
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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Kristiansen, K.U., Vereshchagin, M., Goździewski, K. et al. The two-body problem of a pseudo-rigid body and a rigid sphere. Celest Mech Dyn Astr 112, 169–190 (2012). https://doi.org/10.1007/s10569-011-9390-y
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DOI: https://doi.org/10.1007/s10569-011-9390-y