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

K. Uldall Kristiansen, M. Vereshchagin, K. Go´zdziewski, P. L. Palmer and M. Roberts

 

In this paper we consider the two-body problem of a spherical pseudo rigid body
and a 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 in planar relative equilibria.

 

Paper: Pseudo Rigid Body

Ref: Uldall Kristiansen, K., Vereshchagin, M., Gozdziewski, K., Palmer, P.L. & Roberts, M., J Celestial Mechanics & Dynamical Astronomy, 112 , No 2, pp. 169-190, 2012.

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