@misc{10481/77200,
year = {2022},
month = {9},
url = {https://hdl.handle.net/10481/77200},
abstract = {We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual
gravitational influence. We assume that the spin axis of each ellipsoid coincides with
its shortest physical axis and is perpendicular to the orbital plane. Due to such assumptions,
the problem is planar and depends on particular parameters of the ellipsoids,
most notably, the equatorial oblateness and the flattening with respect to the shortest
physical axes. We consider two models for such configuration: while in the full
model, there is a coupling between the orbital and rotational motions, in the Keplerian
model, the centers ofmass of the bodies are constrained to move on coplanarKeplerian
ellipses. The Keplerian case, in the approximation that includes the coupling between
the spins of the two ellipsoids, is what we call spin–spin problem, that is a generalization
of the classical spin–orbit problem. In this paper we continue the investigations of
Misquero (Nonlinearity 34:2191–2219, 2021) on the spin–spin problem by comparing it with the spin–orbit problem and also with the fullmodel. Beside detailing the models
associated to the spin–orbit and spin–spin problems, we introduce the notions of standard
and balanced resonances, which lead us to investigate the existence of periodic
and quasi-periodic solutions.We also give a qualitative description of the phase space
and provide results on the linear stability of solutions for the spin–orbit and spin–spin
problems.We conclude by providing a comparison between the full and the Keplerian
models with particular reference to the interaction between the rotational and orbital
motions.},
organization = {Istituto Nazionale di Alta Matematica (INDAM)},
organization = {Ministry of Education, Universities and Research (MIUR)	CUP E83C18000100006},
organization = {EU-ITN Stardust-R},
organization = {Spanish Government	PGC2021-125535NB-I00	
PGC2021-122954NB-I00},
organization = {NextGenerationEU within the Spanish national Recovery, Transformation and Resilience plan},
organization = {Ministry of Education, Universities and Research (MIUR)},
organization = {Research Projects of National Relevance (PRIN)	20178CJA2B},
publisher = {Springer},
keywords = {Spin–spin model},
keywords = {Spin–orbit model},
keywords = {Two-body problem},
keywords = {Resonances},
keywords = {Periodic orbits},
keywords = {Quasi-periodic solutions},
title = {The Spin–Spin Problem in Celestial Mechanics},
doi = {10.1007/s00332-022-09840-7},
author = {Celletti, Alessandra and Misquero Castro, Mauricio Paul},
}