@misc{10481/99362,
year = {2020},
url = {https://hdl.handle.net/10481/99362},
abstract = {We study the classical planar spin-orbit model from an analytical point of view,
with no requirements of smallness of the orbital eccentricity and taking into account
dissipative forces. The problem depends on e, the eccentricity of the orbit, and on
Λ, the oblateness of the spinning body. Our main concern is the capture into the
1:1 resonance for points of the (e,Λ)-plane. First, we find a region of uniqueness
of the 1:1 resonance, which is the continuation from the solution for e = 0. Then,
a subregion of linear stability is estimated. We also study a separatrix close to the
line e = e∗ ≈ 0.682, beyond which the resonance is unstable. Finally, we study
the dissipative case by giving estimations for regions of asymptotic stability of
the solution (capture into resonance) depending on the strength of the dissipation
applied.},
publisher = {SIAM Publications},
keywords = {spin-orbit problem},
keywords = {forced pendulum},
keywords = {dissipative systems},
keywords = {synchronous resonance},
keywords = {capture into resonance},
keywords = {asymptotic stability},
title = {Some Rigorous Results on the 1:1 Resonance of the Spin-Orbit Problem},
doi = {https://doi.org/10.1137/19M1294241},
author = {Misquero, Mauricio and Ortega Ríos, Rafael},
}