Please use this identifier to cite or link to this item: https://doi.org/10.3934/dcdss.2020067
Title: Almost all 3-body relative equilibria on S2 and H2 are inclined
Authors: Diacu, F. 
Zhu, S.
Keywords: Celestial mechanics
Central configurations
Curved 3-body problem
Relative equilibria
Three-body problem
Issue Date: 2019
Publisher: American Institute of Mathematical Sciences
Citation: Diacu, F., Zhu, S. (2019). Almost all 3-body relative equilibria on S2 and H2 are inclined. Discrete and Continuous Dynamical Systems - Series S 13 (4) : 1131-1143. ScholarBank@NUS Repository. https://doi.org/10.3934/dcdss.2020067
Rights: Attribution 4.0 International
Abstract: We answer here a question posed by F. Diacu in 2012 that asked whether there exist relative equilibria on S2 and H2 that move in a plane non-perpendicular to the rotation axis. For 3-body non-geodesic ordinary central configurations on S2 and H2, we find all relative equilibria that move in a plane perpendicular to the rotation axis. We also show that the set of shapes of 3-body non-geodesic ordinary central configurations on S2 and H2 is a 3-dimensional manifold. Then we conclude that almost all 3-body relative equilibria move in planes non-perpendicular to the rotation axis. © 2019 American Institute of Mathematical Sciences. All rights reserved.
Source Title: Discrete and Continuous Dynamical Systems - Series S
URI: https://scholarbank.nus.edu.sg/handle/10635/209615
ISSN: 1937-1632
DOI: 10.3934/dcdss.2020067
Rights: Attribution 4.0 International
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