TY - JOUR
T1 - The Number of Relative Equilibria in the PCR4BP
AU - Figueras, Jordi Lluís
AU - Tucker, Warwick
AU - Zgliczynski, Piotr
N1 - Funding Information:
We are very greatful to Professor Carles Simó for bringing this problem to our attention and for fruitful discussions. W.T. has been partially supported by VR Grant 2013-4964. P.Z. has been partially supported by the NCN Grant 2019/35/B/ST1/00655. J-Ll.F. has been partially supported by VR Grant 2019-04591.
Publisher Copyright:
© 2022, The Author(s).
PY - 2024
Y1 - 2024
N2 - The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial mechanics. The new approach allows for a very efficient computer-aided proof, and opens a potential pathway to proving harder instances of the n-body problem.
AB - The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial mechanics. The new approach allows for a very efficient computer-aided proof, and opens a potential pathway to proving harder instances of the n-body problem.
KW - n-body problem
KW - Relative equilibrium
KW - Set-valued computation
UR - http://www.scopus.com/inward/record.url?scp=85143172115&partnerID=8YFLogxK
U2 - 10.1007/s10884-022-10230-6
DO - 10.1007/s10884-022-10230-6
M3 - Article
AN - SCOPUS:85143172115
SN - 1040-7294
VL - 36
SP - 2827
EP - 2877
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
ER -