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This article is cited in 2 scientific papers (total in 2 papers)
Stability of the Planar Equilibrium Solutions of a Restricted $1+N$ Body Problem
Dieter Schmidta, Claudio Vidalb a Department of Computer Science,
University of Cincinnati, Ohio, USA
b Facultad de Ciencias, Universidad del Bío-Bío, Casilla 5-C, Concepción, VIII-Región, Chile
Abstract:
We started our studies with a planar Eulerian restricted four-body
problem (ERFBP) where three masses move in circular orbits such that
their configuration is always collinear. The fourth mass is small and does
not influence the motion of the three primaries. In our model we assume
that one of the primaries has mass 1 and is located at the origin and two
masses of size $\mu$ rotate around it uniformly. The problem was studied
in [3], where it was shown that there exist noncollinear
equilibria, which are Lyapunov stable for small values of $\mu$. KAM
theory is used to establish the stability of the equilibria. Our
computations do not agree with those given in [3] , although
our conclusions are similar.
The ERFBP is a special case of the $1+N$ restricted body problem with
$N=2$. We are able to do the computations for any $N$ and find that the
stability results are very similar to those for $N=2$. Since the $1+N$
body configuration can be stable when $N>6$, these results could be of
more significance than for the case $N=2$.
Keywords:
$1+N$ body problem, relative equilibria, normal form, KAM stability.
Received: 22.04.2014 Accepted: 21.08.2014
Citation:
Dieter Schmidt, Claudio Vidal, “Stability of the Planar Equilibrium Solutions of a Restricted $1+N$ Body Problem”, Regul. Chaotic Dyn., 19:5 (2014), 533–547
Linking options:
https://www.mathnet.ru/eng/rcd180 https://www.mathnet.ru/eng/rcd/v19/i5/p533
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Abstract page: | 171 | References: | 27 |
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