1982
DOI: 10.1007/bf01230656
|View full text |Cite
|
Sign up to set email alerts
|

Collinear relative equilibria of the planarN-body problem

Abstract: The collinear relative equilibrium solutions are among the few explicitly known periodic solutions of the Newtonian three-body problem. When the energy and angular momentum constants are varied slightly, these unstable periodic orbits become normally hyperbolic invariant spheres whose stable and unstable manifolds form separatrices in the integral manifolds. The goal of this paper is to construct simple isolating blocks for these invariant spheres analogous to those introduced by Conley in the restricted three… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
17
0
1

Year Published

1982
1982
2017
2017

Publication Types

Select...
8
1

Relationship

0
9

Authors

Journals

citations
Cited by 26 publications
(18 citation statements)
references
References 5 publications
0
17
0
1
Order By: Relevance
“…1). The other possibility, i.e., when the three nonzero masses form a collinear central configuration, was studied by Palmore [8], who proved that there are exactly two symmetrical planar central configurations for all positive values of the masses.…”
Section: Introductionmentioning
confidence: 98%
“…1). The other possibility, i.e., when the three nonzero masses form a collinear central configuration, was studied by Palmore [8], who proved that there are exactly two symmetrical planar central configurations for all positive values of the masses.…”
Section: Introductionmentioning
confidence: 98%
“…Palmore [12] studied the collinear case in general, showing that there are always n + 3 locations to continue a collinear relative equilibrium of the n-body problem into the full n + 1-body problem. For n = 3, four of these points lie on the line containing the collinear relative equilibrium while the other two are positioned symmetrically about this line.…”
Section: The Planar Circular Restricted Four-body Problemmentioning
confidence: 99%
“…For the three series z 1 (t), z 2 (t), z 3 (t) described in Eqs. (12), (13) and (14), the order is the vector α = (1, 0, −1/2). For the case when a Puiseux series solution exists, the vector α generates a system of reduced Eqs.…”
Section: Bkk Theorymentioning
confidence: 99%
“…Motions in a multi-body system constitute a difficult problem of considerable interest (Hadjidemetriou 1977(Hadjidemetriou , 1979Meyer 1981;Palmore 1982). The dynamical study of multi-body systems can be simplified by using simpler N-body models based on the geometrical properties of the system (Markellos et al 1997;Kalvouridis 1999a,b).…”
Section: Introductionmentioning
confidence: 99%