\(2+1\)-Moulton configuration. (English) Zbl 1416.70012

Yoshimi, Naoko; Yoshioka, Akira

J. Geom. Symmetry Phys. 50, 79-95 (2018).

Summary: We pose a new problem of collinear central configuration in Newtonian \(n\)-body problem. For a given two-body, we ask whether we can add a new body in a way such that i) the configuration of the total three-body is also collinear central with the configuration of the initial two-body being fixed and further ii) the initial two-body keeps its motion without any change during the process. We find three solutions to the above problem. We also consider a similar problem such that while the condition i) is satisfied but by modifying the condition ii) the motion of the initial two-body is not necessarily equal to the original one. We also find explicit solutions to the second problem.

MSC:

70F15	Celestial mechanics
70F10	\(n\)-body problems
70F07	Three-body problems
35Q70	PDEs in connection with mechanics of particles and systems of particles

Keywords:

celestial mechanics; collinear central configuration; three-body problem