Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 80, pp. 134.
Simultaneous binary collisions in the equalmass collinear
fourbody problem
Tiancheng Ouyang, Duokui Yan
Abstract:
In the fourbody problem, it is not clear what initial conditions can lead
to simultaneous binary collision (SBC), even in the collinear case.
In this paper, we study SBC in the equalmass collinear fourbody problem and
have a partial answer for initial conditions leading to SBC.
After introducing a LeviCivita type transformation, we analyze the new
transformed differential system of SBC and solve for all possible solutions.
The problem is studied in two cases: decoupled case and coupled case.
In the decoupled case where SBC is treated as two separated binary collisions,
the initial conditions leading to SBC satisfy several simple algebraic identities.
This result gives insights to the coupled case, which is SBC in the equalmass
collinear fourbody problem. Furthermore, we show from a different perspective
that solutions passing through SBC must be analytic in the transformed system
and the initial condition set leading to SBC has a measure 0.
Submitted October 1, 2014. Published March 31, 2015.
Math Subject Classifications: 70F10, 70F16.
Key Words: Nbody problem; simultaneous binary collision; regularization.
Show me the PDF file (382 KB),
TEX file, and other files for this article.

Tiancheng Ouyang
Department of Mathematics
Brigham Young University
Provo, UT 84602, USA
email: ouyang@math.byu.edu


Duokui Yan
School of Mathematics and System Science
Beihang University
Beijing 100191, China
email: duokuiyan@buaa.edu.cn

Return to the EJDE web page