Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1175.70013
Lei, J.; Santoprete, M.
Rosette central configurations, degenerate central configurations and bifurcations. (English)
[J] Celest. Mech. Dyn. Astron. 94, No. 3, 271-287 (2006). ISSN 0923-2958; ISSN 1572-9478/e

Summary: In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of mass $m_1$ lie at the vertices of a regular $n$-gon, $n$ particles of mass $m_2$ lie at the vertices of another n-gon concentric with the first, but rotated of an angle $\pi /n$, and an additional particle of mass $m_0$ lies at the center of mass of the system. This system admits two mass parameters $\mu = m_0/m_1$ and $\epsilon = m_2/m_1$. We show that, as $\mu$ varies, if $n > 3$, there is a degenerate central configuration and a bifurcation for every $\epsilon > 0$, while if $n = 3$ there is a bifurcation only for some values of $\epsilon$.

MSC 2000:: *70F10 n-body problem

Keywords: bifurcations; central configurations; degenerate central configurations; $n$-body problem

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]