Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials

Details Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials

2009-09-27

arxiv.org/abs/0909.4907v1

Celestial Mechanics and Dynamical Astronomy, Volume 94, Number 1 / January, 2006, 17-35

Physics

Mathematical Physics

21 pages 4 figures

Scientific paper

10.1007/s10569-005-2288-9

In this paper we study the linear stability of the relative equilibria for homogeneous and quasihomogeneous potentials. Firstly, in the case the potential is a homogeneous function of degree $-a$, we find that any relative equilibrium of the $n$-body problem with $a>2$ is spectrally unstable. We also find a similar condition in the quasihomogeneous case. Then we consider the case of three bodies and we study the stability of the equilateral triangle relative equilibria. In the case of homogeneous potentials we recover the classical result obtained by Routh in a simpler way. In the case of quasihomogeneous potentials we find a generalization of Routh inequality and we show that, for certain values of the masses, the stability of the relative equilibria depends on the size of the configuration.

Affiliated with

Also associated with

No associations

Rating

Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-316390