11 research outputs found
Rotating saddle trap as Foucault's pendulum
One of the many surprising results found in the mechanics of rotating systems
is the stabilization of a particle in a rapidly rotating planar saddle
potential. Besides the counterintuitive stabilization, an unexpected
precessional motion is observed. In this note we show that this precession is
due to a Coriolis-like force caused by the rotation of the potential. To our
knowledge this is the first example where such force arises in an inertial
reference frame. We also propose an idea of a simple mechanical demonstration
of this effect.Comment: 13 pages, 9 figure
Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials
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 , we find that any relative equilibrium
of the -body problem with 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.Comment: 21 pages 4 figure
Detectability of quasi-circular co-orbital planets: application to the radial velocity technique
Several celestial bodies in co-orbital configurations exist in the solar system. However, co-orbital exoplanets have not yet been discovered. This lack may result from a degeneracy between the signal induced by co-orbital planets and other orbital configurations. Here we determine a criterion for the detectability of quasi-circular co-orbital planets and develop a demodulation method to bring out their signature from the observational data. We show that the precision required to identify a pair of co-orbital planets depends only on the libration amplitude and on the planet's mass ratio. We apply our method to synthetic radial velocity data, and show that for tadpole orbits we are able to determine the inclination of the system to the line of sight. Our method is also valid for planets detected through the transit and astrometry techniques