3 research outputs found
Bifurcation for Dynamical Systems of Planet-Belt Interaction
The dynamical systems of planet-belt interaction are studied by the
fixed-point analysis and the bifurcation of solutions on the parameter space is
discussed. For most cases, our analytical and numerical results show that the
locations of fixed points are determined by the parameters and these fixed
points are either structurally stable or unstable. In addition to that, there
are two special fixed points: the one on the inner edge of the belt is
asymptotically stable and the one on the outer edge of the belt is unstable.
This is consistent with the observational picture of Asteroid Belt between the
Mars and Jupiter: the Mars is moving stablely close to the inner edge but the
Jupiter is quite far from the outer edge.Comment: AAS Latex file, 31 pages, accepted for publication in International
Journal of Bifurcation and Chao
Dynamical Effects from Asteroid Belts for Planetary Systems
The orbital evolution and stability of planetary systems with interaction
from the belts is studied using the standard phase-plane analysis. In addition
to the fixed point which corresponds to the Keplerian orbit, there are other
fixed points around the inner and outer edges of the belt. Our results show
that for the planets, the probability to move stably around the inner edge is
larger than the one to move around the outer edge. It is also interesting that
there is a limit cycle of semi-attractor for a particular case. Applying our
results to the Solar System, we find that our results could provide a natural
mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and
thus successfully explain the absence of these objects beyond 50 AU.Comment: accepted by International Journal of Bifurcation and Chaos in Aug.
2003, AAS Latex, 27 pages with 6 color figure
Bifurcation for dynamical systems of planet-belt interaction
[[abstract]]The dynamical systems of planet-belt interaction are studied by the fixed-point analysis, and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of fixed points are determined by the parameters and these fixed points are either structurally stable or unstable. In addition to that, there are two special fixed points: The one on the inner edge of the belt is asymptotically stable and the one on the outer edge of the belt is unstable. This is consistent with the observational picture of Asteroid Belt between Mars and Jupiter: Mars moves steadily close to the inner edge but Jupiter is quite far from the outer edge.[[fileno]]2010503010011[[department]]天文