Title: Poincaré surfaces of section around a 3-D irregular body: The case of asteroid 4179 Toutatis,
Abstract: In general, small bodies of the solar system, e.g., asteroids and comets,
have a very irregular shape. This feature affects significantly the
gravitational potential around these irregular bodies, which hinders dynamical
studies. The Poincaré surface of sec- tion technique is often used to look
for stable and chaotic regions in two-dimensional dynamic cases. In this work,
we show that this tool can be useful for exploring the surroundings of
irregular bodies such as the asteroid 4179 Toutatis. Considering a rotating
system with a particle, under the effect of the gravitational field computed
three-dimensionally, we define a plane in the phase space to build the
Poincaré surface of sections. Despite the extra dimension, the sections
created allow us to find trajec- tories and classify their stabilities. Thus,
we have also been able to map stable and chaotic regions, as well as to find
correlations between those regions and the contri- bution of the third
dimension of the system to the trajectory dynamics as well. As examples, we
show details of periodic(resonant or not) and quasi-periodic trajectories.