摘要
It is of great interest to study the dynamical environment on the surface of non-spherical small bodies, especially for asteroids. This paper takes a simple case of a cube for instance, investigates the dynamics of a particle on the surface of a rotating homogeneous cube, and derives fruitful results. Due to the symmetrical characteristic of the cube, the analysis includes motions on two different types of surfaces. For each surface, both the frictionless and friction cases are considered. (i) Without consideration of friction, the surface equilibria in both of the different surfaces are examined and periodic orbits are derived. The analysis of equilibria and periodic orbits could assist understanding the skeleton of motions on the surface of asteroids. (ii) For the friction cases, the conditions that the particle does not escape from the surface are examined. Due to the effect of the friction, there exist the equilibrium regions on the surface where the particle stays at rest, and the locations of them are found. Finally, the dust collection regions are predicted. Future work will extend to real asteroid shapes.
It is of great interest to study the dynamical environment on the surface of non-spherical small bodies, especially for asteroids. This paper takes a simple case of a cube for instance, investigates the dynamics of a particle on the surface of a rotating homogeneous cube, and derives fruitful results. Due to the symmetrical characteristic of the cube, the analysis includes motions on two different types of surfaces. For each surface, both the frictionless and friction cases are considered. （i） Without consideration of friction, the surface equilibria in both of the different surfaces are examined and periodic orbits are derived. The analysis of equilibria and periodic orbits could assist understanding the skeleton of motions on the surface of asteroids. （ii） For the friction cases, the conditions that the particle does not escape from the surface are examined. Due to the effect of the friction, there exist the equilibrium regions on the surface where the particle stays at rest, and the locations of them are found. Finally, the dust collection regions are predicted. Future work will extend to real asteroid shapes.
基金
supported by the National Basic Research Program of China (Grant No. 2012CB720000)
the National Natural Science Foundation of China (Grant No. 11072122)
