**34th Meeting of the AAS Division on Dynamical Astronomy, May 2003**

* 4 Energetic Dynamics*

Oral, Monday, May 5, 2003, 4:15-5:35pm,
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## [4.03] Stability of Surface Motion on Rotating Ellipsoids

*V. M. Guibout, D. J. Scheeres (U. Michigan, Aerospace Engineering Dept.)*

The dynamical environment on the surface of a rotating,
solid ellipsoid is studied, with applications to surface
motion on an asteroid. The analysis is performed using a
combination of classical dynamics and geometrical analysis.
Due to the small size of most asteroids, their shapes tend
to differ from the spheroidal shapes found for the planets.
The tri-axial ellipsoid model provides a non-trivial
approximation of the gravitational potential of an asteroid
and is amenable to analytical computation. Using this model,
we develop the conditions for equilibrium on the surface. In
general an ellipsoid will only have 6 unique equilibrium
points (each symmetric about the origin), but we also find
situations where every point on the surface may be in
equilibrium. We also study stability of these equilibria and
show that it is intimately related to the well-known
families of Jacobi and MacLaurin ellipsoids. Using
geometrical analysis we can define global constraints on
motion as a function of shape, rotation rate, and density.
We find that some asteroids should have accumulation of
material at their ends, while others should have
accumulation of surface material at their poles, depending
on what their shape and rotation rate are in relation to the
classical figures of equilibrium.

The current analysis ignores the small scale geometry of a
real surface and considers frictionless dynamics. Although
we use such an idealized model, this study has implications
for the global trends of natural material distribution on
asteroids and for the ballistic motions of an artificial
vehicle close to the surface of an asteroid.

The author(s) of this abstract have provided an email address
for comments about the abstract:
guibout@umich.edu

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Bulletin of the American Astronomical Society, **35** #4

© 2003. The American Astronomical Soceity.