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

* 2 Small Bodies*

Oral, Monday, May 5, 2003, 10:40am-12:10pm,
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## [2.03] Rotational Dynamics of a Deformable Symmetric Ellipsoid

*I. Sharma, J. T. Jenkins, J A. Burns (Dept. of Theoretical and Applied Mechanics, Cornell University)*

As a first step towards following the rotational evolution
of wobbling asteroids we consider the rotational dynamics of
deformable ellipsoids. In general, a full set of balance
equations need to be solved. However, it's difficult to
obtain analytical or numerical solutions to these for
general constitutive laws. Even in the case of a linear
elastic body, where analytical solutions are available
(assuming quasi-statics), the solutions are much too
unwieldy. One way to reduce the problem's complexity and
still include the effects of elasticity, viscosity, and/or
friction is to successively approximate the deformation in
terms of its linear (homogeneous), quadratic, cubic, etc.
parts. This can be done very systematically via the virial
method (Chandrasekhar S., 1969). The advantage of this
method is that it allows us to investigate a wide variety of
constitutive laws, include the effects of internal gravity
and external force fields, and make better estimates of the
amount of internal energy dissipated. To demonstrate the
method, we present analytical solutions obtained for the
case of an axi-symmetric, linearly elastic ellipsoid
executing free Eulerian motion.

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

© 2003. The American Astronomical Soceity.