**DPS 2001 meeting, November 2001**

*Session 41. Asteroids Posters*

Displayed, 9:00am Tuesday - 3:00pm Saturday, Highlighted, Friday, November 30, 2001, 9:00-10:30am, French Market Exhibit Hall
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## [41.02] Nutational Damping Times in Solids of Revolution

*I. Sharma, J. A. Burns, C.-Y. Hui (Dept. of Theoretical and Applied Mechanics, Cornell University)*

Energy loss in isolated spinning bodies aligns the bodies's
angular momentum vectors with their axes of maximum inertia.
For freely rotating asteroids, energy loss depends on the
time-varying stresses induced by nutation, which
consequently specifies the nutational damping time \tau.
Previous damping estimates have disagreed, perhaps because
(a) different body shapes were used to estimate stresses,
and (b) alternate techniques were employed to calculate
stresses. To solve the full 3-D elasticity problem for a
given body is a formidable task due to (a) complex asteroid
shapes, (b) the presence of an acceleration field that is
not derivable from a potential, and (c) the material's
anelasticity. The first two contradict Love's model (a
common estimate of stresses inside celestial bodies). To
simplify the geometry, we consider an anelastic triaxial
ellipsoid, thereby capturing the asteroid's free Eulerian
motion, which makes even the elastic triaxial case hard. As
a first step toward the general solution for an
\textbf{anelastic} triaxial ellipsoid, we provide the full
3-D solution for \textbf{elastic} solids of revolution. We
choose an elastic material over an anelastic one because (a)
it simplifies the problem considerably and (b) given the
body's unknown internal structure, no particular
viscoelastic model (say Maxwell) is preferred over an
elastic one with dissipation depending only on Q. With
stresses known, the energy loss comes by averaging the
time-varying part of the strain energy over a cycle,
assuming that stresses oscillate much more rapidly than
damping occurs. We compare damping times derived using this
estimate of energy loss to values available in the
literature. With our exact 3-D calculation for an oblate
ellipsoid we can vary shape from a disk to a cylinder,
exploring how damping depends on shape and the exactness of
the stress calculation.

The author(s) of this abstract have provided an email address
for comments about the abstract:
is42@cornell.edu

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