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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