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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.