Stress field and spin axis relaxation for inelastic triaxial ellipsoids

Abstract

A compact formula for the stress tensor inside a self-gravitating, triaxial ellipsoid in an arbitrary rotation state is given. It contains no singularity in the incompressible medium limit. The stress tensor and the quality factor model are used to derive a solution for the energy dissipation resulting in the damping (short axis mode) or excitation (long axis) of wobbling. In the limit of an ellipsoid of revolution, we compare our solution with earlier ones and show that, with appropriate corrections, the differences in damping times estimates are much smaller than it has been claimed. This version implements corrections of misprints found in the MNRAS published text.Comment: 14 pages, 6 figures, published in Monthly Notices RAS (containing misprints

Precession relaxation of viscoelastic oblate rotators

“…They also ignored the oscillating part of gravity, i.e., did not distinguish between bgr and bgr. In this notation and approximation, our formula (30) becomeswhich coincides with the equation (26) in Breiter et al (2012). 11 Using the notations h 1 ≡ b/a and h 2 ≡ c/b , (Breiter et al 2012, eqns.…”

“…The constant part bgr is simply the gravity force of an undeformed ellipsoid. In a point x, y, z inside a spheroid (and, more generally, inside a triaxial ellipsoid of dimensions a b c), it is linear in the body coordinates:Derived by Gauss (1813) and Rodrigues (1816), the coefficients γi can be found, e.g., in Breiter et al (2012). …”

“…So we cannot extend our treatment to liquid bodies with no rigidity. )Plugging the formulae (13) into the formula (46), we obtain the relaxation rate:Inserting therein the expression (57) for the power, and integrating, we obtain the nutational damping time: We have written down this expression in a form that would facilitate comparison with the result from Breiter et al (2012). For convenience, below we cite their result in the equation (65).…”

“…For convenience, below we cite their result in the equation (65). Our T should be compared with the quantity T3 in Breiter et al (2012).The dependence of the relaxation time T upon the shape parameter h = c/a , as given by our expression (59), is presented graphically in the upper panel of Figure 1. There, three curves depict the evolution of the nutation angle θ from three initial values θ0 = 20…”

The young Datura asteroid family

“…This is because the available data can be fit with a model in which the body rotates about the shortest principal axis of the inertia tensor with a single sidereal rotation frequency. Consider, however, that the standard theory of the rotation wobble damping (e.g., Harris 1994;Sharma et al 2005;Breiter et al 2012;Pravec et al 2014) would predict a characteristic de-excitation timescale of 6 Gyr (assuming µ Q 10 11 , SI units, where µ is rigidity and Q quality factor). This is four orders of magnitude longer than the age of the Datura family.…”