Energy dissipation by internal stresses in a free-rotating symmetric ellipsoid: Application to Comet P/Halley

¹ Departamento de Física Aplicada, University of Granada, C/ Fuentenueva s/n 18071 Granada, Spain e-mail: fmartine@ugr.es
² Instituto de Astrofísica de Andalucía, CSIC, PO Box 3004, 18080 Granada, Spain e-mail: fernando@iaa.es

Corresponding author: A. Molina, molina@iaa.es, amolina@ugr.es

Received: 17 July 2002
Accepted: 5 November 2002

Abstract

Internal stresses dissipate energy in a rotating body, unless it spins about one of its principal axes. If the body is rotating around a non-principal axis, its major-inertia axis and its angular velocity will be nutating about the constant vector of angular momentum. In the course of time, the half-angles of the appropriate precession cones will be slowly shrinking due to dissipative effects. In this way, the body will be approaching the state of minimal kinetic energy. We establish here expressions for the components of the stress tensor in the case of a symmetric ellipsoid continuum body, which is a more suitable shape than the rectangular prism studied in earlier works. Using classical expressions of linear elasticity, we obtain the strain energy per unit volume and the temporal average of the total strain energy. In our model, the relative contribution from the double-frequency mode to the inelastic-dissipation effect is larger than the contribution established by Lazarian & Efroimsky (1999), Efroimsky & Lazarian (2000), and Efroimsky (2001) for a prism. We come up with an expression for the relaxation time and compare it with similar expressions previously derived in the literature. In terms of the overall intensity of the effect, our result is in between the result derived in Lazarian & Efroimsky (1999), Efroimsky & Lazarian (2000), and Efroimsky (2002) and that in Burns & Safronov (1973). We apply our model to the comet P/Halley. Following the model proposed by Belton et al. (1991) for the rotation of Halley's comet, we estimate a relaxation time of 10² to 10⁴ million years depending on the quality factor assumed.