Dynamics of an isolated, viscoelastic, self-gravitating body

Author(s)

Ragazzo, C. ^[1] ; Ruiz, L. S. ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Fed Itajuba, Inst Matemat Comp, BR-37500903 Itajuba, MG - Brazil

• Document type: Journal article
• Source: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY; v. 122, n. 4, p. 303-332, AUG 2015.
• Web of Science Citations: 4

Abstract

This paper is devoted to an alternative model for a rotating, isolated, self-gravitating, viscoelastic body. The initial approach is quite similar to the classical one, present in the works of Dirichlet, Riemann, Chandrasekhar, among others. Our main contribution is to present a simplified model for the motion of an almost spherical body. The Lagrangian function L and the dissipation function D of the simplified model are: L = omega.I omega/2 + 1/36I(o) (parallel to(Q) over circle parallel to(2) - gamma parallel to Q parallel to(2)) and D = nu/36I(o) parallel to(Q) over circle parallel to(2) where omega is the angular velocity vector, Q is the quadrupole moment tensor, I = I-o Id - Q/3 is the usual moment of inertia tensor with I-o equal to the moment of inertia of the spherical body at rest, gamma is an elastic constant, and nu is a damping coefficient. The angular momentum I omega transformed to an inertial reference frame is conserved. The constants gamma and nu must be determined experimentally. We believe this to be the simplest model one can get without loosing the symmetries and the conserved quantities of the original problem. This model can be used as a building block for the study of many-body planetary systems. (AU)

• FAPESP's process: 11/16265-8 - Low dimensional dynamics
• Grantee: Edson Vargas
• Support Opportunities: Research Projects - Thematic Grants