Vibrational stability of the rotating Roche model
type: Item
instance of: scholarly article
title: Vibrational stability of the rotating Roche model
zbMATH Open document ID: 0643.70008
DOI: 10.1007/BF00637428
published in: Astrophysics and Space Science
publication date: 1987-01-01T00:00:00Z
review text: The explicit form of the linearized differential equations governing to arbitrary oscillations of small amplitudes of the rotating Roche model in Clairaut coordinates is given. Then, these equation are solved in closed form. The obtained solution shows that the linear oscillations are unstable, as soon as the centrifugal force will cause the deformation of every equilibrium surface from a sphere. The Laplace equation is set up in Clairaut and in Roche coordinates associated with the rotating Roche model. The solution of this equation is expressed in terms of Clairaut harmonics and of Roche harmonics respectively. These functions represent a generalization of Legendre functions which are similarly associated with a sphere.
reviewed by: V.Ureche
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70G10
Mathematics Subject Classification ID: 85A15
Mathematics Subject Classification ID: 31A05
Mathematics Subject Classification ID: 70J25
zbMATH DE Number: 4049181
zbMATH Keywords: linearized differential equations
zbMATH Keywords: oscillations of small amplitudes
zbMATH Keywords: rotating Roche model
zbMATH Keywords: Clairaut coordinates
zbMATH Keywords: centrifugal force
zbMATH Keywords: equilibrium surface
zbMATH Keywords: Laplace equation
zbMATH Keywords: generalization of Legendre functions
author: Zdenek Kopal
MaRDI profile type: Publication
cites work: Effects of rotation on internal structure of the stars
full work available at URL: https://doi.org/10.1007/bf00637428
OpenAlex ID: W188642003
Recommended article: Vibrational stability of double-star Roche model
Recommended article: Stability of rotating spherical stellar systems
Recommended article: Q4725950
Recommended article: Stability of kinematically excited oscillations of a rotating spherical shell
Recommended article: Q3787668
Recommended article: Roche harmonics for tidally-distorted stellar models
Recommended article: A framework for perturbations and stability of differentially rotating stars
Recommended article: Q3323326
Recommended article: Self-consistent models of quasi-relaxed rotating stellar systems
Recommended article: On the Stability of Rotating Systems
description: scientific article; zbMATH DE number 4049181