Vibrational stability of the rotating Roche model
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.
scientific article; zbMATH DE number 4049181