Displacements of Points of a Viscoelastic Ball Caused by Tides

Abstract

The derivation of equations of motion is considered in the problem of motion of two viscoelastic bodies in the central gravitational field of massive spherical rigid homogenous body with the help of the d’Alembert Lagrange variation principle. It was used the Kelvin– Voigt model of viscous forces and classical theory of small strains. The method for separation of motions was applied in order to get an approximate solution of quasi-static equation of the theory of elasticity on the unperturbed motion. There were obtained the displacements of each point of the bodies, caused by centrifugal, elastic and dissipative forces.