Helical motion of elastic spheres

TL;DR

This paper investigates the elastic deformations of spheres in helical motion under gravitational forces, providing theoretical analysis and explicit solutions for both Newtonian and Schwarzschild backgrounds.

Contribution

It offers a comprehensive review of existence and uniqueness theorems and explicit solutions for elastic deformations in helical motion within gravitational fields.

Findings

Explicit solutions to linearized elastostatic equations

Existence and uniqueness theorems for elastic deformations

Analysis in both Newtonian and Schwarzschild backgrounds

Abstract

We study the elastic deformations that appear due to tidal and centrifugal forces acting on an elastic sphere in helical motion in a spherically symmetric gravitational field, where gravity is considered to be given by either a Newtonian or a Schwarzschild background. We review an existence/uniqueness theorem based on the implicit function theorem for the nonrelativistic case and give explicit solutions to the linearized elastostatic equations in both cases.