Relativistic Elastostatics I: Bodies in Rigid Rotation

TL;DR

This paper investigates elastic bodies in rigid rotation within both classical and relativistic frameworks, establishing the existence of solutions to the elastic equations at low angular velocities.

Contribution

It proves the existence of solutions for elastic bodies in rotation in both nonrelativistic and relativistic contexts, assuming natural states without rotation.

Findings

Existence of solutions at small angular velocities

Applicability to both classical and relativistic elasticity

Theoretical foundation for rotating elastic bodies

Abstract

We consider elastic bodies in rigid rotation, both nonrelativistically and in special relativity. Assuming a body to be in its natural state in the absence of rotation, we prove the existence of solutions to the elastic field equations for small angular velocity.