The moment of inertia tensor of an oloid

TL;DR

This paper derives an analytical expression for the moment of inertia tensor of an oloid, a convex shape formed by two perpendicular unit circles, and confirms the result through numerical validation.

Contribution

It provides the first explicit analytical formula for the inertia tensor of an oloid, advancing understanding of its physical properties.

Findings

Analytical expression for the inertia tensor derived

Numerical confirmation of the formula

Enhanced understanding of oloid's physical characteristics

Abstract

The oloid is defined as the convex hull of two unit circles in perpendicular planes, each passing through the center of the other. In this paper we derive an analytical expression for the moment of inertia tensor of an oloid with uniform density and confirm the result numerically.