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The moment of inertia tensor of an oloid

Sander G. Huisman

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.

The moment of inertia tensor of an oloid

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.
Paper Structure (1 section, 17 equations, 1 figure)

This paper contains 1 section, 17 equations, 1 figure.

Table of Contents

  1. Introduction

Figures (1)

  • Figure 1: Left: Geometry of the two intersecting circles, here shown as colored disk. The two unit circles lie in perpendicular planes and their centers are located at a distance $1/2$ from the origin O. Right: Convex hull of the configuration on the left, with an added mesh to visualize the 3D surface. The orange mesh-lines are for constant $m$ and the blue mesh-lines are for constant $t$. Both figures include the directions of the axes $x$, $y$, and $z$, see the gnomons in the bottom left, the origin (O) is at the geometrical center of the shape which coincides with the center of mass.