Spherical Cyclic Motions in Euclidean Space E3

TL;DR

This paper investigates the properties of spherical cyclic motions in Euclidean space, establishing a connection between cyclic matrices and homothetic motions, especially for curves on a unit sphere.

Contribution

It introduces a novel approach linking cyclic matrices with homothetic motions for spatial curves, including those on a sphere, expanding understanding of cyclic motions in Euclidean space.

Findings

Cyclic matrices are homothetic and correspond to homothetic motions.

Curves on a unit sphere induce spherical cyclic motions.

The paper provides a mathematical framework for analyzing cyclic motions in Euclidean space.

Abstract

By considering a spatial curve in a Euclidean space, we use its components, together with attaining a cyclic matrix, to show that this matrix is homothetic too and is in correspondence with a homothetic motion. Furthermore, if the curve lies on a unit sphere, then the motion is a spherical cyclic motion.