Motion of four-dimensional rigid body around a fixed point: an elementary approach. I

TL;DR

This paper provides an explicit, elementary solution to the Euler-Frahm equations for a four-dimensional rigid body, utilizing classical results to facilitate understanding of higher-dimensional top dynamics.

Contribution

It offers a novel elementary approach to solving four-dimensional rigid body motion, extending classical methods to higher dimensions.

Findings

Explicit solution to four-dimensional Euler-Frahm equations

Utilizes classical results from 19th-century mathematicians

Potentially applicable to n-dimensional top problems

Abstract

The goal of this note is to give the explicit solution of Euler-Frahm equations for the Manakov four-dimensional case by elementary means. For this, we use some results from the original papers by Schottky [Sch 1891], Koetter [Koe 1892], Weber [We 1878], and Caspary [Ca 1893]. We hope that such approach will be useful for the solution of the problem of $n$-dimensional top.