On the Work of Benjamin Olinde Rodrigues (1795-1851) -- in particuler, on Expression of Spatial Motions

TL;DR

This paper explores Benjamin Olinde Rodrigues's contributions to Euclidean motion, highlighting his invention of the Rodrigues rotation formula, its historical context, and its applications in quaternion mathematics.

Contribution

It provides a detailed analysis of Rodrigues's work on rotation expressions, including a new proof of the Rodrigues formula and its significance in the development of quaternion theory.

Findings

Rodrigues formula predates Hamilton's quaternion product rule.

Explicit calculation formulas for rotation products are derived.

Application of Rodrigues expression to time derivatives of rotation.

Abstract

This is a translation of Proceedings of 22 th Symposium on History of Mathematics, Tsuda University 2011, on the work of Benjamin Olinde Rodrigues and on his life. His chef-d'oeuvre is the work on Euclidean motion group in 1840. He invented Rodrigues expression of rotation and give explicit calculation formula for product of two rotations, which might be considered as a discovery of quaternion product rule ahead of Hamilton. We follow a new proof of E. Cartan in his book on spineurs in 1938 for Rodrigues formula, which was called as Euler-Olind-Rodrigues formula mistakenly. We add as Appendix important parts of Lecture Note on applications of quaternion. Description of rotation in Rodrigues expression and an interesting compact formula for time derivative of rotation, applicable in many purposes.