Rodrigues, Olinde: "Des lois g\'{e}om\'{e}triques qui r\'{e}gissent les d\'{e}placements d'un syst\`{e}me solide...", translation and commentary

TL;DR

This paper offers the first English translation of Rodrigues's 1840 work on the geometric laws of solid system motions, including detailed notes, proofs, and clarifications to enhance understanding of this foundational text.

Contribution

It provides a comprehensive translation with annotations, making Rodrigues's pioneering work accessible and understandable to a modern audience for the first time.

Findings

Clarifies Rodrigues's geometric laws of motion

Provides detailed proofs and explanations

Enhances understanding of 19th-century mechanics

Abstract

I provide for the first time in English a line-by-line translation of the entire text of the monumental 1840 memoir of Olinde Rodrigues, "On the geometrical laws governing the motions of a solid system..." published in French in the Journal de Math\'{e}matiques Pures et Appliqu\'{e}es. I accompany the translation with copious notes in italics, in which I explicate some passages whose meaning is obscure in the direct translation, supply detailed proofs, where lacking, of assertions in the original, and clarify the overall organization of the memoir and the relation of its sections to one another.