An Historical Note on Finite Rotations

[+] Author and Article Information
Hui Cheng, K. C. Gupta

Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Ill. 60680

J. Appl. Mech 56(1), 139-145 (Mar 01, 1989) (7 pages) doi:10.1115/1.3176034 History: Received March 07, 1988; Revised August 17, 1988; Online July 21, 2009


It is shown in this paper that Euler was first to derive the finite rotation formula which is often erroneously attributed to Rodrigues, while Rodrigues was responsible for the derivation of the composition formulae for successive finite rotations and the so-called Euler parameters of finite rotation. Therefore, based upon historical facts, the following nomenclature is suggested: Euler’s finite rotation formula, Rodrigues’ composition formulae of finite rotations, and Euler-Rodrigues parameters. The text of the paper contains modern symbols and formula forms, while the Appendices contain brief summaries from relevant historical sources with minor alterations in symbols at the most.

Copyright © 1989 by ASME
Topics: Rotation
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