Bernoulli Numbers and Rotational Kinematics

[+] Author and Article Information
F. Pfister

IPG Automotive Engineering Software + Consulting GmbH Postfach 210522, D-76155 Karlsruhe, Germany

J. Appl. Mech 65(3), 758-763 (Sep 01, 1998) (6 pages) doi:10.1115/1.2789120 History: Received June 06, 1997; Revised March 10, 1998; Online October 25, 2007


The representation of rotation operators in the form of infinite tensor power series, R = exp(Ψ̂ ), has been found to be a valuable tool in multibody dynamics and nonlinear finite element analysis. This paper presents analogous formulations for the kinematic differential equations of the Euler-vector Ψ and elucidates their connection to Bernoulli-numbers. New power series such as the Bernoulli- and the Gibbs series are shown to provide compact expressions and a simple means for understanding and computing some of the fundamental formulae of rotational kinematics. The paper includes an extensive literature review, discussions of isogonal rotations, and a kinematic singularity measure.

Copyright © 1998 by The American Society of Mechanical Engineers
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