On the Transitivity Equations of Rigid-Body Dynamics

[+] Author and Article Information
John G. Papastavridis

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

J. Appl. Mech 59(4), 955-962 (Dec 01, 1992) (8 pages) doi:10.1115/1.2894066 History: Received June 01, 1990; Revised December 19, 1990; Online March 31, 2008


This paper presents direct derivations of the various forms of the famous transitivity equations of rigid-body kinematics from a simple and unified viewpoint. These forms are indispensable in the derivation of the Eulerian (gyro) equations of motion via the Lagrangean (analytical mechanics) method. Both true (holonomic) and quasi (nonholonomic) coordinate forms are presented. A vectorial derivation of the Eulerian equations from the Central Equation and from Hamilton’s Principle is also included in the Appendix.

Copyright © 1992 by The American Society of Mechanical Engineers
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