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Shock and Vibration
Volume 1, Issue 2, Pages 121-134

Motion of a Rigid Body Supported at One Point by a Rotating Arm

Jeffrey D. Stoen and Thomas R. Kane

Department of Mechanical Engineering, Division of Applied Mechanics, Stanford University, Stanford CA 94305, USA

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This article details a scheme for evaluating the stability of motions of a system consisting of a rigid body connected at one point to a rotating arm. The nonlinear equations of motion for the system are formulated, and a method for finding exact solutions representing motions that resemble a state of rest is presented. The equations are then linearized and roots of the eigensystem are classified and used to construct stability diagrams that facilitate the assessment of effects of varying the body's mass properties and system geometry, changing the position of the attachment joint, and adding energy dissipation in the joint.