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Stability Analysis of a Rigid Body with Attached Geometrically Nonlinear Rod by the Energy-Momentum Method

Posbergh, T. A. and Simo, J. C. and Marsden, J. E. (1989) Stability Analysis of a Rigid Body with Attached Geometrically Nonlinear Rod by the Energy-Momentum Method. In: Dynamics and control of multibody systems : proceedings of the AMS-IMS-SIAM. Contemporary Mathematics . No.97. American Mathematical Society , pp. 371-398. ISBN 0821851047 http://resolver.caltech.edu/CaltechAUTHORS:20100915-112730894

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Abstract

This paper applies the energy-momentum method to the problem of nonlinear stability of relative equilibria of a rigid body with attached flexible appendage in a uniformly rotating state. The appendage is modeled as a geometrically exact rod which allows for finite bending, shearing and twist in three dimensions. Application of the energy-momentum method to this example depends crucially on a special choice of variables in terms of which the second variation block diagonalizes into blocks associated with rigid body modes and internal vibration modes respectively. The analysis yields a nonlinear stability result which states that relative equilibria are nonlinearly stable provided that; (i) the angular velocity is bounded above by the square root of the minimum eigenvalue of an associated linear operator and, (ii) the whole assemblage is rotating about the minimum axis of inertia.


Item Type:Book Section
Additional Information:© 1989 American Mathematical Society. January 30, 1989. Paper presented by T. A. Posbergh. Research supported by AFOSR contract nwnbcrs 2-DJA-544 and 2-DJA-771 with Stanford Univcrsity. Research partially supported by DOE contract DE-AT03-88ER-12097 and MSI at Cornell University. We thank P. S. Krishnaprasad, Debbie Lewis, John Maddocks and Tudor Ratiu for their input during innumerable discussions about this work.
Funders:
Funding AgencyGrant Number
Air Force Office of Science Research (AFOSR)2-DJA-544
Air Force Office of Science Research (AFOSR)2-DJA-771
Department of EnergyDE-AT03-82ER-12097
Classification Code:1985 Subject Classification 70K, 58F
Record Number:CaltechAUTHORS:20100915-112730894
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100915-112730894
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19972
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 Sep 2010 21:32
Last Modified:26 Dec 2012 12:25

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