Posbergh, T. A. and Krishnaprasad, Perinkulam S. and Marsden, Jerrold E. (1987) Stability Analysis of a Rigid Body with a Flexible Attachment Using the Energy-Casimir Method. In: Differential geometry: the interface between pure and applied mathematics. Contemporary Mathematics. No.68. American Mathematical Society , Providence, RI, pp. 253-273. https://resolver.caltech.edu/CaltechAUTHORS:20100820-143039517
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Abstract
We consider a system consisting of a rigid body to which a linear extensible shear beam is attached. For such a system the Energy-Casimir method can be used to investigate the stability of the equilibria. In the case we consider, it can be shown that a test for (formal) stability reduces to checking the positive definiteness of two matrices which depend on the parameters of the system and the particular equilibrium about which the stability is to be ascertained.
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| Additional Information: | © 1987, Research supported in part by National Science Foundation grant OIR-8S-00108 to the Systems Research Center, AFOSR-URI grant AFOSR-87-OO73. and by a Design Project Grant from NASA Headquarters through the Universities Space Research Association. Research supported in part by DOE Contract DE-AT03-8SER-12097 and by AFOSR-URI grant AFOSR-87-o073. 'This paper is in final form and no version or it is submitted elsewhere. We would like to thank Prof. Juan Simo for helpful remarks.' | ||||||||||||||
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| Series Name: | Contemporary Mathematics | ||||||||||||||
| Issue or Number: | 68 | ||||||||||||||
| Record Number: | CaltechAUTHORS:20100820-143039517 | ||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100820-143039517 | ||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||
| ID Code: | 19566 | ||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||
| Deposited By: | INVALID USER | ||||||||||||||
| Deposited On: | 01 Sep 2010 21:03 | ||||||||||||||
| Last Modified: | 03 Oct 2019 01:58 |
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