Lewis, D. and Marsden, J. and Ratiu, T. (1987) Stability and bifurcation of a rotating planar liquid drop. Journal of Mathematical Physics, 28 (10). pp. 2508-2515. ISSN 0022-2488. doi:10.1063/1.527740. https://resolver.caltech.edu/CaltechAUTHORS:LEWjmp87
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Abstract
The stability and symmetry breaking bifurcation of a planar liquid drop is studied using the energy-Casimir method and singularity theory. It is shown that a rigidly rotating circular drop of radius r with surface tension coefficient τ and angular velocity Ω/2 is stable if (Ω/2)^2 <3τ/r^3. A new branch of stable rigidly rotating relative equilibria invariant under rotation through π and reflection across two axes bifurcates from the branch of circular solutions when (Ω/2)^2=3τ/r^3.
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| Additional Information: | © 1987 American Institute of Physics. Received 23 January 1987; accepted 17 June 1987. We thank H. Abarbanel, D. Holm, R. Montgomery, and C. Rosenkilde for useful conversations and helpful remarks. D.L. and J.M. were partially supported by DOE Contract No. DE-AT03-85ER 12097. T.R. was partially supported by a NSF postdoctoral fellowship and a Sloan Foundation fellowship. | |||||||||
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| Issue or Number: | 10 | |||||||||
| DOI: | 10.1063/1.527740 | |||||||||
| Record Number: | CaltechAUTHORS:LEWjmp87 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:LEWjmp87 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 11461 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 22 Aug 2008 03:39 | |||||||||
| Last Modified: | 08 Nov 2021 21:59 |
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