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Stability and bifurcation of a rotating planar liquid drop

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.

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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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Ratiu, T.0000-0003-1972-5768
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.
Funding AgencyGrant Number
Department of Energy (DOE)DE-AT03-85ER 12097
Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:10
Record Number:CaltechAUTHORS:LEWjmp87
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11461
Deposited By: Tony Diaz
Deposited On:22 Aug 2008 03:39
Last Modified:08 Nov 2021 21:59

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