Gay-Balmaz, François and Marsden, Jerrold E. and Ratiu, Tudor S. (2012) Reduced Variational Formulations in Free Boundary Continuum Mechanics. Journal of Nonlinear Science, 22 (4). pp. 463-497. ISSN 0938-8974 http://resolver.caltech.edu/CaltechAUTHORS:20121005-103335650
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We present the material, spatial, and convective representations for elasticity and fluids with a free boundary from the Lagrangian reduction point of view, using the material and spatial symmetries of these systems. The associated constrained variational principles are formulated and the resulting equations of motion are deduced. In addition, we introduce general free boundary continua that contain both elasticity and free boundary hydrodynamics, extend for them various classical notions, and present the constrained variational principles and the equations of motion in the three representations.
|Additional Information:||© 2012 Springer Science+Business Media, LLC. Received: 18 April 2011; Accepted: 2 July 2012; Published online: 18 July 2012. F. Gay-Balmaz was partially supported by a Swiss NSF postdoctoral fellowship. J.E. Marsden was partially supported by the California Institute of Technology. T.S. Ratiu was partially supported by Swiss NSF grant 200021-140238 and by the government grant of the Russian Federation for support of research projects implemented by leading scientists, Lomonosov Moscow State University under the agreement No. 11.G34.31.0054. We thank D.D. Holm for helpful discussions.|
|Subject Keywords:||Symmetry; Reduction; Variational principle; Constraints; Material representation; Spatial representation; Convective representation; Lagrangian; Rigid body; Ideal fluid; Elastic material|
|Classification Code:||Mathematics Subject Classification: 37K05; 37K65; 75B20; 35R35|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||05 Oct 2012 20:24|
|Last Modified:||05 Oct 2012 20:24|
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