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dc.contributor.advisorJohn W. M. Bushen_US
dc.contributor.authorAristoff, Jeffrey Michaelen_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2010-04-28T17:16:30Z
dc.date.available2010-04-28T17:16:30Z
dc.date.copyright2009en_US
dc.date.issued2009en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/54661
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (p. 117-123).en_US
dc.description.abstractThis thesis has two parts. In Part I, we present the results of a combined experimental and theoretical investigation of the vertical impact of spheres on a water surface. Particular attention is given to characterizing the shape of the resulting air cavity in the limit where cavity collapse is strongly influenced by surface tension. A parameter study reveals the dependence of the cavity structure on the governing dimensionless groups. A theoretical description is developed to describe the evolution of the cavity shape and yields an analytical solution for the pinch-off time and depth. We also examine low-density spheres that decelerate substantially following impact, and characterize the deceleration rate and resulting change in behavior of the associated water-entry cavities. Theoretical predictions compare favorably with our experimental observations. Finally, we present a theoretical model for the evolution of the splash curtain formed at high speeds, and couple it to the underlying cavity dynamics. In Part II, we present the results of a combined experimental and theoretical investigation of the motion of a sphere on an inclined flexible beam. A theoretical model based on Euler-Bernoulli beam theory is developed to describe the dynamics, and in the limit where the beam reacts instantaneously to the loading, we obtain exact solutions for the sphere trajectory and descent time. For the case of an initially horizontal beam, we calculate the period of the resulting oscillations. Theoretical predictions compare favorably with our experimental observations in this quasi-static regime. Inertial effects are also addressed.en_US
dc.description.abstract(cont.) The time taken for descent along an elastic beam, the elastochrone, is shown to always exceed the classical brachistochrone, the shortest time between two points in a gravitational field.en_US
dc.description.statementofresponsibilityby Jeffrey Michael Aristoff.en_US
dc.format.extent123 p.en_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleOn falling spheres : the dynamics of water entry and descent along a flexible beamen_US
dc.title.alternativeDynamics of water entry and descent along a flexible beamen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.identifier.oclc606901132en_US


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