Neutrally Floating Objects of Density ½ in Three Dimensions. Issue 3 (16th November 2012)

• Record Type: Journal Article
• Authors: Várkonyi, P. L.
• Is Part Of: Studies in applied mathematics. Volume 130:Issue 3(2013)
• Page Start: 295
• Page End: 315
• Publication Date: 2012-11-16
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/j.1467-9590.2012.00569.x
• Languages: English
• ISSNs: 0022-2526

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>This paper is concerned with the Floating Body Problem of S. Ulam: the existence of objects other than the sphere, which can float in liquid in any orientation. Despite recent results of F. Wegner pointing towards an affirmative answer, a full proof of their existence is still unavailable. For objects with cylindrical symmetry and density 1/2, the conditions of neutral floating are formulated as an initial value problem, for which a unique solution is predicted in certain cases by a suitable generalization of the Picard–Lindelöf theorem. Numerical integration of the initial value problem provides a rich variety of neutrally floating shapes.</p> </abstract>