Floating Bodies of Equilibrium in Three Dimensions. The central symmetric case

Details Floating Bodies of Equilibrium in Three Dimensions. The central symmetric case Floating Bodies of Equilibrium in Three Dimensions. The central symmetric case

2008-03-07

arxiv.org/abs/0803.1043v2

Physics

Classical Physics

29 pages, 2 figures, some misprints corrected

Scientific paper

Three-dimensional central symmetric bodies different from spheres that can float in all orientations are considered. For relative density rho=1/2 there are solutions, if holes in the body are allowed. For rho different from 1/2 the body is deformed from a sphere. A set of nonlinear shape-equations determines the shape in lowest order in the deformation. It is shown that a large number of solutions exists. An expansion scheme is given, which allows a formal expansion in the deformation to arbitrary order under the assumption that apart from x=0,+1,-1 there is no x, which obeys P_{p,2}(x)=0 for two different integer ps, where P are Legendre functions.

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