2008/03/07 by Franz Wegner, Wegner, Franz
Mathematics · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Functional Equations Stability Results #General Physics (physics.gen-ph) #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.0803.1043
openalex publication_date 2008/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Pp,2(x)=0 for two different integer ps, where P are Legendre functions.