Floating Bodies of Equilibrium. Explicit Solution

Abstract

Explicit solutions of the two-dimensional floating body problem (bodies that can float in all positions) for relative density rho different from 1/2 and of the tire track problem (tire tracks of a bicycle, which do not allow to determine, which way the bicycle went) are given, which differ from circles. Starting point is the differential equation given in archive physics/0205059 and Studies in Appl. Math. 111 (2003) 167-183.

25 pages, two figures. Factors and signs in eqs. 48,61,64,65,70,73,74, 150,176,177,186 corrected. Minor corrections in the text