Floating Bodies of Equilibrium in 2D, the Tire Track Problem and Electrons in a Parabolic Magnetic Field
arXiv:physics/0701241
Abstract
Explicit solutions of the two-dimensional floating body problem (bodies that can float in all positions) for relative density 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 by the author in archive physics/0205059 and Studies in Appl. Math. 111 (2003) 167-183. The curves are also trajectories of charges in a perpendicular magnetic field.
67 pages including more than 100 eps-figures, gzipped tar file, misprints corrected, text improved, animations in http://www.tphys.uni-heidelberg.de/~wegner/Fl2mvs/Movies.html