Floating Bodies of Equilibrium in 2D, the Tire Track Problem and Electrons in an Inhomogeneous Magnetic Field

Explicit solutions of the two-dimensional floating body problem (bodies that can float in all positions) for relative density ρ 6= 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 [12, 13]. The curves are also trajectories of charges in a perpendicular parabolic magnetic field.