Floating Bodies of Equilibrium II

Details Floating Bodies of Equilibrium II Floating Bodies of Equilibrium II

2002-05-22

arxiv.org/abs/physics/0205059v2

Physics

Classical Physics

Latex, 12 pages, 4 figures; figure 3 reflected, two signs corrected

Scientific paper

In a previous paper (physics/0203061) ''Floating bodies of equilibrium I'' I have shown that there exist two-dimensional non-circular cross-sections of bodies of homogeneous densities rho not equal 1/2 which can float in any orientation in water, which have a p-fold rotation axis. For given p they exist for p-2 different densities. However, this was found only in a Taylor-expansion in a parameter which describes the distortion from the circular shape up to seventh order. Here a differential equation for the boundary curve is given and the non-circular boundary curve can be expressed in terms of an elliptic integral.

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