相关论文: Floating Bodies of Equilibrium in Three Dimensions…
Bodies of density one half (of the fluid in which they are immersed) that can float in all orientations are investigated. It is shown that expansions starting from and deforming the (hyper)sphere are possible in arbitrary dimensions and…
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,…
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…
This paper is concerned with the Floating Body Problem of S. Ulam: the existence of objects other than the sphere, which can float in a liquid in any orientation. Despite recent results of F. Wegner pointing towards an affirmative answer, a…
A long cylindrical body of circular cross-section and homogeneous density may float in all orientations around the cylinder axis. It is shown that there are also bodies of non-circular cross-sections which may float in any direction. Apart…
We study a long standing open problem by Ulam, which is whether the Euclidean ball is the unique body of uniform density which will float in equilibrium in any direction. We answer this problem in the class of origin symmetric n-dimensional…
We present a simple experimental realization of a two-dimensional floating body that can remain in equilibrium in any orientation. This system is based on a class of shapes known as Zindler curves, which possess the remarkable geometric…
Consider a deformable body immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we investigate the deformations of the body. The…
The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body…
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…
We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary…
Ulam's problem 19 from the Scottish Book asks: {\it is a solid of uniform density which floats in water in every position necessarily a sphere?} We obtain several results related to this problem.
An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…
We define floating bodies in the class of $n$-dimensional ball-convex bodies. A right derivative of volume of these floating bodies leads to a surface area measure for ball-convex bodies which we call relative affine surface area. We show…
We consider a rigid body acted upon by two forces, a constant force and the collective force of interaction with a continuum of particles. We assume that some of the particles that collide with the body reflect elastically (specularly),…
We consider the Clairaut theory of the equilibrium ellipsoidal figures for differentiated non-homogeneous bodies in non-synchronous rotation adding to it a tidal deformation due to the presence of an external gravitational force. We assume…
The linear boundary value problem under consideration describes time-harmonic motion of water in a horizontal three-dimensional layer of constant depth in the presence of an obstacle adjacent to the upper side of the layer (floating body).…
Consider a deformable body immersed in an incompressible liquid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we investigate the motion of the body, calculate its…
In the $2$-dimensional $n$-body problem, $n\ge 3$, in spaces of constant curvature, $\kappa\ne 0$, we study polygonal homographic solutions. We first provide necessary and sufficient conditions for the existence of these orbits and then…
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…