Thread configurations for ellipsoids
arXiv:0902.1421
Abstract
We discuss Darboux-Staude type of thread configurations for the ellipsoid similar to Chasles-Graves type of thread configurations for the ellipse. These threads are formed by rectilinear segments, geodesic and line of curvature segments on the considered ellipsoid and with tangents tangent to the given ellipsoid and a fixed confocal hyperboloid with one sheet and preserve constant length when the vertices of the configuration move on confocal ellipsoids.