Stabilizing techniques are provided that prevent whirl-type instabilities during the operation of magnetically levitated rotating systems. Examples include tensioned foil and tensioned wire based designs, where a restraining force arises from contact between a rotating shaft and the tensioned elements, which elements may be of either metallic or non-metallic composition. Another stabilizing technique provides a variation with azimuth in the tension of an array of foils (or wires) so as to create anisotropic stiffness for displacements that are 90.degree. apart in azimuth. Another exemplary technique restrains displacements that have components that are transverse to (i.e., parallel with) the axis of rotation.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
 The United States Government has rights in this invention pursuant to Contract No. DE-AC52-07NA27344 between the U.S. Department of Energy and Lawrence Livermore National Security, LLC, for the operation of Lawrence Livermore National Laboratory.