Based on prior work at the Lawrence Livermore National Laboratory ambient-temperature passive magnetic bearings are being adapted for use in high-power flywheel energy storage systems developed at the Trinity Flywheel Power company. En route to this goal specialized test stands have been built and computer codes have been written to aid in the development of the component parts of these bearing systems. The Livermore passive magnetic bearing system involves three types of elements, as follows: (1) Axially symmetric levitation elements, energized by permanent magnets., (2) electrodynamic ''stabilizers'' employing axially symmetric arrays of permanent magnet bars (''Halbach arrays'') on the rotating system, interacting with specially wound electrically shorted stator circuits, and, (3) eddy-current-type vibration dampers, employing axially symmetric rotating pole assemblies interacting with stationary metallic discs. The theory of the Livermore passive magnetic bearing concept describes specific quantitative stability criteria. The satisfaction of these criteria will insure that, when rotating above a low critical speed, a bearing system made up of the three elements described above will be dynamically stable. That is, it will not only be stable for small displacements from equilibrium (''Earnshaw-stable''), but will also be stable against whirl-type instabilities of the types that can arise from displacement-dependent drag …