Stability of whirling shafts with internal and external damping

Necessary and sufficient conditions for the stability of motion of whirling shafts are established using the direct method of Liapunov. The non-linear mathematical model employed is based on the work of V. V. Bolotin and includes the effects of both internal and external damping. A coordinate transformation is used to facilitate the analysis. In effect, this transformation establishes a mathematical equivalence between the governing equations for a whirling shaft with both internal and external damping, and the governing equations for a whirling shaft with internal damping only.