Gyroscopic stabilization in the presence of nonconservative forces

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Abstract
Stability of a linear autonomous non- conservative system in presence of potential, gyroscopic, dissipative, and non-conservative positional forces is stud- ied. It is known that marginal stability of a gyroscopic sys- tem can be destroyed or improved up to asymptotic stabil- ity due to action of small non-conservative positional and damping forces. The present paper shows that the bound- ary of the asymptotic stability domain of the perturbed sys- tem possesses singularities such as "Dihedral angle" and "Whitney umbrella" that govern stabilization and desta- bilization. Approximations of the stability boundary near the singularities and estimates of the critical gyroscopic parameter are found in an analytic form. As an example, stability of the Crandall gyropendulum with stationary and rotating damping is considered in detail.

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