Does the Addition of Linear Damping Always Cause Instability in a Gyroscopically Stabilized System?

What is it about?

This paper deals the well-known Kelvin-Tait-Chetaev Theorem which is an important and celebrated paradigm. This paradigm, which was established in 1867, is one of the cornerstones of the theory of linear stability. It states that gyroscopically stabilized linear systems are ALWAYS made unstable by the addition of dissipative damping (more technically, damping that is characterized by matrices that are positive definite). This paper shows a new result that alters this long-accepted paradigm. It proves that gyroscopically stabilized systems CAN be made stable, and even exponentially stable, by the addition of damping that is characterized by matrices that are indefinite.

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