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Gyroscopically stabilized oscillators and heat baths. (English) Zbl 1066.70014

The authors investigate the stability of a gyroscopically stabilized system interacting with a finite or infinite-dimensional heat bath. As a standard model for a gyroscopic system, they consider a particle on rotating disc and a charged oscillator in magnetic field. The authors show that coupling to a finite (that is nonthermal) system of oscillators with sufficient coupling strength induces instability. The authors also consider the infinite-dimensional limit. In this case dissipation plays a crucial role. A graphical criterion is given for determining the onset of instability. Moreover, the authors also discuss other types of infinite-dimensional coupling.

MSC:

70K20 Stability for nonlinear problems in mechanics
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