Bloch, Anthony M.; Hagerty, Patrick; Rojo, Alberto G.; Weinstein, Michael I. Gyroscopically stabilized oscillators and heat baths. (English) Zbl 1066.70014 J. Stat. Phys. 115, No. 3-4, 1073-1100 (2004). 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. Reviewer: Messoud A. Efendiev (Berlin) Cited in 3 Documents MSC: 70K20 Stability for nonlinear problems in mechanics Keywords:onset of instability; infinite-dimensional coupling PDFBibTeX XMLCite \textit{A. M. Bloch} et al., J. Stat. Phys. 115, No. 3--4, 1073--1100 (2004; Zbl 1066.70014) Full Text: DOI