Geodesic
Bifurcation of the roots of the characteristic polynomial and the destabilization paradox in friction induced oscillations
Theoretical and applied mechanics, Tome 34 (2007) no. 2.

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Paradoxical effect of small dissipative and gyroscopic forces on the stability of a linear non-conservative system, which manifests it-self through the unpredictable at first sight behavior of the critical non-conservative load, is studied. By means of the analysis of bi-furcation of multiple roots of the characteristic polynomial of the non-conservative system, the analytical description of this phenomenon is obtained. As mechanical examples two systems possessing friction induced oscillations are considered: a mass sliding over a conveyor belt and a model of a disc brake describing the onset of squeal during the braking of a vehicle.
Keywords: friction-induced oscillations, circulatory system, destabilization paradox due to small damping, characteristic polynomial, multiple roots, bifurcation, stability domain, Whitney umbrella singularity 
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     author = {O. N. Kirillov},
     title = {Bifurcation of the roots of the characteristic polynomial and the destabilization paradox in friction induced oscillations},
     journal = {Theoretical and applied mechanics},
     pages = {87 - 109},
     publisher = {mathdoc},
     volume = {34},
     number = {2},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/TAM_2007_34_2_a0/}
}
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O. N. Kirillov. Bifurcation of the roots of the characteristic polynomial and the destabilization paradox in friction induced oscillations. Theoretical and applied mechanics, Tome 34 (2007) no. 2. http://geodesic.mathdoc.fr/item/TAM_2007_34_2_a0/