Specific character of disk motion on the rheologicalground

This paper proposes a new mathematical model of disk motion onthe rheological ground on the basis of Kelvins model. A system of differential equations of thedisk motion is derived in the form of modified Chaplygin equations involving generalizedrheological response force as well as nonholonomic constraints equations. The instability of undisturbedmotion is studied by equations of the first approximation. It is shown that the rectilinearmotion of the disk and spinning around a vertical diameter are unstable with respect to the nutationangle ƒ.

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