Specific character of disk motion on the rheological ground

This paper proposes a new mathematical model of disk motion on the rheological ground on the basis of Kelvin's model. A system of differential equations of the disk motion is derived in the form of modified Chaplygin equations involving generalized rheological response force as well as nonholonomic constraints equations. The instability of undisturbed motion is studied by equations of the first approximation. It is shown that the rectilinear motion of the disk and spinning around a vertical diameter are unstable with respect to the nutation angle $\theta$.