Stability of disk motion on the rheological ground - Georgiy V Pavlov; Mariya A Kalmova; Elena S Vronskaya; Igor N Ignatov (Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2011)
In this paper a new mathematical model of the disk motion on the basis of the Kelvin body is constructed. Accepting the hypothesis of a point contact with the drive base, 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 three stationary constraint equations, two of which are nonholonomic. The analysis of the drive permanent movements stability was carried out. It is shown that the rectilinear motion of the disk and spinning around a vertical diameter are unstable in relation to the nutation angle θ.