On Steady-State Motions of an Axisymmetric Rigid Body on a »String« Suspension

Summary

Studies of rotating bodies, suspended on a string or fiber, began, in fact, in the days of the Great Patriotic War with experiments of M.A.Lavrentiev and S.V.Malaschenko concerned at first with effect of rotation on a cumulation phenomenon and later with stability of liquid-filled bodies. In 1943 Malaschenko proposed quite a simple string suspension, originally designed as a thin steel string with one of its ends attached to a vertical drive rotor and another one-to the body to be studied.in this design high speeds of rotation (up to 3000 s^-1 and higher) could be achieved, and a lot of stability studies had been made with such a suspension, particularly for bodies, partly filled with liquid. In these studies the influence of string properties on rotating body behaviour was investigated. The string first was assumed as being infinitely flexible and completely inextensible (i.e. providing a simple geometrical constraint). However later the string was found to be inadequate for rotating large-size bodies. So the existing design of the “string” suspension had been made as a set of rather heavy axisymmetric bodies (rods), coupled through Hooke’s joints. An interesting apparent paradox was observed in fifties, namely, the coexistence of several varions stable steady-state configurations of the axisymmetric rotating body with a string suspension for certain identical values of angular speed W . The analysis of behaviour of bodies with fiber or “string” suspension is the principal aim of this report. Analysis of a suspension mass effect has shown, that substituting heavy rod for an ideal string doesn’t lead to qualitative changes of rotation patterns, the bifurcational values of rotation speed being located between similar values for the string case.