On Stability of Motion of a Chain of $n$ Driven Bodies

The article deals with the problem of stability of rectilinear motions of multi-link chains of rigid bodies moving in a resisting medium. The authors propose a simple mechanical model that allows them to give a reasonable explanation of instability phenomena observed in reality. The main idea of the article is based on the assumption that lateral forces acting upon lengthy bodies are large enough. This assumption results in the consideration of a nonintegrable constraint as a limiting case. It is well-known that in studies of nonintegrable constraints two different approaches are distinguished. The classical one leads to a nonholonomic constraint, while the other one developed recently by V.V. Kozlov leads to a vakonomic constraint. The authors have shown that instability is typical (in some sense) in both cases though the phase portraits are completely different from the topological point of view.