Qualitative dynamics of planar chains

Abstract

In this paper we derive the equations of motion and analyze some aspects of the dynamics of planar chains. We show that (a) for any integer vector n=(n1,...,nN) (where N is the number of joints) there exists a periodic motion such that the angle of jth joint changes by 2[pi]nj during one period; (b) the straight configuration is (nonlinearly) stable and that any "folded" rectilinear configuration is unstable; (c) the Coriolis effects play no role in stability of these rectilinear configurations, in contrast to other problems such as the stabilizing effect on the spinning top.