Stability Analysis of a Rigid Body with a Flexible Attachment Using the Energy-Casimir Method.

Abstract

We consider a system consisting of a rigid body to which a linear extensible shear beam is attached. For such a system the Energy- Casimir method can be used to investigate the stability of the equilibria. In the case we consider, it can be shown that a test for (formal) stability reduces to checking the positive definiteness of two matrices which depend on the parameters of the system and the particular equilibrium about which the stability is to be ascertained.