SOME ASPECTS OF DESTABILIZATION IN REVERSIBLE DYNAMICAL-SYSTEMS WITH APPLICATION TO FOLLOWER FORCES

This paper examines the destabilization of the equilibria of reversibl e dynamical systems which is induced by the addition of irreversible p erturbations. Attention is restricted to reversible dynamical systems which have frequently appeared in the literature on elastic stability. There they are often referred to as follower force problems. The dest abilization phenomenon is linear in nature and explicit criteria are e stablished to determine the particular eigenvalue splittings. The post -destabilization dynamics are also examined using the appropriate norm al forms for two specific cases, one where the eigenvalues are non-res onant and the other where the eigenvalues are in a strong one-to-one r esonance. Finally, the destabilization criteria and certain features o f the post-destabilization dynamics are illustrated using two examples of follower force systems.