On the passive stabilization of the equilibrium state of Lagrangian systems (Q1300702)

The content of the paper is a parallel to results published somewhat earlier by \textit{K. Pfeiffer} and \textit{A. Ya. Savchenko} [see the foregoing entry], although it was apparently written at about the same time. Here the authors consider a passive stabilization of a (practically) conservative system subject to a coupling with a viscous damping device. The resulting damping term is added to Lagrangian equations. The Lyapunov standard form of order four exhibits a critical case with two purely imaginary eigenvalues. The method of analysis follows the procedure described in chapter 4, of \textit{I. G. Malkin}'s book [Theorie der Stabilität der Bewegung. (Russian), Moskau, Verlag `Nauka'. Hauptredaktion für physikalisch-mathematische Literatur (1966; Zbl 0136.08502)]. Two slightly different illustrative examples are presented.