On stabilization of nonconservative systems motion by means of stochastic and deterministic excitation (Q2719537)

The author studies a linear nonconservative mechanical system NEWLINE\[NEWLINE \ddot y+\varepsilon dB_0\dot y + \varepsilon\Lambda y + \varepsilon\ddot\xi(t)Qy=0\tag{1} NEWLINE\]NEWLINE exposed to the parametric excitation \(\xi(t)\). Under some assumptions on the function \(\xi(t)\) it is proposed to transform system (1) to the other system such that for \(\,\xi(t)=0\,\) the expansion of stability domain of the initial system is possible. Stabilization of the equilibrium state of the Ziegler's pendulum is considered as an example.