Shvets, A. Yu. On the stability of a double pendulum with vibrating suspension point in the presence of lags in the equation of motion. (Russian) Zbl 0572.70024 Approximate methods in the investigation of nonlinear oscillations, Collect. sci. Works, Kiev 1983, 161-172 (1983). [For the entire collection see Zbl 0523.00005.] The influence of time delays on the stability of stationary motions of a double pendulum with vibrating suspension point under viscous friction is analyzed. To study this dynamic system the author uses the averaging method for differential equations. All the results are obtained by analyzing only the first approximation equations from averaged ones. It is shown that time delays essentially influence the stability of equilibrium states. As a rule, these states can become stable under properly changing time delays depending on system parameters. References, 6 in number, fully cover the considered problem. Reviewer: V.Chernyatin MSC: 70K20 Stability for nonlinear problems in mechanics 70J30 Free motions in linear vibration theory 70J25 Stability for problems in linear vibration theory Keywords:time delays; stability of stationary motions; double pendulum; vibrating suspension point; viscous friction; averaging method Citations:Zbl 0523.00005 PDFBibTeX XML