Mikhlin, Yuri V.Shmatko, TatyanaRudneva, GayaneGoloskubova, Natalyia S.2022-04-172022-04-172019Stability of stationary regimes in nonlinear systems: analytical and numerical approaches / Yuri V. Mikhlin [at al.] // NODYCON 2019 : book of abstr. of the 1st Nonlinear dynamics conf., February 17-20, 2019. – Rome : SUR, 2019. – [2 p.].https://repository.kpi.kharkov.ua/handle/KhPI-Press/56479A stability of stationary regimes in the form of nonlinear normal modes (NNMs) with rectilinear or nearrectilinear trajectories is analysed by using the Ince algebraization when a variable associated with the vibration mode is chosen as the new independent argument. In this case the variational equations are transformed to equations with singular points. Other approach is realized for NNMs with regular or chaotic behavior in time. Namely, a test which is a consequence of the well-known Lyapunov criterion of stability is used. Both approaches are also used in analysis of stability of other stationary regimes, namely, standing or traveling nonlinear waves.ennonlinear normal vibration modesNODYCONalgebraization by InceGegenbauer polynomialsнелінійні нормальні режими вібраціїалгебраїзація за Inceполіноми ГегенбауераThesis