Awrejcewicz, JanPuzyrov, VolodymyrLosyeva, NataliyaSavchenko, NinaNikolaieva, Oksana2021-12-032021-12-032021Puzyrov V., Awrejcewicz J., Losyeva N., Savchenko N., Nikolaieva O., Estimation the Domain of Attraction for a System of Two Coupled Oscillators with Weak Damping. W: DSTA-2021 Conference Books – Abstracts (16th International Conference : Dynamical Systems Theory and Applications DSTA 2021 ABSTRACTS), Awrejcewicz J. (red.), Kaźmierczak M. (red.), Olejnik P. (red.), Mrozowski J. (red.), Wydawnictwo Politechniki Łódzkiej ; Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki, Łódź 2021, s. 704-705, ISBN 978-83-66741-20-1.978-83-66741-20-1http://hdl.handle.net/11652/4136When solving a wide class of problems of nonlinear dynamics, the stability property of a given system regime is a prerequisite for design. An important role is played by the concept of the domain of attraction (DoA) of the equilibrium point (or limit cycle). However, as a rule, this domain is difficult to find and describe in explicit form. Therefore, the search for DoA estimate has been a fundamental problem in the control theory since the middle of the last century. Currently, methods based on Lyapunov functions predominate in the literature. We have studied the problem of obtaining the estimates of the DoA for equilibrium of the mechanical systems. The method for using Lyapunov function of special kind for a system with polynomial right-hand side to find the estimates for DoA is proposed. This procedure is illustrated by the example of a mechanical system which consists of two coupled nonlinear oscillators with weak damping.enAll rights reservedFair use conditionWszystkie prawa zastrzeżoneDla wszystkich w zakresie dozwolonego użytkudomain of attractionnonlinear oscillatorweak dampingdomena przyciąganiaoscylator nieliniowysłabe tłumienieAbstraktLUT LicenseLicencja PŁLodz University of Technology. Faculty of Mechanical Engineering. Department of Automation, Biomechanics and Mechatronics.Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.