Application of first integrals in the construction of the Lyapunov function for the random response stability testing

0557023 - ÚTAM 2023 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Náprstek, Jiří - Fischer, Cyril
Application of first integrals in the construction of the Lyapunov function for the random response stability testing.
Engineering mechanics 2022. Book of full texts. Prague: Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, 2022 - (Fischer, C.; Náprstek, J.), s. 281-284. ISBN 978-80-86246-48-2. ISSN 1805-8248. E-ISSN 1805-8256.
[International Conference Engineering mechanics 2022. Milovy (CZ), 09.05.2022-12.05.2022]
Grant CEP: GA ČR(CZ) GC21-32122J
Institucionální podpora: RVO:68378297
Klíčová slova: stochastic stability * Lyapunov function * first integrals * cyclic coordinates
Obor OECD: Civil engineering
https://www.engmech.cz/im/proceedings/show_p/2022/281

The paper deals with a possibility of using the properties of first integrals for the construction of Lyapunov function for the analysis of a dynamic system stability in the stochastic domain. It points out certain characteristics of first integrals resulting in the necessity to introduce additional constraints to assure the principal properties of the Lyapunov function. A number of these constraints has their physical interpretation with reference to system stability. The advantage of this method constructing the Lyapunov function consists in the fact that the Lyapunov function itself contains information on the examined system and, consequently, it is not merely a positive definite function without any relation to the actual case concerned. The presented theory finds application in many dynamical systems. The procedure is illustrated by a nonlinear SDOF example.
Trvalý link: http://hdl.handle.net/11104/0331328