Qualitative analysis of a mechanical system of coupled nonlinear oscillators
In this paper we investigate nonlinear systems of second order ODEs describing the dynamics of two coupled nonlinear oscillators of a mechanical system. We obtain, under certain assumptions, some stability results for the null solution. Also, we show that in the presence of a time-dependent external...
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| Format: | Article |
| Language: | English |
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University of Szeged
2023-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10303 |
| _version_ | 1797352336959471616 |
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| author | Gheorghe Moroșanu Cristian Vladimirescu |
| author_facet | Gheorghe Moroșanu Cristian Vladimirescu |
| author_sort | Gheorghe Moroșanu |
| collection | DOAJ |
| description | In this paper we investigate nonlinear systems of second order ODEs describing the dynamics of two coupled nonlinear oscillators of a mechanical system. We obtain, under certain assumptions, some stability results for the null solution. Also, we show that in the presence of a time-dependent external force, every solution starting from sufficiently small initial data and its derivative are bounded or go to zero as the time tends to $+\infty$, provided that suitable conditions are satisfied. Our theoretical results are illustrated with numerical simulations. |
| first_indexed | 2024-03-08T13:14:58Z |
| format | Article |
| id | doaj.art-0c82a600810a4b1689cd05e3cd09f3e6 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-03-08T13:14:58Z |
| publishDate | 2023-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-0c82a600810a4b1689cd05e3cd09f3e62024-01-18T08:28:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752023-05-0120231612610.14232/ejqtde.2023.1.1610303Qualitative analysis of a mechanical system of coupled nonlinear oscillatorsGheorghe Moroșanu0Cristian Vladimirescu1Babes-Bolyai Univ Cluj-Napoca, RomaniaUniversity of Craiova, Craiova, RomaniaIn this paper we investigate nonlinear systems of second order ODEs describing the dynamics of two coupled nonlinear oscillators of a mechanical system. We obtain, under certain assumptions, some stability results for the null solution. Also, we show that in the presence of a time-dependent external force, every solution starting from sufficiently small initial data and its derivative are bounded or go to zero as the time tends to $+\infty$, provided that suitable conditions are satisfied. Our theoretical results are illustrated with numerical simulations.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10303coupled oscillatorsuniform stabilityasymptotic stabilityuniform asymptotic stability |
| spellingShingle | Gheorghe Moroșanu Cristian Vladimirescu Qualitative analysis of a mechanical system of coupled nonlinear oscillators Electronic Journal of Qualitative Theory of Differential Equations coupled oscillators uniform stability asymptotic stability uniform asymptotic stability |
| title | Qualitative analysis of a mechanical system of coupled nonlinear oscillators |
| title_full | Qualitative analysis of a mechanical system of coupled nonlinear oscillators |
| title_fullStr | Qualitative analysis of a mechanical system of coupled nonlinear oscillators |
| title_full_unstemmed | Qualitative analysis of a mechanical system of coupled nonlinear oscillators |
| title_short | Qualitative analysis of a mechanical system of coupled nonlinear oscillators |
| title_sort | qualitative analysis of a mechanical system of coupled nonlinear oscillators |
| topic | coupled oscillators uniform stability asymptotic stability uniform asymptotic stability |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10303 |
| work_keys_str_mv | AT gheorghemorosanu qualitativeanalysisofamechanicalsystemofcouplednonlinearoscillators AT cristianvladimirescu qualitativeanalysisofamechanicalsystemofcouplednonlinearoscillators |