Asymptotic Stability of Coupled Oscillators with Time-Dependent Damping
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The present paper is devoted to an investigation on the asymptotic stability for the damped oscillators with multiple degrees of freedom, $$\begin{aligned} {\mathbf {x}}'' + h(t)\,{\mathbf {x}}' + A\,{\mathbf {x}} = {\mathbf {0}} \end{aligned}$$and its generalization $$\begin{aligned} M\,{\mathbf {x}}'' + C(t)\,{\mathbf {x}}' + K\,{\mathbf {x}} = {\mathbf {0}}, \end{aligned}$$where \(h: [0,\infty ) \rightarrow [0,\infty )\) is a function, A, M and K are \(n \times n\) real constant matrices. and C is an \(n \times n\) matrix whose elements are real-valued functions. The functions h and C correspond to the damping coefficient and the damping matrix, respectively. The origin \(({\mathbf {x}},{\mathbf {x}}') = ({\mathbf {0}},{\mathbf {0}})\) is the only equilibrium of the above-mentioned damped oscillators. Necessary and sufficient conditions are presented for the equilibrium of these oscillators to be asymptotically stable. 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Monatsh Math. doi:10.1007/s00605-014-0695-2 Copyright information© Springer Basel 2015Authors and AffiliationsJitsuro Sugie1Email author1.Department of Mathematics and Computer ScienceShimane University MatsueJapan About this article CrossMark Print ISSN 1575-5460 Online ISSN 1662-3592 Publisher Name Springer International Publishing About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s12346-015-0175-7_Asymptotic Stability of Coupled Os", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s12346-015-0175-7_Asymptotic Stability of Coupled Os", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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