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 Trudy Mat. Inst. Steklova, 2007, Volume 258, Pages 154–161 (Mi tm481)

Invariant Planes, Indices of Inertia, and Degrees of Stability of Linear Dynamic Equations

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Spectral properties of linear dynamic equations linearized at equilibrium points are analyzed. The analysis involves a search for invariant planes that are uniquely projected onto the configuration plane. In turn, the latter problem reduces to the solution of a quadratic matrix equation of special form. Under certain conditions, the existence of two different solutions is proved by the contraction mapping method. An estimate for the degree of stability is obtained in terms of the index of inertia of potential energy.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 258, 147–154

Bibliographic databases:

UDC: 517.925.51+531.36
Received in December 2006

Citation: V. V. Kozlov, “Invariant Planes, Indices of Inertia, and Degrees of Stability of Linear Dynamic Equations”, Analysis and singularities. Part 1, Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 258, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 154–161; Proc. Steklov Inst. Math., 258 (2007), 147–154

Citation in format AMSBIB
\Bibitem{Koz07} \by V.~V.~Kozlov \paper Invariant Planes, Indices of Inertia, and Degrees of Stability of Linear Dynamic Equations \inbook Analysis and singularities. Part~1 \bookinfo Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday \serial Trudy Mat. Inst. Steklova \yr 2007 \vol 258 \pages 154--161 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm481} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2400528} \zmath{https://zbmath.org/?q=an:1155.70012} \elib{https://elibrary.ru/item.asp?id=9549687} \transl \jour Proc. Steklov Inst. Math. \yr 2007 \vol 258 \pages 147--154 \crossref{https://doi.org/10.1134/S008154380703011X} \elib{https://elibrary.ru/item.asp?id=13549526} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35148879786}