Aleksandr lyapunov biography examples
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Lyapunov stability
Property of a dynamical system where solutions near an equilibrium point remain so
This article is about asymptotic stability of nonlinear systems. For stability of linear systems, see exponential stability.
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis). The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to
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Lyapunov, Aleksandr Mikhailovich
(b. Yaroslavl, Russia, 6 June 1857; d. Odessa, U.S.S.R., 3 November 1918)
mathematics, mechanics.
Lyapunov was a son of the astronomer Mikhail Vasilievich Lyapunov, who worked at Kazan University from 1840 until 1855 and was director of the Demidovskt Lyceum in Yaroslavl from 1856 until 1863; his mother was the former Sofia Aleksandrovna Shilipova. Lyapunov’s brother Sergei was a composer; another brother, Boris, was a specialist in Slavic philology and a member of the Soviet Academy of Sciences.
Lyapunov received his elementary education at home and later with an uncle, R. M. Sechenov, brother of the physiologist I. M. Sechenov, With R. M. Sechenov’s daughter Natalia Rafailovna (whom he married in 1886), he prepared for the Gymnasium. In 1870 Lyapunov’s mother moved to.Nizhny Novgorod (now Gorky) with her children. After graduating from the Gymnasium in Nizhny Novgorod 876, Lyapunov enrolled in the Physics and ematics Faculty of St. Peter
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layout: person nodeid: bookofproofs$Lyapunov categories: history,19th-century parentid: bookofproofs$603 tags: origin-russia orderid: 1857 title: Lyapunov, Aleksandr Mikhailovich born: 1857 died: 1918 keywords: aleksandr mikhailovich lyapunov,lyapunov description: Aleksandr Lyapunov was a Russian mathematician best known for his development of the stability theory of a dynamical system. He also made contributions to mathematical physics and probability theory. references: bookofproofs$6909 contributors: @J-J-O'Connor,@E-F-Robertson,bookofproofs
Aleksandr Lyapunov was a Russian mathematician best known for his development of the stability theory of a dynamical struktur. He also made contributions to mathematical physics and probability theory.
Mathematical Profile (Excerpt):
- Lyapunov graduated in 1880 and remained at St Petersburg to undertake research.
- Although Lyapunov's Master's thesis did not answer this question, the work of the thesis was motivated by it.
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