Aleksandr lyapunov biography of michael jackson

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Aleksandr lyapunov biography of michael jackson

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Video Audio icon An illustration of an audio speaker. Audio Software icon An illustration of a 3. Software Images icon An illustration of two photographs. Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. He later dealt with the problem of stability of fluid ellipsoids basing his investigations on the Thomson - Tait variational principle.

He showed that a sufficient condition for stability is that the second and higher variations of the potential energy are positive. Lyapunov admitted that the imposition of certain additional constraints on the first variation reduced the generality of his method, but writes:- But in this respect hardly any other method of investigation could be said to be completely satisfactory.

Lyapunov established that with variation in the angular velocity of revolution Maclaurin ellipsoids pass into Jacobi ellipsoids. The transition point is an ellipsoid of bifurcation corresponding in this case to a Jacobi ellipsoid of revolution. In Lyapunov was elected to the Russian Academy of Sciences in St Petersburg and in the following year became an academician in applied mathematics of the Academy.

Grigorian writes [ 1 ] :- In St Petersburg, Lyapunov devoted himself completely to scientific work. He returned to the problem that Chebyshev had placed before him and, in an extensive series of papers which continued until his death, developed the theory of figures of equilibrium of rotating heavy liquids. He taught at the university but in the spring of his wife's health began to deteriorate rapidly.

Natalia Rafailovna suffered from a form of tuberculosis and Lyapunov was greatly disturbed to watch her health fail. On 31 October Lyapunov's wife died and later that day Lyapunov shot himself. He died three days later in hospital. We have described Lyapunov's main work which was on the theory of rotating liquids. There are, however, other aspects of his work we should mention.

One is certainly his contributions to probability which he became interested in because of courses he was teaching on that subject. Biography [ edit ]. Early life [ edit ]. Education [ edit ]. Teaching and research [ edit ]. Later years [ edit ]. Death [ edit ]. Work [ edit ]. Selected publications [ edit ]. See also [ edit ]. Lyapunov equation Lyapunov exponent Lyapunov fractal Lyapunov function Lyapunov stability Lyapunov time Lyapunov's central limit theorem Lyapunov's condition Lyapunov—Malkin theorem Lyapunov—Schmidt reduction.

Notes [ edit ]. His surname is variously romanized as LjapunovLiapunovLiapounoff or Ljapunow. References [ edit ]. Lyapunov The general problem of the stability of motion. Kharkov: Kharkov Mathematical Society. Further reading [ edit ]. Lyapunov, A. Smith: Automatica vol. Lyapunov's work", International Journal of Control55 3 : —doi : External links [ edit ].

Wikimedia Commons has media related to Aleksandr Lyapunov. Chaos theory. Bifurcation theory Control of chaos Dynamical system Ergodic theory Quantum chaos Stability theory Synchronization of chaos. Yorke Lai-Sang Young. Multifractal system.