LYAPUNOV

RUSSIA (see also List of Individuals)

\

25.5.1857 Jaroslav/RU - 3.11.1918 Odessa/RU

\

Aleksandr Mikhailovich Lyapunov graduated in physics and mathematics from the Saint Petersburg University in 1880. Based on a notable work on rotational flow, he was appointed Lecturer at the University of Charkov in 1885. He there submitted a PhD thesis in 1892 and was appointed professor in 1893. Lyapunov served as vice-president at Charkov University from 1891 to 1898 and then took over as president for the four following years. In 1900 he was elected Member of the Saint Petersburg Academy of Sciences. From 1902, Lyapunov retired to contribute exclusively to sciences. He was elected Foreign Member of the Italian Accademia dei Lincei in 1909, as also of Académie des Sciences, Paris, in 1916.

\

Lyapunov worked all through his career mainly on the stability of motion, which had a significant impact on theoretical and applied mechanics, on aerodynamics and on astronomy. Questions on this problem were first formulated in the 18th century with regard to the movement of planets, and the entire solar system. It was realized that the sun has the dominant effect on the planets, but that the latter have also a disturbing influence which was proved to be stable because of small positive and negative variations in the attractive forces. Lyapunov may be considered a founder of the stability analysis by using first order perturbing effects. Complicated differential equations were linearized and investigated in terms of stability, a procedure currently widely used in hydrodynamics for stability analysis. Another problem considered by Lyapunov were equilibrium shapes of rotating fluids, as considered extensively also by French mathematicians in the early 19th century. Based on the approaches of Pierre-Simon de Laplace (1749-1827) and Siméon-Denis Poisson (1781-1840) Lyapunov applied his stability analysis to the governing equations instead of a simplified version and determined for instance the density distribution in a rotating sphere. He also was able to demonstrate that the ellipsoidal fluid shape is stable provided the eccentricity remains in certain limits. The works of Jules Henri Poincaré (1854-1912) have set an end to long discussions on Lyapunov's theory of equilibrium figures.

\

_{Anonymous (1948). A.M. Lyapunov. Akademija Nauk SSSR Prikl. Mat. Meh. 12: 469-475. P Grigorian, A.T. (1975). Lyapunov, A.M. Scienziati e tecnologi 2: 307-308. Mondadori: Milano. Lyapunov, A.M. (1947). Problème général de stabilité du mouvement. University Press:Princeton.}

_{Steklov, V.A. (1919). A.M. Lyapunov. Iszvestiya Rossiskoy Akademi Nauk 13(1): 367-388. P http://www-gap.dcs.st-and.ac.uk/%7Ehistory/Mathematicians/Lyapunov.html http://www-gap.dcs.st-and.ac.uk/LYAPUNOVhistory/Mathematicians/Lyapunov.html P}