Aleksandr Mikhailovich Lyapunov (Александр Михайлович Ляпунов) (June 6, 1857 – November 3, 1918, all new style) was a Russian mathematician, mechanician and physicist. June 6 is the 157th day of the year in the Gregorian calendar (158th in leap years), with 208 days remaining. ...
1857 was a common year starting on Thursday (see link for calendar). ...
November 3 is the 307th day of the year (308th in leap years) in the Gregorian Calendar, with 58 days remaining. ...
1918 (MCMXVIII) was a common year starting on Tuesday of the Gregorian calendar (see link for calendar) or a common year starting on Wednesday of the Julian calendar. ...
In Britain and countries of the British Empire, Old Style or O.S. after a date means that the date is in the Julian calendar, in use in those countries until 1752; New Style or N.S. means that the date is in the Gregorian calendar, adopted on 14 September...
This article is in need of attention from an expert on the subject. ...
Mechanics refers to: a craft relating to machinery (from the Latin mechanicus, from the Greek mechanikos, meaning one skilled in machines), or a range of disciplines in science and engineering. ...
A physicist is a scientist trained in physics. ...
Lyapunov was born in Yaroslavl, Imperial Russia. His father Mikhail Vasilyevich Lyapunov (18201868) was a well known astronomer and a head of the Demidovski lyceum. Because of the reaction of the university administration, after the departure of Lobachevsky, he gave up his work entirely in 1864 at the observatory of the University of Kazan. He moved with his family on his wife's estate in Simbirsk province (now Ulyanovsk Oblast), where he devoted his time to the education of his oldest sons, Aleksandr and Sergei (18591924). During long winter nights he stayed with his sons and he taught them assiduously with the aid of games on maps of the world. He possessed a lot of books in Russian, German and French on subjects as varied as mathematics, astronomy, philosophy, history, ethnography, political economy and literature. After the sudden death of his father Aleksandr was educated by his uncle R. M. Sechenov, brother of the famous philosopher Ivan Mikhailovich Sechenov. At his uncle's Lyapunov learned with his cousin, his intended Nataliya Rafailovna. In 1870 his mother moved with her sons to Nizhny Novgorod, where he started to attend the third class of the gymnasium. He passed gymnasium in 1876 with distinction. Aleksandr Lyapunov File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Aleksandr Lyapunov File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Yaroslavl (Russian: ) is a city in Russia, an administrative center of Yaroslavl Oblast, located 250 km NE of Moscow at 57Â°37â€² N 39Â°51â€² E The historical part of the city is located at confluence of Volga and Kotorosl. ...
Imperial Russia is the term used to cover the period of history from the expansion of Russia under Peter the Great, through the expansion of the Russian Empire from the Baltic to the Pacific Ocean, to the deposal of Nicholas II of Russia, the last tsar, at the start of...
Mikhail Vasilyevich Lyapunov (18201868), astronomer and a head of the Demidovski lyceum, father of Aleksandr and Sergei. ...
1820 was a leap year starting on Saturday (see link for calendar). ...
1868 was a leap year starting on Wednesday (see link for calendar). ...
An astronomer or astrophysicist is a scientist whose area of research is astronomy or astrophysics. ...
A lyceum can be an educational institution (often a school of secondary education in Europe), or a public hall used for cultural events like concerts. ...
Nikolay Ivanovich Lobachevsky Nikolai Ivanovich Lobachevsky (ÐÐ¸ÐºÐ¾Ð»Ð°ÌÐ¹ Ð˜Ð²Ð°ÌÐ½Ð¾Ð²Ð¸Ñ‡ Ð›Ð¾Ð±Ð°Ñ‡ÐµÌÐ²ÑÐºÐ¸Ð¹) (December 1, 1792â€“February 24, 1856 (N.S.); November 20, 1792â€“February 12, 1856 (O.S.))) was a Russian mathematician. ...
1864 was a leap year starting on Friday (see link for calendar). ...
Observatory of Strasbourg An observatory is a location used for observing terrestrial and/or celestial events. ...
Kazan State University is located in Kazan, Tatarstan, Russia. ...
Ulyanovsk Oblast (Улья́новская о́бласть) is an administrative division of the Russian Federation. ...
Sergei Mikhailovich Lyapunov (November 30, 1859  November 8, 1924) was a Russian composer. ...
1859 is a common year starting on Saturday. ...
1924 (MCMXXIV) was a leap year starting on Tuesday (link will take you to calendar). ...
Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has media related to: Mathematics Inter. ...
Astrology: the study of the positions of the celestial objects relative to the Earth and how these positions affect happenings on the lives of cultures, nations and the natural environment. ...
These five broad types of question are called analytical or logical, epistemological, ethical, metaphysical, and aesthetic respectively. ...
One of the most famous quotations about history and the value of studying history, by Spanish philosopher, George Santayana, reads: Those who cannot remember the past are condemned to repeat it. ...
Ethnography (from the Greek ethnos = nation and graphein = writing) refers to the qualitative description of human social phenomena, based on fieldwork. ...
Political economy was the original term for the study of production, the acts of buying and selling, and their relationships to laws, customs and government. ...
...
1870 was a common year starting on Saturday (see link for calendar). ...
Nizhny Novgorod (Russian: ÐÐ¸ÌÐ¶Ð½Ð¸Ð¹ ÐÐ¾ÌÐ²Ð³Ð¾Ñ€Ð¾Ð´), colloquially shortened as Nizhny and also transliterated into English as Nizhniy Novgorod or Nizhni Novgorod, is the fourth largest city of the Russian Federation, ranking after Moscow, Saint Petersburg and Novosibirsk. ...
A gymnasium is a type of school of secondary education in parts of Europe. ...
1876 is a leap year starting on Saturday. ...
He studied at the PhysicoMathematical department of the University of Saint Petersburg, where he was a schoolfellow of Markov. In the beginning he listened to Mendeleyev's lectures on chemistry. After a month he transferred to the mathematics department of the university, but he continued attending the chemistry lectures. Mathematics was taught at that time by Chebyshev and his students Aleksandr Nikholaevich Korkin and Egor Ivanovich Zolotarev. Lyapunov wrote his first independent scientific works under the guidance of professor of mechanics, D. K. Bobylev. In his fourth year he received the gold medal for a work on hydrostatics, which had been suggested by the faculty. This was the basis for his first published scientific work About the equilibrium of solid bodies in vessels with arbitrary forms, filled with dense fluids (О равновесии тяжелых тел в тяжелых жидкостях, содержащихся в сосуде определенной формы) and About the potential of hydrostatic pressure (О потенциале гидростатических давлений). In both works he used many new approaches and developed new rigorous proofs of a few earlier incomplete theorems from hydrostatics. With the first work he gained the title of candidate in mathematical sciences. Now he was able to leave the university to prepare for a professorial calling. Seal of Saint Petersburg State University Saint Petersburg State University (Ð¡Ð°Ð½ÐºÑ‚ÐŸÐµÑ‚ÐµÑ€Ð±ÑƒÑ€Ð³ÑÐºÐ¸Ð¹ Ð“Ð¾ÑÑƒÐ´Ð°Ñ€ÑÑ‚Ð²ÐµÐ½Ð½Ñ‹Ð¹ Ð£Ð½Ð¸Ð²ÐµÑ€ÑÐ¸Ñ‚ÐµÑ‚) one of the oldest Russian educational institutions, established in the city of Saint Petersburg on January 28, 1724 by decree of Peter the Great. ...
Andrey Andreyevich Markov (Андрей Андреевич Марков) (June 14, 1856 N.S. _ July 20, 1922) was a Russian mathematician. ...
Portrait of Dmitri Mendeleyev by Ilya Repin Dmitriy Ivanovich Mendeleyev (Russian: â–¶(?)) (8 February [O.S. 27 January] 1834 in Tobolsk â€“ 2 February [O.S. 20 January] 1907 in Saint Petersburg), was a Russian chemist. ...
// Introduction The fundamental component of chemistry is that it involves matter in some way (this explains its broad reach). ...
Pafnuty Lvovich Chebyshev Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв) (May 4, 1821  November 26, 1894) was a Russian mathematician. ...
Hydrostatics, also known as fluid statics, is the study of fluids at rest. ...
He graduated in 1880. He received a Master's degree in applied mathematics in 1884 with the thesis About the stability of elliptic forms in the equilibrium of turbulent fluid (Об устойчивости эллипсоидальных форм равновесия вращающейся жидкости). This work treated an important and difficult task about understanding the shapes of celestial bodies. This task was offered by Chebyshev to Zolotarev and to Sofia Vasilyevna Kovalevskaya and Chebyshev was aware of the difficulty. As was said by Vladimir Andreevich Steklov, "Chebyshev saw in the young man such an immense research power, that he had dared to lay on him such a toilsome task". Lyapunov had already begun to study this stability in his previous twoyears attempts at solving the task. After the public announcement his work instantly attracted the attention of mathematicians, mechanicians, physicists and astronomers all over the world. 1880 was a leap year starting on Thursday (see link for calendar). ...
Applied mathematics is a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains. ...
1884 is a leap year starting on Tuesday (click on link to calendar). ...
See lists of astronomical objects for a list of the various lists of astronomical objects in Wikipedia. ...
Sofia Vasilyevna Kovalevskaya (Софья Васильевна Ковалевская) (January 15, 1850–February 10, 1891) was a Russian mathematician and a student of Karl Weierstrass in Berlin. ...
Vladimir Andreevich Steklov (January 9, 1864  May 30, 1926) was a Soviet/Russian mathematician, mechanician and physicist. ...
The word stability has a number of technical meanings, all related to the common meaning of the word. ...
In 1885 he became private reader of the University at Kharkov in the chair of mechanics, where he replaced V. G. Imshenecky, who had been chosen as a member of the Russian Academy of Sciences. Lyapunov had lectured already from 1880 at the Department of Mechanics and this had taken him a lot of time. His student and collaborator, academician Steklov, said about his fine lectures: "A handsome young man, by his appearance almost like the other students, came before the audience, where there was also an old dean, professor Levakovsky, who was respected by all students. After the dean had left, the young man with a trembled voice started to lecture on a theme about the dynamics of a point, instead of a theme from the dynamics of systems. This subject was already in lectures by a professor Delaryu. I was in the fourth class. I had listened to the lectures in Moscow of Davidov, Cinger, Soletov and Orlov. I was in the University of Kharhov already for two years, so I was familiar with the lectures on mechanics. But I hadn't known the subject from the beginning and I had never seen it in any textbook. So in this way boredom with the lecture had collapsed in ruins. Aleksandr Mikhailovich had earned the respect of the audience for an hour with the power of a natural gift so seldom seen in such a youth. He didn't know this of course. From this day on students considered him with different eyes, and they showed him special respect. Many times they even didn't dare to speak with him, to avoid showing their ignorance". Lyapunov lectured at the university on themes from theoretical mechanics, integrals of differential equations and the theory of probability. These lectures were never published and they remained only in the notes of students. He lectured about mechanics in six areas: kinematics, the dynamics of a pointed body, the dynamics of systems of pointed bodies, the theory of attracting forces, the theory of the deformation of solid bodies, and hydrostatics. At the same time he lectured on analytical mechanics between 1887 and 1893 at the Technological institute at Kharkov. 1885 is a common year starting on Thursday. ...
Kharkov (rus: Ха́рьков) or Kharkiv (ukr: Ха́рків) is the second largest city in Ukraine, a center of Kharkivska oblast. It is situated in the northeast of the country and has a population of two million. ...
Russian Academy of Sciences (Росси́йская Акаде́мия Нау́к) is the national academy of Russia. ...
1880 was a leap year starting on Thursday (see link for calendar). ...
The title Academician denotes a Full Member of an art, literary, or scientific academy. ...
Moscow (Russian: ÐœÐ¾ÑÐºÐ²Ð°Ì, Moskva, IPA: â–¶(?)) is the capital of Russia, located on the river Moskva. ...
In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. ...
In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ...
The word probability derives from the Latin probare (to prove, or to test). ...
In physics, kinematics is the branch of mechanics concerned with the motions of objects without being concerned with the forces that cause the motion. ...
Analytical mechanics is a term used for a refined, highly mathematical form of classical mechanics, constructed from the eighteenth century onwards as a formulation of the subject as founded by Isaac Newton. ...
1887 is a common year starting on Saturday (click on link for calendar). ...
1893 was a common year starting on Sunday (see link for calendar). ...
In 1892 he was awarded his Ph.D. with the thesis A general task about the stability of motion (Общая задача об устойчивости движения). A similar thesis had been defended ten years earlier by Nikolai Yegorovich Zhukovsky, a founder of the TsAGI. After the doctorate Lyapunov became a full professor of the University at Kharkov. After the death of Chebyshev in 1894 Lyapunov became in 1901 a head of applied mathematics at the University at Saint Petersburg, where he had entirely devoted to tutorage and research work. 1892 was a leap year starting on Friday (see link for calendar). ...
Nikolai Yegorovich Zhukovsky (Николай Егорович Жуковский) (January 5, 1847 new style – March 17, 1921), Russian scientist, founding father of modern aero and hydrodynamics. ...
TsAGI is a transliteration of the Russian abbreviation for Ð¦ÐµÐ½Ñ‚Ñ€Ð°ÌÐ»ÑŒÐ½Ñ‹Ð¹ Ð°ÑÑ€Ð¾Ð³Ð¸Ð´Ñ€Ð¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÌÑ‡ÐµÑÐºÐ¸Ð¹ Ð¸Ð½ÑÑ‚Ð¸Ñ‚ÑƒÌÑ‚ (Ð¦ÐÐ“Ð˜) or Tsentralniy Aerogidrodinamicheskiy Institut, the Central Aerohydrodynamic Institute. ...
1894 was a common year starting on Monday (see link for calendar). ...
1901 (MCMI) was a common year starting on Tuesday (see link for calendar). ...
His work in the field of differential equations, potential theory, the stability of systems and probability theory is very important. His main preoccupations were the stability of equilibrium and the motion of mechanical system, the model theory for the stability of uniform turbulent liquid, and the particles under the influence of gravity. His work in the field of mathematical physics is very important for the subsequent advance of this field. His work from 1898 About some questions, connected with Dirichlet's tasks (О некоторых вопросах, связанных с задачей Дирихле) contains a study of the properties of potential around charges and dipoles, continuously distributed along any surface. His work in this field is in close connection with the work of Steklov. Lyapunov developed many important approximative methods. His methods, today named Lyapunov methods, which he developed in 1899, make it possible to define the stability of sets of ordinary differential equations. He elaborated the modern rigorous theory of the stability of a system, and the motion of a mechanical system on the basis of a finite number of parameters. In probability theory he generalised the works of Chebyshev and Markov and he finally proved the Central limit theorem using more common conditions than his forerunners. The method he used for the proof is today one of the foundations of probability theory. From 1899 to 1902 he was a head of Kharkov mathematical society and an editor of his News. On the December 2, 1900 he was elected as a corresponding member of the Russian Academy of Sciences, and on the October 6, 1901 as a fully entitled member of the Academy in the field of applied mathematics. Potential theory may be defined as the study of harmonic functions. ...
Probability theory is the mathematical study of probability. ...
Gravity is the force of attraction between massive particles. ...
Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories1. ...
1898 was a common year starting on Saturday (see link for calendar). ...
Peter Gustav Lejeune Dirichlet. ...
It has been suggested that this article or section be merged with Scalar potential. ...
Charge is a word with many different meanings. ...
The Earths magnetic field, which is approximately a dipole. ...
1899 was a common year starting on Sunday (see link for calendar). ...
Central limit theorems are a set of weakconvergence results in probability theory. ...
1899 was a common year starting on Sunday (see link for calendar). ...
1902 (MCMII) was a common year starting on Wednesday (see link for calendar). ...
December 2 is the 336th day (337th in leap years) of the year in the Gregorian calendar. ...
1900 (MCM) is a common year starting on Monday. ...
October 6 is the 279th day of the year (280th in Leap years). ...
1901 (MCMI) was a common year starting on Tuesday (see link for calendar). ...
Among others he wrote such works as: About constant spiral motion of a rigid body in a fluid (О постоянных винтовых движениях твердого тела в жидкости) in 1890, and many articles, which were published by the Russian Academy of Sciences: 1890 was a common year starting on Wednesday (see link for calendar). ...
 About a series in the theory of linear differential equations (Sur une série dans la théorie des équations differentielles linéaires etc.) 1902,
 Researches in the theory of celestial bodies (Recherches dans la théorie des corps célestes) 1903,
 About Clairaut's equation, etc. (Sur l'équation de Clairaut etc.) 1904,
 A new form of the theorem on the limit of probability (Nouvelle forme du théorème sur la limite de probabilité),
 About a proposition in the probability theory (Sur une proposition de la théorie des probabilités) 1906.
With his researches on celestial mechanics he opened a new page in the history of global science and he showed the inaccuracy in the knowledge of several foreign scientists. In 1908 he participated at the 4th Mathematical congress in Rome. At this time he took part in the publication of Euler's selected works, and he was an editor of the 18th and 19th part of this miscellany. By the end of June 1917 he went with his wife, who was seriously ill, to his brother Boris in Odessa, Russia (now Ukraine). His wife's impending death, his own partial blindness, and the generally bad conditions for life, all contributed to his anxiety. In spite of this he delivered his last lecture about the form of celestial bodies at the invitation of the Department of Physics and Mathematics at Odessa. On October 31 his wife died, and on the same day he shot himself. He then lay unconscious a few days till his death. 1902 (MCMII) was a common year starting on Wednesday (see link for calendar). ...
1903 (MCMIII) was a common year starting on Thursday (see link for calendar). ...
1904 is a leap year starting on a Friday (link will take you to calendar). ...
1906 (MCMVI) was a common year starting on Monday (see link for calendar). ...
Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ...
A scientist is a person who is an expert in at least one area of science and who uses the scientific method to research that area. ...
1908 (MCMVIII) is a leap year starting on Wednesday (link will take you to calendar). ...
City motto: Senatus Populusque Romanus â€“ SPQR (The Senate and the People of Rome) Founded 21 April 753 BC mythical, 1st millennium BC Region Latium Mayor Walter Veltroni (LeftWing Democrats) Area  City Proper 1290 kmÂ² Population  City (2004)  Metropolitan  Density (city proper) 2,546,807 almost 4,000,000 1...
Leonhard Euler by Emanuel Handmann Leonhard Euler (IPA ) (April 15, 1707 â€“ September 18, 1783) was a Swiss mathematician and physicist. ...
1917 (MCMXVII) was a common year starting on Monday of the Gregorian calendar (see link for calendar) or a common year starting on Tuesday of the Julian calendar. ...
ODESSA (German Organisation der ehemaligen SSAngehÃ¶rigen; The Organization of Former SSMembers) was an alleged NaziGerman fugitive network set up towards the end of World War II by a group of SS officers, among whom Martin Bormann and Heinrich Himmler. ...
October 31 is the 304th day of the year (305th in leap years) in the Gregorian Calendar, with 61 days remaining, as the final day of October. ...
He usually worked four to five hours at night, and many times even the whole night. Once or twice he visited the theatre or he went to some concert. He had many students. But for the few who really knew him, Lyapunov was a rather raptured man. He had a lean figure, outwardly he acted pretty rude, otherwise he had a hotblooded and sensitive temper. He was an honorary member of many universities, an external member of the Academy in Rome and a corresponding member of the Academy of Sciences in Paris. The Eiffel Tower has become the symbol of Paris throughout the world. ...
See also:
 Lyapunov's central limit theorem,
 Lyapunov's condition,
 Lyapunov's characteristic number—see Lyapunov exponent,
 Lyapunov equation,
 Lyapunov exponent,
 Lyapunov fractal,
 Lyapunov function,
 Lyapunov stability,
 Lyapunov test,
 Lyapunov time,
 Lyapunov tube.
In probability theory, Lyapunovs central limit theorem is one of the variants of the central limit theorems. ...
Central limit theorems are a set of weakconvergence results in probability theory. ...
The Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a measure that characterizes rate of separation of infinitesimaly close trajectories. ...
In control theory, the discrete Lyapunov equation is a system of the form where is a hermitian matrix. ...
The Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a measure that characterizes rate of separation of infinitesimaly close trajectories. ...
Standard Lyapunov logistic fractal with iteration sequence AB Generalized Lyapunov logistic fractal with iteration sequence AABAB In mathematics Lyapunov fractals (also known as MarkusLyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches...
In the theory of dynamical systems, and control theory, Lyapunov functions, named after Aleksandr Mikhailovich Lyapunov, are a family of functions that can be used to demonstrate the stability of some state points of a system. ...
Lyapunov stability is applicable to only unforced (no control input) dynamical systems. ...
This article needs cleanup. ...
Categories: Wikipedia cleanup  Stub  Dynamical systems ...
Artists concept of the Interplanetary Superhighway The Interplanetary Superhighway has come to denote a set of transfer orbits between various planets and moons in the solar system. ...
External links and resources:  Biography at the MacTutor archive (in English)
 http://www.mathsoc.spb.ru/pantheon/lyapunov/be.html (in Russian)
 http://www.spbu.ru/History/275/Chronicle/spbu/Persons/L_yapunov.html (in Russian)
 http://wwwmechmath.univer.kharkov.ua/theormech/lapunov.html (in Russian)
