Nikolay Mitrofanovich Krylov
Encyclopedia
Nikolay Mitrofanovich Krylov ' onMouseout='HidePop("7866")' href="/topics/Russian_Empire">Russian Empire
— May 11, 1955, Moscow
, USSR) was a Russia
n and Soviet mathematician known for works on interpolation
, non-linear mechanics, and numerical methods for solving equations of mathematical physics
.
to become Professor at the Crimea University. He worked there until 1922 and then moved to Kiev
to become chairman of the mathematical physics department at the Ukrainian Academy of Sciences.
Nikolay Krylov was a member of the Société Mathématique de France
and the American Mathematical Society
.
s, and made significant contributions to the foundations of non-linear mechanics. They proved the first theorems on existence of invariant measures known as Krylov-Bogolyubov theorem
s, introduced the Krylov-Bogoliubov averaging method
and, together with Yurii Mitropolskiy
, developed the Krylov-Bogoliubov-Mitropolskiy asymptotic method for approximate solving equations of non-linear mechanics.
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
— May 11, 1955, Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
, USSR) was a Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n and Soviet mathematician known for works on interpolation
Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
, non-linear mechanics, and numerical methods for solving equations of mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
.
Biography
Nikolay Krylov graduated from St. Petersburg State Mining Institute in 1902. In the period from 1912 until 1917, he held the Professor position in this institute. In 1917, he went to the CrimeaCrimea
Crimea , or the Autonomous Republic of Crimea , is a sub-national unit, an autonomous republic, of Ukraine. It is located on the northern coast of the Black Sea, occupying a peninsula of the same name...
to become Professor at the Crimea University. He worked there until 1922 and then moved to Kiev
Kiev
Kiev or Kyiv is the capital and the largest city of Ukraine, located in the north central part of the country on the Dnieper River. The population as of the 2001 census was 2,611,300. However, higher numbers have been cited in the press....
to become chairman of the mathematical physics department at the Ukrainian Academy of Sciences.
Nikolay Krylov was a member of the Société Mathématique de France
Société Mathématique de France
The Société Mathématique de France is the main professional society of French mathematicians.The society was founded in 1872 by Émile Lemoine and is one of the oldest mathematical societies in existence...
and the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
.
Research
Nikolay Krylov developed new methods for analysis of equations of mathematical physics, which can be used not only for proving the existence of solutions but also for their construction. Since 1932, he worked together with his student Nikolay Bogoliubov on mathematical problems of non-linear mechanics. In this period, they invented certain asymptotic methods for integration of non-linear differential equations, studied dynamical systemDynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
s, and made significant contributions to the foundations of non-linear mechanics. They proved the first theorems on existence of invariant measures known as Krylov-Bogolyubov theorem
Krylov-Bogolyubov theorem
In mathematics, the Krylov–Bogolyubov theorem may refer to any of the two related fundamental theorems within the theory of dynamical systems...
s, introduced the Krylov-Bogoliubov averaging method
Krylov-Bogoliubov averaging method
The Krylov–Bogolyubov averaging method is a mathematical method for approximate analysis of oscillating processes in non-linear mechanics. The method is based on the averaging principle when the exact differential equation of the motion is replaced by its averaged version...
and, together with Yurii Mitropolskiy
Yurii Mitropolskiy
Yurii Alekseevich Mitropolskiy was a renowned Soviet, Ukrainian mathematician known for his contributions to the fields of dynamical systems and nonlinear oscillations. He received his Ph.D. from Kiev State University, under the supervision of theoretical physicist and mathematician Nikolay...
, developed the Krylov-Bogoliubov-Mitropolskiy asymptotic method for approximate solving equations of non-linear mechanics.
See also
- Describing functionDescribing functionThe Describing function method of Nikolay Mitrofanovich Krylov and Nikolay Bogolyubov is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by an LTI system transfer...
- Krylov-Bogolyubov theoremKrylov-Bogolyubov theoremIn mathematics, the Krylov–Bogolyubov theorem may refer to any of the two related fundamental theorems within the theory of dynamical systems...
- Krylov-Bogoliubov averaging methodKrylov-Bogoliubov averaging methodThe Krylov–Bogolyubov averaging method is a mathematical method for approximate analysis of oscillating processes in non-linear mechanics. The method is based on the averaging principle when the exact differential equation of the motion is replaced by its averaged version...
- Krylov-Bogoliubov-Mitropolskiy asymptotic method
Publications
Nikolay Krylov published over 200 papers on analysis and mathematical physics and two monographs:- Nicolas Kryloff (1931): Les Méthodes de Solution Approchée des Problèmes de la Physique Mathématique. Paris: Gauthier-Villars [in French].
- N. M. Krylov, N. N. Bogoliubov (1947): Introduction to Nonlinear Mechanics. Princeton: Princeton University Press. ISBN 978-0-691-07985-1.