# Sergei Chaplygin

## Chaplygin, Sergei Alekseevich

Born Mar. 24 (Apr. 5), 1869, in the city of Ranenburg, Riazan’ Province, now the city of Chaplygin, Lipetsk Oblast; died Oct. 8,1942, in Novosibirsk. Soviet specialist in theoretical mechanics, one of the founders of modern aerohydrodynamics. Academician of the Academy of Sciences of the USSR (1929; corresponding member, 1924). Hero of Socialist Labor (1941). Student and colleague of N. E. Zhukovskii.

In 1890, Chaplygin graduated from the faculty of physics and mathematics at Moscow University, where he had specialized in applied mathematics. On Zhukovskii’s recommendation he was allowed to remain at the university to prepare for a position as a professor. Over a period beginning in 1893, Chaplygin taught physics at a women’s secondary educational institution and mechanics at the Moscow Higher Technical School, the Moscow Engineering School, the Moscow Advanced Courses for Women, and Moscow University. He helped organize the Moscow Advanced Courses for Women in 1905 and served as director until 1918; under his leadership the advanced courses developed into a large higher educational institution offering instruction in all the principal branches of knowledge. Chaplygin wrote a university textbook on analytic mechanics—*The Mechanics of a System* (parts 1–2, 1905–07)—and later produced a more concise textbook—*Introductory Course in Mechanics* (1915)—for higher technical educational institutions and for natural science faculties of universities.

Chaplygin’s first works were influenced by Zhukovskii and dealt with hydromechanics. The laws of the motion of a body in a fluid had been found in analytic form in a number of studies carried out by Russian and foreign scientists. Chaplygin gave a geometric interpretation of these laws in his two articles under the title “On Certain Cases of the Motion of a Solid Body in a Fluid” (1894, 1897); the second article was his master’s dissertation. In its simplicity and completeness his interpretation bears the same classic character as L. Poinsot’s famous geometric interpretation of the motion of a body by inertia.

Chaplygin’s subsequent scientific works were devoted mainly to two classic problems in theoretical mechanics: the problem of the motion of a body in the presence of nonintegrable constraints and the problem of the motion of a heavy body about a fixed point. In “On the Motion of a Heavy Body of Revolution in a Horizontal Plane” (1897) he gave the first presentation of the general equations for the motion of nonholonomic systems. His equations are generalizations of the Lagrange equations, from which they differ in the presence of additional terms. Other works of Chaplygin’s in this field include “On a Certain Possible Generalization of the Theorem of Areas” (1897) and “On the Rolling of a Sphere Along a Horizontal Plane” (1903). In 1899 the St. Petersburg Academy of Sciences awarded Chaplygin an honorary gold medal for his studies on the theory of the motion of a body in a fluid and on the motion of bodies with nonintegrable constraints.

In the late 19th and early 20th centuries Chaplygin did his first work on jet flows. He produced a series of papers on the theory of jets in an incompressible fluid. In 1902 he presented his doctoral dissertation, *On Gas Streams*, at Moscow University; it gave a method of studying jet flows of a gas at any subsonic speed (*see*GAS DYNAMICS). At that time the investigation of gas flows at speeds near the speed of sound had no practical application in aviation. Three decades later, however, Chaplygin’s dissertation served as a starting point for many studies by aerodynamics specialists and provided a basis for the solution of problems of subsonic flows. After undergoing refinement, the methods developed in the dissertation led to the solution of a number of problems of modern aerodynamics, including the principal problems involved in the behavior of wings at high subsonic speeds.

In 1910, Chaplygin presented a paper at a meeting of the Moscow Mathematical Society in which he advanced a postulate that permitted determination of the rate of circulation flow around a wing section. This postulate constituted the necessary supplement to Zhukovskii’s theorem that confirmed the theorem as the fundamental principle explaining the lift acting on a wing.

Problems in aerodynamics became the central concern of Chaplygin’s research. His paper “On the Pressure Exerted by a Plane-parallel Flow on an Impeding Body” and Zhukovskii’s paper “On the Contours of Airfoils in Airplanes” appeared almost simultaneously in 1910. These two works gave the first presentation of methods for the quantitative determination of the lift on a wing section. They completed the establishment of the principles of aerodynamics and proved of seminal importance in the field’s subsequent development. Chaplygin’s principle regarding the descent of jet flows from the sharp edge of a wing was applied by him in his paper to the determination of flows around a number of specific profiles. The paper contains the now generally known formulas for determining the lift and moment from the characteristic functions of the flow and provided the first methods for plotting the flow around wing profiles with a sharp trailing edge and a rounded leading edge. In particular, Chaplygin introduced the well-known inverted-parabola profiles that were found in a different way by Zhukovskii and that are often called Zhukovskii, or Joukowski, profiles.

Chaplygin’s important work “Theory of Cascaded Airfoils” appeared in 1914. It set forth the fundamentals of the theory of the circulation around cascades; this theory underlies the design of propellers, turbines, and other hydraulic machines. In subsequent works Chaplygin solved a number of complex problems relating to aeromechanics and aviation—for example, the determination of the lift application point, the determination of the forces in unsteady flight, the theory of high-lift wings, and several problems of wing stability in flight.

Chaplygin made important contributions to mathematics. His investigations in the approximate integration of differential equations are major achievements of mathematical thought. His ideas proved applicable not only to the solution of broad classes of differential equations but also to the approximate solution of very general classes of functional equations.

After the October Revolution of 1917, Chaplygin took an active part in the building of a socialist state. In 1918 he was associated with the Commission on Special Artillery Tests of the Main Artillery Directorate and with the Scientific Experimental Institute of Railroad Transport. In late 1918 he was enlisted by Zhukovskii to help organize the Central Aerodynamic and Hydrodynamic Institute (TsAGI), the largest institute of its kind in the world. Chaplygin was chairman of the institute’s collegium from 1921 to 1930 and executive director of the institute from 1928 to 1931. From 1931 to 1941, as head of the institute’s scientifc work, he supervised the organization of its largest aerodynamic and hydrodynamic laboratories. At the same time, in his capacity as a member of the Academy of Sciences of the USSR, Chaplygin helped the Academy deal with the task of involving science in the building of a socialist state.

Chaplygin received the Zhukovskii Prize in 1925; he was awarded two Orders of Lenin and two other orders.

In 1942 the Academy of Sciences of the USSR established the S. A. Chaplygin Prize “for the best original work in theoretical research in the field of mechanics.” A bust of Chaplygin was dedicated in Moscow in 1961, and a monument was erected at the TsAGI in 1959. Chaplygin’s name has been given to streets in Moscow and Novosibirsk, an aerodynamic laboratory at the TsAGI, a memorial museum-apartment in Moscow, and a crater on the back side of the moon.

### WORKS

*Sobr. soch*., vols. 1–4. Moscow-Leningrad, 1948–50.

*Izbr. trudy*. Moscow, 1976. (In the

*Klassiki nauki*series).

### REFERENCES

Keldysh, M. V. In S. A. Chaplygin,*Izbr. trudy*. Moscow, 1976. (Contains bibliography.)

Golubev, V. V.

*Sergei Alekseevich Chaplygin*. Moscow, 1947.

*S. A. Chaplygin: Materialy k nauchnoi biografii: K stoletiiu so dnia rozhdeniia, 1869–1969. (Trudy TsAGI*, issue 1429.) Moscow, 1972.

M. V. KELDYSH