# Krutkov, Iurii Aleksandrovich

# KRUTKOV, IURII ALEKSANDROVICH

(*b*. St. Petersburg [now Leningrad], Russia, 29 May 1890; *d.* Leningrad, U.S.S.R., 12 September 1952), physics.

Krutkov’sfather, Aleksandr Fedorovich Krutkov, was a teacher of Russian and ancient languages. Soon after Krutkov’s birth the family moved to the Ukraine; there, in the small town of Lubny his father was the master of the classical gymnasium. In 1906 the family returned to St. Petersburg, where in 1908 Krutkov graduated from the gymnasium with a gold medal and then entered the mathematics section of the Faculty of Mathematics and Physics of the university. The decade 1906– 1916 was a remarkable period in the history of this faculty; at that time many brilliant mathematicians (A. S. Besikovich, R. O. Kuz’min, N. I. Muskhelishvili, V. I. Smirnov, la. D. Tamarkin, A. A. Friedmann, I. M. Vinogradov) and physicists (L. V. Mysovskii, P. I. Lukirskii, I. V. Obreimov, N. N. Semenov, D. V. Skobel’tsyn, la. I. Frenkel, and others) studied there. Krutkov, who belonged to this group, was the first “pure theorist” in Russia— he was never involved in experimental work. He was a pupil of Paul Ehrenfest and an active member of his seminar (1908–1912); in 1913 he continued his studies with Ehrenfest at Leiden.

The first series of Krutkov’s scientific publications continued the work of Ehrenfest on adiabatic invariants. Before Krutkov’s papers, the adiabatic invariants of a given physical quantity could be found only by inspired guessing; he was the first to work out a general tool. His papers on this subject played a part in preparation of the conceptual construction of quantum mechanics. Also along Ehrenfest’s lines. Krutkov confirmed that the hypothesis of the independent quanta *hv* of energy of an oscillator leads to Wien’s formula and that only the idea of the association of quanta results in Planck’s formula.

Krutkov was the first Soviet physicist to receive a stipend from the Rockefeller Foundation; he spent two years (1922–1923) in Germany and Holland. This time was an important period not only in his life but also in the history of relativistic cosmology: in a number of talks with Einstein in the spring of 1923 Krutkov showed that Einstein’s criticism of Friedmann’s paper on a nonstationary (expanding) universe was wrong.

The theory of oscillations and statistical mechanics occupied an important place in Krutkov’s work. In a series of his papers (1933–1936) related to the theory of Brownian motion, he considered the nonlinear case of rotational Brownian motion of a particle. Using his results on the Brownian motion of an oscillator, Krutkov built up the theory of the rolling motion of a ship on a “random” (nonperiodic) sea. In this way he established the connection between the rolling angle and the sea characteristics, obtaining simple and important expressions for the function of distribution of the rolling angle together with average values of various characteristics of the rolling motion.

Krutkov turned to problems of classical and statistical mechanics, under the influence of A. N. Krylov, a distinguished expert in the theory of ships. This collaboration produced a classical treatise on the theory of gyroscopes presented in both a vector (Krutkov) and a usual (Krylov) form. Some of Krutkov’s papers were devoted to the theory of rotation of a solid body. The last (postwar) series of papers concerns the theory of elasticity.

Though Krutkov taught for some time at the Faculty of Physics and Mechanics of the Leningrad Polytechnical Institute, his closest ties were with Leningrad University, where he was a professor (with a short break) from 1921 to 1952. During World War II, though imprisoned, he worked on aviation engineering problems under A. N. Tupolev. In his last years he was the head of the department of mechanics of the Faculty of Mechanics and Mathematics. Among Krutkov’s pupils at the university was V. A. Fock, with whom he published a paper on the theory of the Rayleigh pendulum (here one can easily see a connection with Krutkov’s interests in the theory of adiabatic invariants).

In 1933 the U.S.S.R. Academy of Sciences elected Krutkov a corresponding member. In 1952 he was awarded the State Prize for a series of papers on mechanics.

Krutkov had married Lidiia Dmitrievna Khudiakova in 1949. They had no children.

## BIBLIOGRAPHY

1. Original Works. “Bemerkungen zu Herrn Wolfkes Note: ‘Welche Strahlungsformel folgt aus der Annahme der Lichtatome?’” in *Physikalische Zeitschrift*, **15** (1914), 363–364; “O kvantovanii uslovnoperiodicheskikh sistem” (on the quantization of conditionally periodic systems), in *Zhurnal Russkogo fiziko-khimicheskogo obshchestva*, chast’ fizicheskaia, **50** , no. 4–6 (1918), 134–142; “Contribution to the Theory of Adiabatic Invariants,” in Pro *ceedings of the Royal Academy of Amsterdam*, **21** (1919), 1112ff.; “On the Determination of Quanta Conditions by Means of Adiabatic Invariants,” *ibid*., **23** (1921), 826ff.; “Über das Rayleigsche Pendel,” in Zeitschrift für *Physik*, **13** , no. 3 (1923), with V. A. Fock; “Zur Schwankungs theorie,” *ibid*., 203–205; “Notiz über die mechanischen Grundgleichungen der statistischen Mechanik,” *ibid*., **36** (1926). 623–627.

*Obshchaia teoria giroskopov i nekotorikh tekhnicheskikh ikh primenenii* (The general theory of gyroscopes and some of its technical applications; Leningrad. 1932), with A. N. Krylov; “Zur Theorie der Brownischen Bewegung,” in *Zeitschrift für Physik der Sowjetunion*. **5** no. **2** (1934), 287–300; “O lineinikh zadachakh teorii brounovskogo dvizheniia” (On linear problems of the theory of Brownian motion), in *Doklady Akademii nauk* SSSR. n.s. **1** (1934), 479–482 (German trans., 482–485). pt 2, n.s. **3** (1934). 215–217 (German trans., 218–220). pt.3 n.s. **4** (1934). 120–122 (German trans., 122–124); “Zamechanieo bokovoi kachke korablia na volnenii” (Note on the rolling motion of a ship in heavy seas), *ibid* n.s. **2** (1934), 158–159 (German trans., 160–161); “Issledovaniia po teorii brounovskogo dvizheniia” (Studies on the theory of Brownian motion), in B. I. Davydov, ed., *Brounovskoie dvizhenie*, *A. Einstein, M. Smoluchovski* (Moscow.1936): and *Tenzor* funktsii napriazheniia i obshchii resheniia v statike teorii uprugosii (The stress function tensor and the general solutions in the static of the elastic theory; Moscow and Leningrad. 1949).

11. Secondary Literature. V. ia. Frenkel, “Iurii Aleksandrovich Krutkov,” in *Uspekhi fizicheskikh nauk*, **102,** no. **4** (1970). 639–654.

V. J. Frenkel

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