## Moiseev, Nikolay Dmitrievich

# MOISEEV, NIKOLAY DMITRIEVICH

(*b*. Perm, Russia, 16 December 1902; *d*. Moscow, U.S.S.R., 6 December 1955)

*celestial mechanics, astronomy, mathematics.*

After graduating from the Perm Gymnasium in 1919, Moiseev entered the Faculty of Physics and Mathematics of Perm State University, where he also worked as a laboratory assistant. In 1922 he transferred to Moscow University, from which he graduated in 1923, having specialized in astronomy. In 1922 he became a junior scientific co-worker at the State Astrophysics Institute (since 1931 part of the P. K. Sternberg Astronomical Institute). After completing his graduate work there, in 1929 Moiseev defended his dissertation “O nekotorykh osnovnykh voprosakh teorii proiskhozhdenia komet, meteorov i kosmicheskoy pyli” (“On Certain Basic Questions of the Theory of the Origin of Comets, Meteors, and Cosmic Dust”). From 1929 to 1947 he taught mathematics at the N. E. Zhukovsky Military Air Academy. In 1935 he was awarded the degree of doctor of physics and mathematical sciences and the title of professor. He was director of the department of celestial mechanics at the University of Moscow from 1938 to 1955 and was head of the P. K. Sternberg Astronomical Institute from 1939 to 1943.

The recognized leader of the Moscow school of celestial mechanics, Moiseev published more than 120 works on the mechanical theory of cometary forms; the cosmogony of comets, meteors, and cosmic dust; theoretical gravimetry, including an original method (the “nonregularized earth”) used in the theory of determining the forms of geoids from gravimetric observations; and dynamic cosmogony. To the study of the general characteristics of the trajectories of celestial bodies he applied qualitative methods based on the use of differential equations of movement and certain known integrals. He introduced qualitative regional characteristics of the trajectory, such as its contacts with certain given curves and surfaces and its longitudinal and transversal stability.

Moiseev applied qualitative methods to problems of certain specific celestial bodies, and his investigations of the characteristics of stability of orbital motion found many applications in problems of airplane and missile dynamics. His 1949 monograph *Ocherki razvitia teorii ustoychivosti* (“Essays of the Development of the Theory of Stability”) presented a historical analysis of the subject from antiquity to the twentieth century.

From 1940 to 1955 Moiseev published the results of his investigations on secular and periodic perturbations and the motions of celestial bodies. He developed concepts of the internal and external environments and twofold averaging. Moiseev established his own, interpolational-average scheme to supplement those of Gauss and Delaunay. Approximate empirical integrals of motion, deduced from observations of celestial bodies, were used for averaging the force function. This method allows the integration of the averaged differential equations of motion and the computation of the ephemerides of perturbation of motion.

Moiseev’s chief contributions to mathematics were his two new methods of solving systems of linear differential equations: the method of determinant integrals and the interational method.

## BIBLIOGRAPHY

I. Original Works. Moiseev’s early writings are “O vychislenii kometotsentricheskikh koordinat chastitsy kometnogo khvosta” (“On the Computation of the Cometcentered Coordinates of the Particles of the Comet Tail”), in *Russkii astronomicheskii zhurnal*, **1** , pt. 2 (1924), 79–86; “O khvoste komety 1901 **I** ” (“On the Tail of the Comet of 1901 I”), *ibid.*, **2** , pt. 1 (1925), 73–84; “O vychislenii effektivnoy sily i momenta izverzhenia chastitsy kometnogo khvosta” (“On the Computation of the Effective Force and Moment of Ejection of the Particles of a Comet Tail”), *ibid.*, **2** , pt. 2 (1925), 54–60; and “O stroenii sinkhronnykh konoidov” (“On the Structure of Synchronic Conoids”), *ibid.*, **4** , pt. 3 (1927), 184–190.

Subsequent works are “über einige Grundfragen der Theorie des Ursprungs der Kometen, Meteoren und des kosmischen Staubes (Kosmogonische Studien)” in *Trudy Gosudarstvennogo astrofizicheskogo instituta*, **5** , no. **1** (1930), 1–87; *Trudy Gosudarstvennogo astronomicheskogo instituta im P. K. Sternberga*, **5** , no. 2 (1933), 1–63; *Astronomicheskii Zhurnal*, **9** , nos. 1–2 (1932), 30–52; and *Trudy**Gosudarstvennogo astronomicheskogo instituta im P. K. Sternberga*, **6** , no. 1 (1935), 5–28, 50–58; “Intorno alla legge di resistenza al moto dei corpi in un mezzo pulviscolare,” in *Atti dell’ Accademia nazionale dei Lincei. Rendiconti*, **15** (1932), 135–139, 377–381, 443–447; “Sulle curve definite da un sistema di equazioni differenziali di secondo ordine,” *ibid.*, Ser. 6a, **20** (1934), 178–182, 256–265, 321–327; “O nekotorykh obshchikh metodakh kachestvennogo izuchenia form dvizhenia v problemakh nebesnoy mekhaniki” (“On Certain General Methods of Qualitative Study of the Forms of Motion in Problems of Celestial Mechanics”), in *Trudy Gosudarstvennogo astronomicheskogo instituta im P. K. Sternberga*, **7** , pt. 1 (1936), 5–127; **9** , pt. 2 (1939), 5–45, 47–81, 165–166; **14** , pt. 1 (1940), 7–68; **15** , pt. 1 (1945), 7–26; and “O nekotorykh svoystvakh traektory v ogranichennoy probleme trekh tel” (“On Certain Properties of Trajectories in a Limited Three-Body Problem”), *ibid.*, **7** , pt. 1 (1936), 129–225; **9** , pt. 1 (1936), 44–71; **9** , pt. 2 (1939), 82–114, 116–131, 167–170; **15** , pt. 1 (1945), 27–74.

Also published in the 1930’s were “über die Relativkrummung der zwei benachbarten Trajektorien. Zum Frage über die Stabilität nach Jacobi,” in *Astronomicheskii Zhurnal*, **13** , no. 1 (1936), 78–83; “Su alcune proposizioni di morfologia dei movimenti nei problemi dinamichi analoghi a quello del tre corpi,” in *Revista de ciencias* (Lima), **39** (1937), 45 50; “Über Stabilität Wahrscheinlichkeitsstrehnung,” in *Mathematische Zeitschrift*, **42** , no. 4 (1937), 513–537; “O postroenii oblasley sploshnoy ustoychivosti i neustoychivosti v smysle Lyapunova” (“On the Construction of Areas of Continuous Stability and Instability in Lyapunov’s Sense”), in *Doklady Akademii nauk SSSR*, **20** , no. 6 (1938), 419–422; and “O fazovykh oblastyakh sploshnoy ustoychivosti i neustoychivosti” (“On Phase Areas of Continuous Stability and Instability”), *ibid.*, 423–425.

Moiseev’s later works are “O nekotorykh osnovnykh uproshchennykh skhemakh nebesnoy mekhaniki, poluchaemykh pri pomoshchi osredenenia raznykh variantov problemy trekh tel” (“On Certain Basic Simplified Schemes of Celestial Mechanics Obtained With the Aid of Averaging Different Variants of the Problem of Three Bodies”), in *Trudy Gosudarstvennogo astronomicheskogo instituta im Sternberga*, **15** , pt. 1 (1945), 75–117; **20** (1951), 147–176; **21** (1952), 3–18; **24** (1954), 3–16; and in *Vestnik Moskovskogo gosudarstvennogo universiteta*, no. 2 (1950), 29–37; “A. M. Lyapunov i ego trudy po teorii ustoychivosti” (“A. M. Lyapunov and His Works on the Theory of Stability”), in *Uchenya zapiski Moskovskogo gosudarst vennogo universiteta*, no. 91 (1947), 129–147; “Kosmogonia” (“Cosmogony”), in the collection of papers, *Astronomia v SSSR za 30 let* (“Astronomy in the U.S.S.R. for Thirty Years”; Moscow-Leningrad, 1948), 184–191; *Ocherki razvitia teorii ustoychivosti* (“Essays of the Development of the Theory of Stability”; Moscow Leningrad, 1949); and “Obshchii ocherk razvitia mekhaniki vo Rossii i v SSSR” (“A General Sketch of the Development of Mechanics in Russia and in the U.S.S.R,”), in the collection of papers, *Mekhanika v SSSR za 30 let* (“Mechanics in the U.S.S.R. for Thirty Years”; MoscowLeningrad, 1950), 11–57.

The following were published posthumously: “Ob ortointerpolyatsionnom osrednennom variante ogranichennoy zadachi trekh tochek” (“On the Orthointerpolational Averaging Variant of the Limited Problem of Three Points”), in *Trudy Gosudarstvennogo astronomicheskogo instituta im P. K. Sternberga*, **28** (1960), 9–24; and

*Ocherk razvitia mekhaniki* (“Essay of the Development of Mechanics”; Moscow, 1961).

II. Secondary Literature. On Moiseev and his work, see (listed in chronological order) the obituary in *Astronomicheskii tsirkulyar Akademii nauk SSSR*, no. 166 (1956), 24–25; and the biographies in *Trudy Gosudarstvennogo astrominucheskogo instituta im P. K. Shternberga*, **28** (1960), 5–9, with a list of 15 of Moiseev’s works; *Ocherk razvitia mekhaniki* (cited above), 4–11, with bibliography of 21 works; and E. N. Rakcheev, in *Vestnik Moskovskogo gosudarstvennogo universiteta*, Seria matematika, mekhanika, no. 4 (1961), 71–77, published on the fifth anniversary of his death, with bibliography of 49 works. See also M. S. Yarov-Yarovoy, “Raboty v oblasti nebesnoy mekhaniki v MGU za 50 let (1917–1967 gg.)” (“Works in the Area of Celestial Mechanics at Moscow State University for Fifty Years”), in *Trudy Gosudarstvennogo astronomicheskogo instituta im P. K. Sternberga*, **41** (1968), 86–103.

P. G. Kulikovsky

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