Slobodiansky, Mikhail Grigoryevich

He was born on January 5, 1912 in the village of Makhnovka (from 1935 to 2016 it was called Komsomolskoe ^[1] ) of the Berdychiv district of Kiev province (now the village is part of the Kazatinsky district of the Vinnitsa region of Ukraine ) ^[2] .

After graduating from high school in 1932, he entered the Faculty of Mechanics and Mathematics of Moscow State University , which he graduated in 4 years in 1936. In 1938 he defended his thesis, in 1940 - a doctoral dissertation ^[3] .

In 1940, at the age of 28, he headed the Department of Theoretical Mechanics of the Moscow Power Engineering Institute , which he headed until 1974 ^[4] .

Under the leadership of M. G. Slobodiansky, a training workshop was organized at the department, a small computer was installed, and a special installation was created on which experimental studies of the first domestic design of the KBL-5 axle-piston axial-piston compressor were performed; The results formed the basis for the creation of industrial designs of multistage compressors with a discharge pressure of 10, 20 and 40 MPa. At the department, for several years, methodological seminars operated to prepare young Moscow teachers to conduct practical classes and give lectures on theoretical and technical mechanics; many graduates of the mechmath of that time passed pedagogical practice “at Slobodiansky at MPEI at Termekh” ^{[5] [6]} .

M. G. Slobodyansky was the permanent scientific supervisor of the graduate school at the Department of Theoretical Mechanics, and under his leadership many young teachers of the department (A. M. Alexandrov, N. B. Erofeeva, V. V. Podalkov, Sh. H. Kh. Tubeev, V. F. Ustinov, Ya. Y. Khotin) defended their candidate dissertations ^[7] .

After M.G. Slobodiansky had to leave the department of theoretical mechanics for health reasons, he continued to work at the department for many years as a professor-consultant.

He died on August 3, 1988 in Moscow ^[8] .

The scientific interests of M. G. Slobodiansky included the theory of elasticity , applied mathematics , mathematical physics , methods of teaching theoretical mechanics ^[4] .

In 1939, M. G. Slobodyanskii developed ^{[9] a} new approximate method for solving boundary value problems for elliptic partial differential equations — the direct method . A variant of this method, proposed by Slobodyansky, provides in two-dimensional boundary value problems for the approximate replacement of derivatives in one of the variables with their difference analogues, which allows us to reduce the original problem to the corresponding problem even for a system of ordinary differential equations . Slobodiansky applied this approach, in particular, to the biharmonic equation and the Poisson equation (moreover, in the case of the Poisson equation, he managed to obtain a finite equation for the characteristic determinant and find general expressions for unknown functions); in addition, he investigated the error of the straight line method and outlined the order of its application to spatial problems ^{[10] [11]} . Later, the direct method (applied to other types of partial differential equations) was mainly developed as a purely numerical method , which, with the development of computer technology, has gained a very wide area of ​​application ^[12] .

MG Slobodiansky studied the behavior of some polygonal profiles under torsion , and he used the finite difference method to calculate the tangential stresses and to study the concentration of such stresses in the incoming corners of these profiles ^[13] . In the course of this study, he developed a method for numerically finding the derivative of the solution of a boundary value problem for an elliptic-type equation using the Green function (the method reduces to calculating the grid analog of the derivative of the Green function and then integrating, over the region under consideration, the product of this analog to the right side of the equation) ^{[ 14]} .

M. G. Slobodyansky worked a lot in the field of obtaining two-sided estimates of solutions of equations with self-adjoint operators (both inside and at the boundary of regions) ^{[15] [16]} . The key results related to this topic were presented by him in two articles published in 1952 ^[17] , although he later returned to this topic more than once.

Closely related to this topic are the problems of obtaining two-sided estimates, not for the solutions of the above equations themselves, but for the linear functionals associated with these solutions. In 1953, M. G. Slobodyanskii proposed ^{[18] a} simple and elegant method for solving such problems ^[19] . In the same year, he also proposed an effective method of obtaining a lower bound for the energy functional in problems with self-adjoint operators, later called the Slobodiansky method ^[20] .

Together with L.N. Ter-Mkrtchyan M.G. Slobodiansky made an important addition to the classical result on the possibility of representing the general solution of the equations of elasticity theory in the spatial case as a linear combination of four harmonic functions of real variables and their derivatives ( Papkovich-Neuber representation ): it was shown that of these functions, essentially independent - only three, since it is possible, without violating generality, to take one of them identically equal to zero (if only the Poisson's ratio${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">\nu </span></span>}}$ {\ displaystyle \ nu}   not equal${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">0</span></span>}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">,</span></span>\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">25</span></span>}}$ {\ displaystyle 0.25}   ) ^{[21] [22]} . Moreover, MG G. Slobodyansky in 1954 also proved ^[23] that the restriction both for a simply connected finite region and for an infinite region external to a closed surface${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">\nu </span></span>}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">\ne </span></span>\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">0</span></span>}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">,</span></span>\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">25</span></span>}}$ {\ displaystyle \ nu \ neq 0.25}   can be dropped ^{[24] [25]} .

M. G. Slobodyansky also made a significant contribution to the development of methods for teaching theoretical mechanics in technical universities ^[15] . In the course of lectures on theoretical mechanics, which was given by Slobodiansky, there were many interesting methodological findings. For example, in the section “Solid State Statics” he managed to achieve a compact (and at the same time rigorous) presentation of the material by abandoning the preliminary presentation of the theory of pairs of forces . Instead, he considered the starting point a theorem on reducing a system of forces to two forces, on which he relied heavily both in proving the theorem on reducing a system of forces to a force and a pair of forces, and in deriving the equilibrium conditions of a system of forces (the derivation of the basic properties of a pair of forces followed later it was quite uncomplicated) ^[26] .

Wife - Elena Vasilievna Slobodyanskaya.

Son - Boris Mikhailovich Slobodyansky, candidate of technical sciences (1973) ^[27] ; worked for many years at the Computing Center of MPEI.

• Slobodyansky M. G. Theoretical study of the stress state in elements with a crack // Applied Mathematics and Mechanics . - 1939. - T. 2, no. 4 . - S. 457-466 .
• Slobodyansky M. G. Method for the approximate integration of partial differential equations and its application to problems of the theory of elasticity // Applied Mathematics and Mechanics . - 1939. - T. 3, no. 1 . - S. 75-82 .
• Slobodyansky M. G. Determination of the derivatives of the desired functions in solving problems by the finite difference method // Applied Mathematics and Mechanics . - 1951. - T. 15, no. 2 . - S. 245-250 .
• Slobodyansky M. G. Estimates of the error of the approximate solution in linear problems, which are reduced to variational ones, and their application to the determination of two-sided approximations in static problems of the theory of elasticity // Applied Mathematics and Mechanics . - 1952. - T. 16, no. 4 . - S. 449-464 .
• Slobodiansky M.G. Estimation of the error of the desired value in solving linear problems by the variational method // DAN SSSR . - 1952. - T. 86, No. 2 . - S. 243-246 .
• Slobodyansky M. G. Error estimation for approximate solutions of linear problems // Applied Mathematics and Mechanics . - 1953. - T. 17, no. 2 . - S. 229-244 .
• Slobodiansky M. G. On the approximate solution of linear problems, which are reduced to variational ones // Applied Mathematics and Mechanics . - 1953. - T. 17, no. 5 . - S. 623-626 .
• Slobodiansky M. G. On the transformation of the minimum functional problem to the maximum problem // DAN SSSR . - 1953. - T. 91, No. 4 . - S. 733-736 .
• Slobodyanskiy M.G. General forms of solutions of the equations of elasticity for simply connected and multiply connected areas expressed through harmonic functions // Applied Mathematics and Mechanics . - 1954. - T. 18, no. 1 . - S. 55-74 .
• Slobodiansky M. G. An approximate solution of a self-adjoint boundary-value problem for an ordinary differential equation and determination of regions of eigenvalues ​​location // Applied Mathematics and Mechanics . - 1954. - T. 18, no. 5 . - S. 585-596 .
• Slobodyansky M. G. On estimates for the eigenvalues ​​of a self-adjoint operator // Applied Mathematics and Mechanics . - 1955. - T. 19, no. 3 . - S. 295-314 .
• Slobodyansky M. G. Bilateral approximations in some problems of the theory of elasticity and potential theory // Transactions of MPEI. - 1955. - No. 17 . - S. 122-142 .
• Slobodiansky M. G. On the construction of the main part of the Green's function for a second-order elliptic differential operator // Uspekhi Matematicheskikh Nauk . - 1958. - T. 13, No. 6 (84) . - S. 161-166 .
• Slobodyansky M. G. On general and complete forms of solving the equations of elasticity // Applied Mathematics and Mechanics . - 1959. - T. 23, no. 3 . - S. 468-482 .
• Slobodyansky M. G. Some estimates in the static problems of the theory of elasticity // Transactions of MPEI. - 1959. - No. 32 . - S. 142-175 .
• Slobodiansky M.G. Bending of a plate of variable thickness // Bulletin of the USSR Academy of Sciences. Department of Technical Sciences. - 1959. - No. 5 . - S. 99-108 .
• Slobodyansky M. G. Improvement of some estimates for stresses in problems of the theory of elasticity // Izvestiya AN SSSR. Department of Technical Sciences. - 1965. - No. 1 . - S. 139-141 .
• Slobodiansky M. G. Construction and presentation in the course of theoretical mechanics of the section “Statics of a solid body” // Theoretical mechanics in technical colleges: Sat. Articles / Ed. A. A. Yablonsky. - M .: Higher school, 1971. - 352 p. - S. 156-170.
• Collection of problems in theoretical mechanics. Part 1 / Ed. M.G. Slobodiansky. - M .: MPEI, 1972.- 163 p. ^[28]
• Slobodyansky M. G. Some estimates for stresses in the absence of mass forces // Transactions of MPEI. - 1975. - No. 246 . - S. 45-51 .

• Gavurin M.K., Kantorovich L.V. Approximate and numerical methods // Mathematics in the USSR for forty years. 1917-1957. T. 1. Review articles / Ch. ed. A. G. Kurosh . - M .: Fizmatgiz , 1959. - 1000 p. - S. 809-856.
• Kantorovich L.V. , Krylov V.I. Approximate methods // Mathematics in the USSR for thirty years. 1917-1947 / Ed. A. G. Kurosh , A. I. Markushevich , P. K. Rashevsky . - M.-L .: Gostekhizdat , 1948 .-- 1044 p. - S. 759-801.
• Mikhlin S.G. Variational methods in mathematical physics. 2nd ed. - M .: Nauka, 1970 .-- 512 p.
• Ustinov V. F. “Termekh” in MPEI is Slobodiansky // MPEI: history, people, years. Collection of memories. T. 3 / Ed. S.V. Serebryannikova . - M .: Publishing House MPEI, 2010 .-- 536 p. - ISBN 978-5-383-00578-1 . - S. 134-138.
• Energomash is 60 years old. - M .: Publishing House of MPEI, 2003 .-- 240 p.

• Slobodiansky Mikhail Grigoryevich (1912-1988)
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