**Mechanics** (механіка; *mekhanika*). Akin to machine science, a discipline encompassing general machine theory, the mathematical theory of mechanisms, problems of materials, strength and elasticity, friction and wear, manufacturing, reliability, efficiency, and automation. Early research in mechanics was conducted in Ukraine in the 19th century Kyiv University, Kharkiv University, and Odesa University, where Mykhailo V. Ostrohradsky, Timofei Osipovsky, V. Imshenetsky, Vladimir Steklov, G. Suslov, and Petro Voronets worked in analytical mechanics. Aleksandr Liapunov’s fundamental studies in the theory of stability were published in Kharkiv in 1892. Research in general mechanics was also carried out at the Kyiv Polytechnical Institute (V. Kirpichov, Stephen Timoshenko, B. Delone, Yevhen Paton) and at the Katerynoslav Higher School of Mining (O. Dynnyk; today the National Mining University in Dnipro).

In Soviet Ukraine the first scientific work in mathematical mechanics at the Academy of Sciences of the Ukrainian SSR (now NANU) was directed by Dmytro Grave, Mykola Krylov, and Kostiantyn Siminsky in Kyiv and O. Dynnyk in Dnipropetrovsk. Advanced research was carried out in analytic and space mechanics, the theory of motion of absolute and deformed solids, and the general theory of motion stability. Dynnyk, Mykola Kilchevsky, Anatolii Kovalenko, Hurii Savin, and Illia Shtaierman studied the theory of elasticity; in the postwar period Mikhail Lavrentev, Aleksandr Ishlinsky, M. Leonov, V. Maizel, and D. Vainberg made important contributions to that field. Today thermal elasticity is researched at the Institute of Mechanics of the National Academy of Sciences of Ukraine by Kovalenko, A. Ulitko, V. Hrinchenko, I. Motovylovets, and Yurii Shevchenko and at the Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine by Yaroslav Pidstryhach, Ya. Burak, Yu. Koliano, and H. Kit. Mathematical methods for solving problems in the theory of elasticity were developed by scientists such as Savin, Kovalenko, Heorhii Polozhii, Oleksander Huz, O. Kosmodamiansky, and Ulitko. Problems in the analytic mechanics of the environment were researched by Shtaierman, Volodymyr Chelomei, I. Rapoport, and Kilchevsky in Kyiv in the 1930s. Fundamental data on the dynamics of solids were obtained after the Second World War at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR by Ishlinsky and V. Koshliakov. Shtaierman, Savin, Ishlinsky, Kilchevsky, Leonov, Anatolii Filipov, Volodymyr Mossakovsky, and Volodymyr Rvachov wrote on the mechanics of contact interaction between deformed bodies. At the Institute of Applied Mathematics and Mechanics of the Academy of Sciences of the Ukrainian SSR P. Kharlamov solved various problems in the dynamics of solids and the stability of motion. The work of Huz and his students on general problems of the three-dimensional theory of the durability of deformed solids with different materials and structures has been widely applied; the physical and mechanical properties of such materials are studied at the Institute of Mechanics of the National Academy of Sciences of Ukraine. Lavrentev’s research in the mechanics of explosion was further developed in various institutes of the Academy of Sciences of the Ukrainian SSR, particularly by O. Vovk at the Institute of Geophysics of the Academy of Sciences of the Ukrainian SSR.

In the field of plasticity and thermal plasticity Aleksandr Ishlinsky and his students developed a theory of plasticity for materials with linear reinforcement, S. Malashenko devised equipment for measuring the plasticity of materials, and Yurii Shevchenko and his students developed a deformation theory of plasticity under variable nonisothermic loading processes. At the Institute for Problems of the Strength of Materials of the Academy of Sciences of the Ukrainian SSR Heorhii Pysarenko and V. Kyselevsky studied creep and boundary conditions under complex stress applications within a wide temperature range, as well as problems of forecasting long-term strength and creep under high temperatures, particularly under irradiation. The new branch of fracture mechanics has been developed intensively in Ukraine by Hurii Savin, Leonov, Volodymyr Panasiuk, Ulitko, Hrinchenko, and Kit.

The theory of mechanical oscillation is developing today as an independent branch of mechanics. In 1929 Mykola Krylov and Nikolai Bogoliubov founded a scientific school of nonlinear oscillations, later recognized throughout the world. Yurii Mytropolsky investigated nonstationary processes in nonlinear oscillations and developed asymptotic methods for the theory of nonlinear oscillations. Heorhii Pysarenko developed methods of nonlinear mechanics for solving oscillation problems in machine building, with an energy dispersion factor in cyclically deformed material. The oscillation of tensile systems was also investigated by Serhii Serensen, I. Tetelbaum, Viktor Kononenko, Mykola Kornoukhov, P. Varnak, Vainberg, and Anatolii Filipov. Vsevolod Lazarian studied mechanical vibrations, particularly in reinforced columns. Mykola Kilchevsky and his students studied the oscillation of multiphase systems. The dissipation of energy that accompanies oscillation has been researched since the 1950s at the Institute for Problems of Materials Science of the Academy of Sciences of the Ukrainian SSR and after 1966 at the Institute for Problems of the Strength of Materials of the Academy of Sciences of the Ukrainian SSR and the Kyiv Polytechnical Institute. In the prewar period Kostiantyn Siminsky, Serensen, Fedir Bieliankin, M. Afanasiev, and Pysarenko made important contributions to research on the strength of materials under cyclic loading. Research on the fatigue of materials and structures was carried out after the Second World War by Serensen, M. Harf, O. Kramarenko, and Ye. Buhlov; Borys Hrozin and D. Draihor researched contact strength. Heorhii Karpenko, Panasiuk, and Heorhii Maksymovych at the Physical-Mechanical Institute of the Academy of Sciences of the Ukrainian SSR researched the influence of corrosive environments on fatigue strength.

In the early 1960s a scientific school devoted to the strength of materials and structural elements in extreme conditions was set up at the Institute for Problems of the Strength of Materials of the Academy of Sciences of the Ukrainian SSR. Among the problems connected with the requirements of new technologies, the strength of materials under high (Heorhii Pysarenko, Valerii Troshchenko, H. Tretiachenko, V. Rudenko) and low (Anatolii Lebedev, Mykola Novykov, V. Stryzhalo) temperatures was studied, as well as fatigue limit and creep at high temperatures (M. Mozharovsky, V. Kovpak), strength of materials and structural elements under high-pressure gas flow (Tretiachenko, L. Kravchuk, R. Kuriat), the effect of neutron irradiation and of corrosive environments on the strength of materials (Kyselevsky, Kravchuk, B. Liashenko), the strength of materials in a wide temperature range (4 to 2,000°K) and under complex stress application (Lebedev, B. Kovalchuk), and impact resistance (H. Stepanov).

Other problems researched include fatigue and thermal fatigue (Valerii Troshchenko, V. Kuzmenko, B. Hriaznov), oscillations in machine building (Heorhii Pysarenko, V. Matveev, A. Yakovlev, M. Vasylenko, V. Khilchevsky), the structural strength of glass (Yu. Rodychev, K. Amelianovych), and physical aspects of strength (A. Krasovsky, V. Naumenko).

Oleg Antonov and V. Kovtunenko contributed to the development of aero- and gas-dynamics; Heorhii Proskura, Ivan Povkh, Ivan Shvets, and Oleksander Shcherban, to industrial aero- and hydrodynamics; and O. Akhiiezer, to magnetic hydrodynamics. Ukrainian scientists also had a major impact on the development of the mining sciences (Mykhailo Fedorov, Mykola Poliakov, Valentin Poturaev, Fedir Abramov), construction sciences (Mykola Kornoukhov, Fedir Bieliankin, Borys Gorbunov), and hydrology and hydro-technology (Mikhail Lavrentev, P. Filchakov, Ivan Liashko).

Research of mechanics scientists in Ukraine is co-ordinated by scientific councils of the National Academy of Sciences of Ukraine. Problems of mechanics are discussed in the journals *Prikladnaia mekhanika* and *Problemy prochnosti*.

Stepan Protsiuk

[This article originally appeared in the *Encyclopedia of Ukraine*, vol. 3 (1993).]