Mykola Pavlovich Petrov (1832-1920) is known to us as an active researcher of track management techniques of domestic railways. He devoted more than 218 of his scientific works to this issue. The contribution of M.P. Petrov deserves special attention of researchers in the development of dynamic railway track calculation. In particular, his hypothesis of equal proportionality between deflection and load under static and dynamic action of the load, etc., is considered.

In connection with the increase in train speed and safety requirements, it was necessary to carry out a dynamic calculation of the railway track. Methods of dynamic track calculation were developed by domestic scientists, mainly Mykola Pavlovich Petrov. He proposed the hypothesis of еqual proportionality between the deflection and the load under static and dynamic action of the latter, formulated and solved in finite differences the differential equation of the movement of the center of inertia of the wheel along the rail.

M.P. Petrov was the first to consider the effect of unevenness of the wheel and track on the tension in the rail. The scientist took into account the forces of inertia of the wheel and elements of the superstructure. He also introduced into the calculation the vectorial components of the unbalanced forces of inertia of the rotating and moving parts of the mechanisms.

1. Zhuravskiy D.I. (1956). O mostakh raskosnoy sistemy Gau [On the bridges of the diagonal Gau system]. Sankt-Peterburg. CH. 2. 161 s. [in Russian]
2. Pauker G.Ye. (1891). Stroitel'naya mekhanika: Kurs Nikolayevskoy inzhenernoy akademii [Structural mechanics: Course of the Nikolaev Engineering Academy]./ Pod red. Kirpicheva. Sankt-Peterburg, 410 s. [in Russian]
3. Enrol'd F.I. (1874). Normal'nyye tipy rel'sov [Normal types of rails]. Inzhenernyye zapiski [Engineering Notes]. T.1, Vyp. 2. 507 s. [in Russian]
4. Holodetskiy A.A. (1888). Ob iznose zheleznodorozhnyih relsov v zavisimosti ot napryazheniy, poyavlyayuschihsya v nih pri deystvii podvizhnoy nagruzki. [On the wear of railway rails depending on the stresses that appear in them under the action of a moving load]. Inzener [Engineer] (Kiev), № 6. С. 224–234. [in Russian]
5. Lipin N.I. (1840). O zheleznykh dorogakh. [About railways]. Zhurnal Ministerstva putey soobshcheniya [Journal of the Ministry of Railways]. T.3. Kn.3. S. 228–227; Kn.4. . 287–330. [in Russian]
6. Stetsevich I.R. (1895). O soprotivlenii verkhnego stroyeniya [About the resistance of the upper structure]. Izvestiya Sobraniya inzhenerov putey soobshcheniya [Proceedings of the Meeting of Railway Engineers]. № 9. S. 129-144. [in Russian]
7. Vasyutinskiy A.L. (1898). Nablyudeniya nad vremennymi deformatsiyami verkhnego stroyeniya puti na Varshavo-Venskoy zheleznoy doroge [Observations on temporary deformations of the track structure on the Warsaw-Vienna railway]. Trudy ХV s"yezda inzhenerov sluzhby puti [Proceedings of the XV Congress of track service engineers]. Moskva. S. 64–67. [in Russian]
8. Kholodetskiy A.A. (1896, 1897). Issledovaniye vliyaniya vneshnikh sil na verkhneye stroyeniye zheleznodorozhnogo puti [Study of the influence of external forces on the upper structure of the railway track]. Inzhener [Engineer] (Kiyev). №12. S.507–5167; №1. S. 8–22. [in Russian]
9. Boguslavskiy N.B. (1899). K voprosu ob usilenii verkhnego stroyeniya zheleznodorozhnogo puti [On the issue of strengthening the upper structure of the railway track]. Zhurnal Ministerstva putey soobshcheniya [Journal of the Ministry of Railways]. № 4. S. 142–156. [in Russian]
10. Petrov N.P. (1905). Vliyaniye postupatel'noy skorosti dvizheniya koles na napryazheniye v rel'se pri otstuplenii kolesa ot krugloy formy i rel'sa, lezhashchego na shesti oporakh ot pryamolineynego vida [The influence of the translational speed of the wheels on the stress in the rail when the wheel deviates from the round shape and the rail lying on six supports from the rectilinear view]. Zapiski Russkogo tekhnicheskogo obshchestva [Notes of the Russian Technical Society]. №1. 52 s. [in Russian].
11. Petrov N.P. (1915). Davleniye koles na rel'sy zheleznykh dorog [Wheel pressure on railroad tracks]. Petrograd. 327 s. [in Russian].
12. Kholodetskiy A.A. (1915). K voprosu o vliyanii skorosti i nepravil'nogo vida koles na dinamicheskiye progiby rel'sov [On the question of the influence of speed and the wrong type of wheels on the dynamic deflections of rails]. Petrograd. 93 s. [in Russian].
13. Godynitskiy-Tsvirko A.M. (1915). O dinamichekskikh raschetakh verkhnego stroyeniya puti [On dynamic calculations of the superstructure of the track]. Zhurnal Ministerstva putey soobshcheniya [Journal of the Ministry of Railways]. Kn. І i ІІ. 238 í 168 s. [in Russian].
14. (1913). Trudy Komissii pod predsedatel'stvom Kunitskogo po voprosam «O napryazheniyakh v rel'sakh i ostal'nykh chastyakh verkhnego stroyeniya zheleznodorozhenogo puti» [Proceedings of the Commission chaired by Kunitsky on the issues "On stresses in the rails and other parts of the upper structure of the railway track"]. Sankt-Peterburg. 238 s. [in Russian].
15. Tseglinskiy K.YU. Zheleznodorozhnyy put' v krivykh [Railway track in curves]. Moskva: Chicherin. 1903. 157 s. [in Russian].
16. (1899). Zhurnal Ministerstva putey soobshcheniya [Journal of the Ministry of Railways]. № 3. 143 s. [in Russian].
17. Pogorel'skiy. (1897). Iz kakogo materiala dolzhny byt' rel'sy. [What material should the rails be from]. Zhurnal Ministerstva putey soobshcheniya [Journal of the Ministry of Railways]. T.6. S. 94–102. . [in Russian].
18. Shakhunyants G.M. (1949). Put' i putevoye khozyaystvo [Way and track facilities]. Moskva: Transzheldorizdat, 632 s. . [in Russian].
19. Grum-Grzhimaylo V.Ye. (1926). Kachestvo rel'sov [Rail quality]. Trudy nauchno-tekhnicheskogo komiteta MPS [Proceedings of the Scientific and Technical Committee of the Ministry of Railways].Vyp. 42. S. 64–89. [in Russian].
20. Petrov N.P. (1907). Napryazheniya v rel'sakh ot vertikal'nykh davleniy katyashchikhsya koles. Vliyaniye skorosti i nepravil'nogo vida koles [Stresses in rails from vertical pressures of rolling wheels. Influence of speed and incorrect type of wheels]. Sankt-Peterburg. 120 s. [in Russian].
21. Boguslavskiy N.B. (1927). Ob inflyuyentnykh liniyakh dlya rascheta prochnosti elementov zheleznodorozhnogo puti [About influent lines for calculating the strength of railway track elements]. Trudy nauchno-tekhnicheskogo komiteta MPS [Proceedings of the Scientific and Technical Committee of the Ministry of Railways].Vyp. 54. S. 63–71. [in Russian].
22. Grigor'yev V.V. (1927). Staticheskiy raschet puti [Static path calculation]. Trudy nauchno-tekhnicheskogo komiteta MPS [Proceedings of the Scientific and Technical Committee of the Ministry of Railways]. Vyp. 54. S. 35– 39. [in Russian].
23. Grigor'yev V.V. (1930). Issledovaniye raschetnoy skhemy rel'sovogo puti [Study of the calculation scheme of the rail track]. Trudy nauchno-tekhnicheskogo komiteta MPS [Proceedings of the Scientific and Technical Committee of the Ministry of Railways].Vyp. 105. S. 56–67. [in Russian].