Volume 14, Issue 4 (2016)






DYNAMICS
of MACHINES


On the problem of dynamic interdependence between the motor and mechanical drive in cyclic machines
St. Petersburg State University of Industrial Technologies and Design: ul. Bol'shaya Morskaya, 18, St.Petersburg 191186 Russia

A R T I C L E I N F O 

A B S T R A C T 



DOI 10.5862/TMM.32.1
Article history:
Received 29.08.2016
Received in revised form 28.09.2016
Accepted 23.11.2016
Keywords:
cyclic machines; dynamics; vibrations; motor.


The results of the study of forced vibrations in machines with cyclic mechanisms taking into account the characteristics of the motor. Revealed specific effects associated with slow change given the inertial and elasticdissipative characteristics of drive. Particular attention is given to the kinematic excitation of vibrations in which the driving force among the other factors are a function of the angular speed of the motor, when in turn, depends on these forces. An engineering method for calculating such problems is based on the use of transition matrices, that are well adapted for computer procedures application. Are given the results of computer simulation. (in Russian).
R E F E R E N C E S
 Mitropolsky YU. A. Problemy asimtoticheskoy teorii nestatsionarnyh kolebaniy.– M.: Nauka, 1964. – 432 p.
 Vulfson I. I., Kolovsky M.Z. Nelineynye zadachi mechaniki mashin. – L.: Mashinostroenie, 1968.–284 p.
 Vulfson I. Dinamicheskie raschety tsiklovyh mekhanismov. – L.: Mashinostroenie, 1976.–328 p.
 Mehanika mashin: uchebnoe posobie dl'a vtuzov / Vulfson I. I., Erihov M,L., Kolovsky M.Z.& et.al.– M.: Vish. Shkola, 1996 – 511p.
 Dresig, H., Vulfson I.I. Dynamik der Ěechanismen. –Wien, New York :Springer, 1989.– 328 p.
 Vulfson I. I. To the problem of multisection technological machines dynamic stability in the vicinity of actuators program movement.– TMM, 2006. ą2. pp. 7–12.
 Vulfson I. I. Some nonlinear effects of machine dynamics. Journal of Vibroingeneering. – 2008. V.10.,No.4. Pp. 442–450.
 Vulfson I. I. On the analytical investigation of nonstationary vibratory systems by the method of fictitious oscillator // Vestnik naucnotehniceskogo razvitia. 2008. ą3 (7). Ń. 26–38.
 Vulfson I. I. Dinamika tsiklovyh mashin. – Spb: Politehnika, 2013. 425 p.
 Vulfson I. I. Dynamics of cyclic machines.– Heidelberg, New York, Dordrecht, London: Springer, 2015. – 410 p.
 Vulfson I. I. On the problem of dynamic characteristics quasistatioarity in cyclic mechanisms.– TMM. 2015. No.1. pp. 6– 15.
 Veyts V. L. Dinamika mashinyh agregatov.– L.: Mashinostroenie, 1969.– 370 p.
 Kolovsky M.Z. Dinamika mashin. – Ë.: Mashinostroenie, 1989. – 264 p.
 Veyts V. L., Kolovsky M. Z., Kochura A. E. Dinamika upravlyaemyh mashinyh agregatov.– M.: Nauka, 1984. – 352 p.
 Kononenko V. O. Voprosy teorii dinamicheskogo vzaimodeistvia mashiny i istochnika energii.– Izv. AN SSSR. MTT. 1973, No4.– pp. 19–30.
 Alifov A. A., Frolov K. V. Vzaimodeisvie nelineinyh kolebatel'nyh sistem s istochnikom energii. –M,: Nauka. – 328 p.







DYNAMICS
of MACHINES


On the problem of retrograde precession of rotor
Saint Petersburg State Marine Technical University: Lotsmanskaya, 3, St. Petersburg 190008, Russian Federation

A R T I C L E I N F O 

A B S T R A C T 



DOI 10.5862/TMM.32.2
Article history:
Received 01.03.2016
Received in revised form 20.10.2016
Accepted 23.11.2016
Keywords:
rotor, direct precession, retrograde precession, centrifugal force, field of support stiffness.


In the article published before the problem of rotor precession was solved as a problem of vibrations. Such way gave a possibility to describe all the forms of precession as Lissajous curves. But discussion with reviewer showed that it is expedient to define the precession velocity without use of vibration theory.
In present work very simple model, based on Jeffcott rotor is used. According this model, the motion of mass point under action of rotating centrifugal force is considered. To implement this model, the system of ordinary differential equation is made up and solved for uniform motion of point which moves round a circle. It means that synchronic precession is considered and the solution of equations is the problem of constant value determination. In considered case these values are velocity and radius of precession.
As result it was shown that precession velocity is equal to angular velocity of intrinsic rotation of the rotor and their directions are the same, if the field of support stiffness is isotropic, and they are opposite this field is anisotropic one.
One more result is the obviousness of the fact that the rotating centrifugal force is the primary factor of rotor precession in the conditions considered in this work. It is true not only for direct precession but also for retrograde precession. The motion of statically unbalanced single mass rotor is investigated. The main results from wellknown textbooks are justified mathematically and physically. Physical meaning of reverse precession is clarified. The solutions for isotropic and anisotropic linear elastic support bearings are received. The notion of asynchronous precession is considered. It is shown that precession in the case of anisotropic supports may be synchronous only if it is reverse and only for one value of the rotor angular velocity. Effectiveness of the theory of complex numbers is demonstrated. (in Russian).
R E F E R E N C E S
 Podol'skii M.E., Cherenkova S.V. Fizicheskajŕ priroda i uslovijŕ vozbuzhdenijŕ prjŕmoi i obratnoi precessii rotora. // Teorijŕ mehanizmov i mashin. 2014. Tom 12. ą1. S. 2740. (Podolsky M.E., Cherenkova S.V. The Physical nature and conditions of excitation of both forward and reverse precession of the rotor. // Theory of mechanisms and machines. 2014. Volume 12. No. 1. S. 2740.)
 Dimentberg F.M. 1959. – 258 s. (Dimentberg F.M. Sciences of the USSR, 1959. – 258 p.)
 Dimentberg F.M. Flexural Vibrations of Rotating Shafts. – London: Butter worths, 1961. – 243 p.
 Vul'fson I.I., Erihov M.L., Kolovskii M.Z., Semenov Yu.A., Sloush A.V. i dr. Mehanika mashin / Pod redakciei G.A. Smirnova. – M.: Vyssh. shk., 1996. – 511 s. (Vulfson I.I.,
Arehow L.M., Kolovsky M.Z., Semenov Yu.A., Sloushch A.V. etc. Mechanics of machines /edited by G.A. Smirnov. – M.: Higher. wk., 1996. – 511 p.)
 Detali mashin /pod red. O.A. Rjŕhovskogo – M.: Izdvo MGTU im. N.Ye. Baumana, 2004 – 520 s. (Machine parts /under the editorship of O.A. Ryakhovsky – M.: Izdvo MGTU im. N. Uh. Bauman, 2004 – p. 520.)
 Dmitriev V.A. Detali mashin. – L.: Sudostroenie, 1970. – 791 s (Dmitriev V.A. Machine Parts. – Leningrad: Sudostroenie, 1970. – 791 p.)
 Ivanov M.N., Finogenov V.A. Detali mashin. – M.: Vyssh. shk., 2008. – 408 s.( Ivanov M.N., Finogenov V.A. Machine Parts. – M.: Higher. wk., 2008. – 408 p.)
 Iosilevich G.B. Detali mashin. – M.: Mashinostroenie, 1988. – 368 s. (Iosilevich G.B. Machine Parts. – M.: Mashinostroenie, 1988. – 368 p.)
 Kraskovskii E.Ja., Druzhinin Yu.A., Filatova E.M. Raschet i konstruirovanie mehanizmov priborov i vychislitel'nyh sistem / Pod redakciei YU.A. Druzhinina. – M.: Vyssh. shk., 1991. – 480 s. (Kraskivske J.E., Druzhinin Yu.A., Filatova E.M. Analysis and design of mechanisms of instruments and computer systems / edited by Yu. a. Druzhinina. – M.: Higher. wk., 1991. – 480 p.)
 Kudrjŕvcev V.N. Detali mashin. – L.: Mashinostroenie, 1980. – 464 s. (Kudryavtsev V.N. Machine parts. – L.: Engineering, 1980. – 464 p.)
 Biderman V.L. Teorijŕ mehanicheskih kolebanii. – M.: Vyssh. shk., 1980. – 408 s. (Biderman V.L. Theory of mechanical vibrations. – M.: Higher. wk., 1980. – 408 p.)
 Vibracijŕ yĺnergeticheskih mashin. Spravochnoe posobie. / N.V. Grigor'ev, N.G. Beljŕkovskii, V.K. Dondoshanskii. Pod red. d.t.n. N.V. Grigor'eva. – L.: Mashinostroenie, 1974. – 464 s. (Vibration energy machines. A reference guide. / N.V. Grigoriev, N.G. Belyakovsky, V.K. Dondushensky. Ed. by D. T. N. N. In. Grigorieva. – L.: Engineering, 1974. – 464 p.)
 Dimentberg F.M., SHatalov K.T., Gusarov A.A. Kolebanijŕ mashin. – M.: Mashinostroenie, 1964. – 307 s. (Dimentberg F.M., Shatalov K.T., Gusarov A.A. Oscillations of machines. – M.: Mashinostroenie, 1964. – 307 p.)
 Kostyuk A.G. Dinamika i prochnost' turbomashin. – M.: Izdatel'skii dom MYeI, 2007. — 476 s. (Kostyuk A.G. Dynamics and strength of turbomachines. – M.: MPEI Publishing house, 2007. — 476 p.)
 Panovko Ja.G. Mehanika deformiruemogo tverdogo tela: Sovremennye koncepcii, oshibki i paradoksy. – M.: Nauka, 1985. – 288 s. (Panovko J. G. Mechanics of deformable solids: Modern concepts, errors and paradoxes. – M.: Nauka, 1985. – 288 p.)
 Panovko Ja.G. Osnovy prikladnoi teorii kolebanii i udara. – L.: Mashinostroenie, 1976. – 320 s. (Panovko J. G. Fundamentals of applied theory of vibrations and shock. – Leningrad: Mashinostroenie, 1976. – 320 p.)
 Poznjŕk Ye.L. Kolebanijŕ rotorov // V spravochnike «Vibracii v tehnike». – M.: Mashinostroenie, 1980. – Tom 3. S. 130189. (Pozniak E. L. Oscillations of the rotor // In the reference book "Vibrations in engineering". – M.: Mashinostroenie, 1980. – Volume 3. P. 130189.)
 Raer G.A. Dinamika i prochnost' centrobezhnyh kompressornyh mashin. – L.: Mashinostroenie, 1968. – 258 s. (Raer G.A. Dynamics and strength of centrifugal compressor machines. – Leningrad: Mashinostroenie, 1968. – 258 p.)
 Timoshenko S.P. Kolebanijŕ v inzhenernom dele. – M.: GIFML, 1959. – 439 s. (Timoshenko S.P. Oscillations in engineering. – M.: GIFML, 1959. – 439 p.)
 Tondl A. Dinamika rotorov turbogeneratorov. / Per. s angl. B.SH. Neimana pod red. V.I. Olimpieva. – M.L.: Yenergijŕ, 1971. – 387 s. (Tondl. A. Dynamics of rotors of turbogenerators. / Per. from English. B. S. Neumann, V. I., ed Olimpieva. – M.L.: Energy, 1971. – 387 p.)
 Frish S.Ye., Timoreva A.V. Kurs obshei fiziki (tom 1). – M.: GIFML, 1962. – 468 s. (Frisch S. C., Timoreva A. V. Course of General physics (vol. 1). – M.: GIFML, 1962. – 468 p.)
 Pasynkova I.A., Saboneev V.S. Iz istorii razvitijŕ dinamiki rotorov // CHetvertye Poljŕhovskie chtenijŕ: Izbrannye trudy. – SPb.: Izdvo VVM, 2006. – S. 644654. (Pasynkova I. A., Sabaneev V. S. From the history of the development of the dynamics of rotors // Fourth polyakhov's reading: Selected works. – SPb.: Publishing house VVM, 2006. – P. 644654.)
 Pasynkova I.A. Dinamika precessionnogo dvizhenijŕ neuravnoveshennogo rotora / Diss. na soisk. uchenoi stepeni dokt. fiz.SPb.: S.Peterb. gos. unt, 2006. – 217 s. (Pasynkova I. A. Dynamics of the precessional motion of unbalanced rotor / Diss. on competition of a scientific degree. academic degree of doctor. Fiz.Peterb. GOS. UNt, 2006. – 217 p.)
 Podol'skii M.E. Fizikomehanicheskie osnovy i nekotorye inzhenernye prilozhenijŕ prjŕmogo tenzornogo ischislenijŕ: monografijŕ. – SPb: Izdvo SPbGMTU, 2011. – 466 s. (Podolsky M. E. Physicomechanical basis and engineering application of the direct tensor calculus]. – SPb: Publishing house Spbgmtu, 2011. – 466 p.)
 Podol'skii M.E., CHerenkova S.V. O kinematike prostranstvennogo dvizhenijŕ tverdogo tela. // Teorijŕ mehanizmov i mashin. 2015. Tom 13. ą1 (25). S. 1620. (Podolsky M. E., Cherenkova S. V. The kinematics of the spatial motion of a rigid body. // Theory of mechanisms and machines. 2015. Volume 13. No. 1 (25). P. 1620.).







MECHANICS 

The calculation of the rotor blades of the expansion turbines of jet type
Sevastopol state university: 7 Kurchatova Street, Sevastopol, 299015 Russia

A R T I C L E I N F O 

A B S T R A C T 



DOI 10.5862/TMM.32.3
Article
history:
Received 25.05.2016
Received in revised form 06.06.2016
Accepted 23.11.2016
Keywords:
The force of inertia, Determination of dynamic forces acting in mechanisms


The method of calculation of the strength of working blades of the expansion turbines of jet type based on the theory of shallow shells. The boundary value problem described by a system of partial differential equations by the method of integral relations is reduced to a system of ordinary differential equations with variable coefficients, integration of which is then modified by the method of successive approximations. A calculation example is given. (in Russian).
R E F E R E N C E S
 Kapitza P.L. A Turboexpander to obtain the low temperatures and its application for purification vestusa. – Technical physics, vol 9, issue.2, 1939, pp. 99123.
 Marguerre K. Zur Theorie der gekrummten Platte gro?er Formanderung. – Jahrbuch 1939 der deutschen Luftfahrforschung. Bd.1, s.413418.
 Grigolyuk E.I., Popovich V.E., and Puhly V.A. Bending of a cylindrical panel with a trapezoidal contour. – In the book..: Theory of shells and plates. – M.: Nauka, 1973, pp. 660664.
 Dorodnicyn A.A. On one method of solving equations of the laminar boundary layer. – Journ. appl. mathem. I tekhn. physics, 1960, No. 3, pp. 111118.
 Lanczos K. Practical methods of applied analysis. – M.: Fizmatgiz, 1961. – 524 p.
 Luke Y.L. Mathematical functions and their approximation. – New York – London: Academic Press. Inc., 1975.  608 p.
 Honegger E. Berechnung von Festigkeit mit Kegelschalem linear veranderlich Wangstarke. – Luzern, Promotionsarbeit, 1919.
 Kovalenko A.D. Bending disks straight profile. – Journal of mechanical engineering, 1947, no. 3, pp. 110.
 Kovalenko A.D., Grigorenko Ya.M., Ilyin L.A. Theory of thin conical shells and its application in engineering. – Kiev: Izdvo an USSR 1963. – 287 S.
 Puhly V.A. Method of analytical solution of twodimensional boundary value problems for systems of elliptic equations. – Journ. calculate. mathem. and mathem. physics., 1978, volume 18, No. 5, pp. 12751282.
 Puhly V.A. About one approach to the solution of boundary value problems of mathematical physics. Differential equations, 1979, volume 15, No. 11, pp. 20392043.
 Puhly V.A. Solution of initialboundary value problems of mathematical physics, that a specialized method of successive approximations. – Surveys of applied and industrial mathematics, vol.22, vol.4, 2015, pp. 49349.







STRUCTURE of MECHANISMS


Links unification for mechanisms structural synthesis
Kovrov State Technological Academy named after V.A. Degtyarev: 19, Mayakovskiy st., Kovrov, V eng ladimir region, Russia, 601910






GEOMETRY of MECHANISMS


Precision analysis movements working device of shovel excavator
National Research University «Bauman University»: ul. Baumanskaya 2ya, 5, Moscow, Russia, 105005

A R T I C L E I N F O 

A B S T R A C T 



DOI 10.5862/TMM.32.6
Article history:
Received 19.10.2016
Received in revised form 21.11.2016
Accepted 23.11.2016
Keywords:
shovel excavator, mathematical model, automatic control system, precision


Excavators are lifting mechanisms of mobile machines and units with hydraulic drive.
They are controlled by different methods like any other robotic systems. Modern machines
have different automatic control systems. Adaptive management methods are the most
widely used. Construction of buildings in close urban areas requires using of precision machinery.
The developed mathematical model allows to evaluate the accuracy of the working
mechanism of the shovel excavator to analyze the possible sources of geometric errors
and to compile the workspace. The article proposes several ways to solve this problem,
which will help to increase the accuracy of the operating mechanism.
The proposed material will help to create a program to control the working device and
significantly reduce the cost of using the shovel excavator. (in Russian).
R E F E R E N C E S
 Aleksandrov M.P. Handling machinery: Proc. for building equipmen. specialist. universities.
6 th ed., Revised. Moscow. Higher. wk, 1985. 520 p.. (in Russian)
 Balovnev V.I., Zelenin A.N., Kerov I.P. Earth moving. – Moscow. Engineering, 1975. 422 p.
(in Russian)
 Drozdov L.G. Excavator: design, installation and repair. Proc. Benefit / LG Drozdov, OA
Kurbatov. Vladivostok: Publishing house FESTU, 2007. 235 p. (in Russian)
 Shcherbakov V.S., Sukharev R.Y. Improving the working body of the control system of the
chain trencher: monograph / Shcherbakov V.S., Sukharev R.Y. Omsk: SibADI, 2011. 152 p.
(in Russian)
 Meshcheryakov V.A. Adaptive management workflows Earthmovers: diss ... doctor. tehn.
sciences.  Omsk: SibADI, 2007. 304 p. (in Russian)
 Shcherbakov V.S. Scientific basis for improving the accuracy of work performed Earthmovers:
diss. ... doctor. tehn. sciences. Omsk: Shiba CI, 2000. 416 p. (in Russian)
 Krushel E.G., Stepanchenko I.V. News delay in digital control systems: monograph / VSTU.
Volgograd, 2004. 124 p. (in Russian)
 Levitsky N.I. Theory of mechanisms and machines: Textbook for high schools. 2nd ed. and
ext. Moscow. Nauka. Ch. Ed. Physics and Mathematics lit., 1990. 592 p. (in Russian)
 Pavlov V.P. Methodology of computeraided design of working equipment shovels: diss. ...
doctor. tehn. sciences. Krasnoyarsk, 2011. 349 p. (in Russian)
 Theory of Mechanisms and Machines: Textbook for high schools. Kolovsky M.Z.,
Evgrafov A.N., Slousch A.V., Semenov Yu.A. Moscow, Publishing House "Academia", 2013.
560 p. (in Russian)
 Semenova N.S., Semenov Yu.A. Course design «Study of the lifting and transport, building
and road machines». Theory of Mechanisms and Machines. 2009. Vol. 7. ą2, pp.6171. (in
Russian)
 Plutalov V.N. Metrology and Technical Regulations. Moscow. Publishing house of the Moscow
State Technical University. 2011. 416 p. (in Russian)
 SNIP 2.04.0284. Water supply. External networks and facilities. Moscow. Stroyizdat, 1985.
136 p. (in Russian)
 SNIP 2.04.0385. Sewerage. External networks and facilities. Moscow. TSITP, 1986. 72 p. (in
Russian)
 SNIP 2.05.1390. Pipelines are laid at the territory ofdelivery and other settlements. Moscow.
Stroyizdat, 1988. 7 p. (in Russian)
 SNIP 3.05.0485 External networks and facilities of water supply and sanitation. Moscow.
TSITP, 1990. 48 p. (in Russian)







HISTORY of MMS


Condition of mechanics and practical mechanics in Russia up to the middle of XIX century
National Research University «Bauman University»: ul. Baumanskaya 2ya, 5, Moscow, Russia, 105005

A R T I C L E I N F O 

A B S T R A C T 



DOI 10.5862/TMM.32.7
Article history:
Received 20.09.2016
Received in revised form 10.10.2016
Accepted 23.11.2016
Keywords:
practical mechanics, mathematics, St. Petersburg Academy of Sciences,
mechanics, Moscow University, scince.


In article is stated the history of development of mechanics in Russia up to the middle of the
19th century. Touched on the contribution in to development of science and education of such scientists
as G. Galilei, R. Descartes, R. Guk, I. Newton, Ja. Bernoulli, A. D. Farkhvarson, G. G.
SkornyakovPisarev, L. Euler and others. The first Russian textbook of mechanics of Skornyakov
Pisarev containing initial data on the elementary machines is considered. Less than in three years
after the edition of this book, in Russia researches on mechanics at other, high level have begun
that has been connected with foundation of the St. Petersburg Academy of Sciences and academic
university. After creation of Academy of Sciences and universities at her, teaching of mechanics
came to higher level. The leading role in it was played by employees and pupils of Academy. In
1755 on an initiative and Lomonosov M. V. idea was founded the Moscow University. The structure
of University of that period is considered (in Russian).
R E F E R E N C E S
 Allen D.H. How Mechanics Shaped the Modern World. Springer, 2014, p.1724
 Andronikov I. Remarkable researches.// "Ogonyek", 1960, ą12.
 Antsupova G. MSTU eyes of the historian.Moscow, MSTU named after Bauman, 2005,
229 p.
 Baldina E. About the first textbooks of analytical geometry in Russian.// S. Since and
technique (history and theory questions), issue. ÓŘ, p. 2, L., 1973.
 Bernshteyn S. Sketches on history of construction mechanics. Moscow: Gosstroyizdat,
1957. 236 p.
 Biryukob B. From a water wheel to the quantum accelerator. Moscow: Mashinostroenie,
1990, 144 p.
 Bogolyubov A. History of mechanics in Russia. Kiev, Naukovka Dumka, 1987, 141 p.
 Bogolyubov A. Mechanics in history of human.Moscow, Nauka, 1978, 137 p.
 Bogolyubov A. Soviet school of mechanics and machines.Moscow: Nauka, 1975, 174 p.
 Bogolyubov A. The theory of machines and mechanisms in historical evolution of ideas.
Moscow: Nauka, 1976, 402 p.
 Venetskiy S. From a fire to plasma.Moscow: Çíŕíčĺ, 1986, 208 p.
 Virginskiy V., Xoteenkov V. Sketches of history of science and techniques since the
most ancient times to the middle of XV c.Moscow: Prosveschenie, 1993, 288 p.
 Virginskiy V. Sketches of history of science and techniques XVIXIX c.Moscow: Prosveschenie, 1984, 287 p.
 Virginskiy V., Xoteenkov V. Sketches of history of science and techniques 1870
1917 y.Moscow: Prosveschenie, 1988, 304 p.
 Volchkevich I. Sketches of history of Moscow Higher Technical School.Moscow,
Mashinostroenie, 2000, 239 p.
 Grigoryan A. Article of history of mechanics.Moscow: AS USSR, 1961
 Grigoryan A. Fradlin B. Mechanics in USSR.Moscow, Nauka, 1977. p.55
 Danilevskiy V. Russian equipment. Leniszdat, 1949, 547 p.
 Ermakov Y. From ancient crafts to modern technologies.Moscow: Prosveschenie, 1992,
127 .
 Ermakov Y. Advantage and harm of historical experience.// Inventor and rationalizer, 1986, ą12, p.1213
 Karavaev Y. From history of creation of department of theoretical mechanics in the Moscow universitete.//History and methodology of natural sciences.Moscow: MSU, issue. 29, 1982, p 134139.
 Kirillin V. Pages of history of science and technology.Moscow:Nauka, 1986, 512 p.
 Kosmdemyanskiy A. Articles of history of mechanics.Moscow: Nauka, 1982, p.108
 Kostomarov V. From activity of the Russian technical society in the field of mechanical
engineering.Moscow:Mashgiz, 1957, 179 p.
 Kudryavtsev P., Konfederatov I. The history of techniques and physics.  Moscow: Minpros, 1960. – 508 p.
 Merkin D. Short history of classical mechanics of Galilei – Newton.  Moscow: Fizmatlit, 1994, p. 1615.
 Mironov B., Stepanov Z. Historian and mathematician.Leningrad: Nauka, 1976, 183 p.
 Moiseev N. Articles of development of mechanics.  Moscow: MSU, 1961
 Nadejdin N. The history of science and techniques.  R. on D.: Fenix, 2006, 621 p.
 Sketches of history of techniques in Russia since the most ancient times to 60th of XIX c.Moscow: Nauka, 1978, 385 p.
 Rakhmaninov I. Few words about introduction to physicalmathematical faculty of teaching of applied sciences //Magazine of Ministry of national education. 1863, p. 118, p. 350381.
 Rojanskiy I. Antic science. – Moscow: Nauka, 1980, 200 p.
 Smolnikov B. Mechanics in the history of science and society.I.: SRC " Regular and chaotic dynamics", 2014, p.402406
 Truesdell K. Scetches of history of mechanics. – Moscow; I.: IKI, 2002. – 316 p.
 Tyulina I. Development of mechanics in Moscow University in VIII č XIX century.// Historymathematical research. Moscow: Nauka. N.8. 1955, p.486520.
 Engels F. Dialectics of nature. Moscow, Gospolitizdat,1955, p.145
 Mechanics in Moscow State University.Moscow: MSU, 1992.













