from 01.01.2009 until now
Ul'yanovsk, Ulyanovsk, Russian Federation
In this paper the usability of descriptive geometry’s methods for solution problems related to theoretical mechanics is considered. Descriptive geometry emerged as a science intended for solution the problems of human activity’s different branches. In connection with development of modern graphical means, the value of descriptive geometry is greatly underestimated, but it is on descriptive geometry’s principles and laws that have been built algorithms used in graphic applications [30]. For a long time descriptive geometry has been used by scientists in various spheres of human activity [27]. In study of general technical disciplines, interdisciplinary connections play an important role, especially between theoretical disciplines, whose understanding is particularly difficult for students [35]. Understanding the possibility of using descriptive geometry’s methods, students can think over aspects of their use in the performance of tasks under study, for example, theoretical mechanics. Methods, which can be use while solving problems from the course of theoretical mechanics, are learned by students in the standard course of descriptive geometry and are not particularly difficult. Therefore, the graphical approach to solving problems of theoretical mechanics is accessible and understandable for majority of successful students. In this paper example problems from the course of theoretical mechanics on the topics "Plane System of Forces" and "Spatial System of Forces" have been considered. Graphical problem solving was performed using the image of force vectors with the help of orthogonal projections. For checking the correctness of graphicalcons.
descriptive geometry, graphic method of problem solving, problems of theoretical mechanics, descriptive geometry’s methods, orthogonal projections
1. Ananov G.D. Metod ortogonal'nyh proekcij v zadachah mekhaniki. [The method of orthogonal projections in problems of mechanics]. Moscow: Gostekhizdat Publ., 1948. 176 p. (in Russian)
2. Anosov V.Ya., Pogodin S.A. Osnovnye nachala fiziko-himicheskogo analiza. [Basic principles of physico-chemical analysis]. Moscow-Leningrad: Izdatel'stvo akademii nauk SSSR, 1947. 876 p. (in Russian)
3. Bat M.I., Dzhanelidze G.Yu., Kelzon A.S. Teoreticheskaya mekhanika v primerah i zadachah. Statika i kinematika. [Theoretical mechanics in examples and problems. Statics and kinematics]. Saint-Petersberg.: Lan Publ., 2013, V. 1, 672 p. (in Russian)
4. Borovikov I.F., Ivanov G.S., Surkova N.G. O primenenii preobrazovanij pri reshenii zadach nachertatel'noj geometrii. [On applicatoin of transformations at diecriptive geometry’s problems solution.] Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 2, pp. 3-22. DOI:https://doi.org/10.12737/article_5b55a35d683a33.30813949. (in Russian)
5. Vasilevsky A.B. Metody resheniya geometricheskih zadach. [Methods for solving geometric problems]. Minsk, "Vysshaya shkola" Publ., 1969. 232 p. (in Russian)
6. Vinogradov V.N., Roitman I.A. Elementy nachertatel'noj geometrii (dlya fakul'tativnyh zanyatij) [Elements of descriptive geometry (for optional classes)]. Moscow.: Prosveshchenie Publ., 1978. 175 p. (in Russian)
7. Glogovsky V.V. Elementarnye konstruktivnye zadachi po nachertatel'noj geometrii [Elementary constructive problems in descriptive geometry]. Lviv: Vishcha shkola. Izdatel'stvo pri L'vovskom universitete, 1981. 152 p. (in Russian)
8. Gordon V.O., Sementsov-Ogievsky M.A. Kurs nachertatel'noj geometrii. [A course in descriptive geometry]. Moscow, Science Publ., 1969. 368 p. (in Russian)
9. Kozhevnikov Yu.G. Opticheskie prizmy. Proektirovanie, issledovanie, raschet. [Optical prisms. Design, research, calculation]. Moscow:Mashinostroenie Publ, 1984. 152 p. (in Russian)
10. Liebscher D.-E. Teoriya otnositel'nosti s cirkulem i linejkoj. [The theory of relativity with a compass and a ruler]. Moscow: Mir Publ., 1980. 148 p. (in Russian)
11. Lyzlov A.N., Rakitskaya M.V., Tikhonov-Bugrov D.E. Nachertatel'naya geometriya. Zadachi i resheniya: Uchebnoe posobie. [Descriptive geometry. Challenges and solutions:a training manual]. Saint-Petersberg: Lan Publ., 2011. 96 p. (in Russian)
12. Meshchersky I.V. Sbornik zadach po teoreticheskoj mekhanike: Uchebnoe posobie. [Collection of problems in theoretical mechanics: Textbook]. Moscow: "Science" Publ., 1986. 448 p. (in Russian)
13. Mushich-Gromyko V.G. Princip dopolnitel'nosti N. Bora i nachertatel'naya geometriya [The principle of complementarity of N. Bohr and descriptive geometry]. Vestnik Chelyabinskogo gosudarstvennogo universiteta [Bulletin of the Chelyabinsk State University]. 2008, pp. 125-130.
14. Nazarova O. N., Zimina N. G., Shishkarev V. V. Obosnovanie graficheskogo resheniya nekotoryh zadach mekhaniki [Justification of graphic solution of some mechanics tasks.] Colloquium-journal. 2019. I. 12 (36). pp. 57-60. DOI:https://doi.org/10.24411/2520-6990-2019-10335. (in Russian)
15. Nazarova O.N., Shagarova A.A., Zimina N.G. Primenenie metodov nachertatel'noj geometrii v reshenii prikladnyh tekhnicheskih zadach [Application of descriptive geometry methods in solving applied technical problems.] Colloquium-journal. 2019, I. 21 (45), pp. 68-72. (in Russian)
16. Nartova L.G. Nachertatel'naya geometriya [Descriptive geometry]. Moscow: Academia Publ., 2018. 512 p. (in Russian)
17. Pavlova A.A., Glazkova I.V. Nachertatel'naya geometriya. Praktikum dlya studentov VUZov. [Descriptive geometry. Workshop for University students]. Moscow: Gumanitarno-izdatel'skij centr «Vlados» Publ., 2005. 95 p. (in Russian)
18. Pavlova A.A., Glazkova I.V. Nachertatel'naya geometriya. Praktikum dlya studentov VUZov. [Descriptive geometry. Workshop for University students]. Moscow: Gumanitarno-izdatel'skij centr «Vlados» Publ., 2005. 95 p. (in Russian)
19. Peklich V.A. Mnimaya nachertatel'naya geometriya [Imaginary descriptive geometry]. Moscow: ASV Publ., 2007. 104 p. (in Russian)
20. Polikarpov Y.V. Soderzhanie vuzovskogo kursa nachertatel'noj geometrii v epohu tret'ej promyshlennoj revolyucii [The content of desriptive geometry course for high educational institution’s in the third industrial revolution’s era]. Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 3, pp. 49-55. DOI:https://doi.org/10.12737/article_5bc453447db654.91666264. (in Russian)
21. Poshekhonov B.L. Grafo-analiticheskaya geometriya v primenenii k opticheskim zadacham [Graph-analytical geometry as applied to optical problems]. Mashinostroenie Publ., Leningradskoe otdelenie, 1967. 159 p. (in Russian)
22. Poshekhonov B.L. Primenenie nachertatel'noj geometrii k resheniyu opticheskih zadach [Application of descriptive geometry to solving optical problems]. Leningrad, LITMO Publ., 1985. 82 p. (in Russian)
23. Rudaev A.K. Sbornik zadach po nachertatel'noj geometrii [Collection of problems in descriptive geometry]. Moscow, 1953. 343 p. (in Russian)
24. Savelyev I.V. Kurs obshchej fiziki: Uchebnoe posobie. v 3-h tt. T.1. Mekhanika. Molekulyarnaya fizika. [Course of General physics: Textbook. in 3 parts. Part 1. Mechanics. Molecular physics]. Saint - Petersberg: Lan Publ., 2007. 432 p. (in Russian)
25. Sal’kov N.A. Geometricheskaya sostavlyayushchaya tekhnicheskih innovacij [The geometric component of technical innovations.] Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 2, pp. 85-93. DOI:https://doi.org/10.12737/article_5b55a5163fa053.07622109. (in Russian)
26. Slyusarev G.G. Metody rascheta opticheskih sistem. [Methods of calculation of optical systems]. Mashinostroenie Publ., Leningradskoe otdelenie, 1969. 672 p. (in Russian)
27. Tarasov B.F. Metody izobrazheniya v transportnom stroitel'stve. Uchebnoe posobie dlya vuzov [Imaging Methods in transport construction. Textbook for universities]. Leningrad: Strojizdat Publ., Leningradskoe otdelenie, 1987. 248 p. (in Russian)
28. Trautman N.F. Sbornik zadach po nachertatel'noj geometrii v primenenii k razlichnym oblastyam nauki i tekhniki. [Collection of problems in descriptive geometry as applied to various fields of science and technology]. Moscow: Mashgiz Publ., 1953. 280 p. (in Russian)
29. Fedoseeva M.A. Metodika podgotovki studentov tekhnicheskih vuzov graficheskim disciplinam [Training procedure in graphic disciplines for students of technical high educational institutions.] Geometriya i grafika [Geometry and graphics]. 2019, V. 7, I. 1, pp. 68-73. DOI:https://doi.org/10.12737/article_5c91fed8650bb7.79232969. (in Russian)
30. Fedotova E. L., Fedotov A. A. Informacionnye tekhnologii v nauke i obrazovanii [Information technologies in science and education]. Moscow: ID FORUM, SIC INFRA-M Publ., 2013. 336 p. (in Russian)
31. Filimonova O.S. Disciplina «Inzhenernaya i komp'yuternaya grafika» v sisteme vysshego voennogo obrazovaniya [«Engineering and computer graphics» discipline in the system of higher military education]. Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 4, pp. 88-99. DOI:https://doi.org/10.12737/article_5c21fba3f26c35.85693389. (in Russian)
32. Frolov S.A. Nachertatel'naya geometriya Sbornik zadach [Descriptive geometry Collection of problems]. Moscow: INFRA-M Publ., 2011. 172 p. (in Russian)
33. Frolov S.A. Nachertatel'naya geometriya [Descriptive geometry]. Moscow: NIC INFRA-M Publ., 2013. 285 p. (in Russian)
34. Shishkarev V.V., Nazarova O.N., Zimina N.G. Osobennosti primeneniya nachertatel'noj geometrii v zadachah tekhnicheskoj optiki [Features of the use of descriptive geometry in the problems of technical optics]. Peredovye resheniya i opyt v «Kruzhkovom dvizhenii» NTI : Materialy Vserossijskoj nauchno-prakticheskoj konferencii (Ul'yanovsk, 24 maya 2019 g.) [Advanced solutions and experience in the "Circle movement" of NTI: Materials of the all-Russian scientific and practical conference (Ulyanovsk, may 24, 2019)]. Ulyanovsk, 2019, pp. 66-73. (in Russian)
35. Yumatova E.G. Sistema mezhintegrativnyh konstruktivno-analiticheskih zadach kak metod formirovaniya professional'no orientirovannyh sposobnostej budushchih inzhenerov [System of interintegraptive constructive-analytical problems as a method for forming of future engineers’ professionally-oriented abilities] Geometriya i grafika [Geometry and graphics]. 2017, V. 5, I. 2, pp. 75-83. DOI:https://doi.org/10.12737/article_5953f350da7151.85721309. (in Russian)
