ABOUT SOME OF THE OSCILLATIONS IN THE MECHANISM OF THE PLANETARY TYPE
Abstract
The article deals with the problem of determining stable and unstable equilibrium positions of the mechanical system of planetary mechanism type with one degree of freedom. The mechanism oscillates in a vertical plane. The function of the potential energy of the mechanism is studied. The features of free nonlinear oscillations of the mechanism are also investigated by the phase plane method. Built phase portraits. The mathematical model of the mechanical system, described by a system of nonlinear differential equations, allows to detect and investigate such moments in the behavior of the system, which are not available in linear theory. The analysis of the dependence of the number of equilibrium positions on changes in the values of some parameters of the system. It is shown that the considered mechanism, depending on its geometric characteristics, can have one or more stable equilibrium positions.
About the Authors
Nikolay I. Bondarenko
Bauman Moscow State Technical University
Russian Federation
Ph. D., associate professor
Russian Federation
Ph. D., associate professor
Konstantin B. Obnosov
Bauman Moscow State Technical University
Russian Federation
Ph. D., associate professor
Russian Federation
Ph. D., associate professor
Alla V. Panshina
Bauman Moscow State Technical University
Russian Federation
Ph. D., associate professor
Russian Federation
Ph. D., associate professor
References
1. Krajnev A.F. Slovar'-spravochnik po mekhanizmam (Dictionary-handbook of mechanisms), Moscow, Mashinostroenie, 1987, 560 p.
2. Alyukov S.V. Informatika i kibernetika, 2012, no. 3, pp. 35–42.
3. Babakov I.M. Teoriya kolebanij (Theory of oscillations), Moscow, Drofa, 2004, 591 p.
4. Aldoshin G.T. Teoriya linejnyh i nelinejnyh kolebanij (Theory of linear and nonlinear oscillations), Saint-Petersburg, Lan', 2013, 320 p.
5. Strelkov S.P. Vvedenie v teoriyu kolebanij (Introduction to the theory of oscillations), Moscow, URSS, LENAND, 2017, 440 p.
6. Biderman V.L. Teoriya mekhanicheskih kolebanij (Theory of mechanical oscillations), Moscow, Vysshaya shkola, 1980, 408 p.
7. Andronov A.A., Vitt A.A., Hajkin S.Eh. Teoriya kolebanij (Theory of oscillations), Moscow, Nauka, 1981, 568 p.
8. Arnol'd V.I. Matematicheskie metody klassicheskoj mekhaniki (Mathematical methods of classical mechanics), Moscow, EHditorial URSS, 2000, 408 p.
9. Bondarenko N.I., Obnosov K.B., Panshina A.V. Estestvennye i tekhnicheskie nauki, 2015, no. 10 (88), pp. 18–22.
10. Bondarenko N.I., Obnosov K.B., Panshina A.V. Uspekhi sovremennoj nauki, 2017, vol. 7, no. 3, pp. 78–82.
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