Multidimensional planar monojet oscillations


Аuthors

Popov I. P.

Kurgan State University, 63/4, Sovetskaya str., Kurgan, 640020, Russia

e-mail: ip.popow@yandex.ru

Abstract

The relevance of the study is determined by the fact that fluctuations of inertial masses are found everywhere. In the field of construction and use of aviation and rocket technology, this topic is of particular importance. Like a three-dimensional plane coordinate system in the coordinate plane Z, a multidimensional system with n axes 0xz1, 0xz2,..., 0xzn shifted relative to each other by angles 2π/n can be considered. There is an arbitrary vector  R emanating from the origin 0. R ⊂ Z . It is proved that the points x1,x2,...,xn, which are the coordinates of the end of the vector R in the coordinate system 0xz1, 0xz2,..., 0xzn, are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector R, i.e. are unchanged. The center of a regular polygon in all cases coincides with the middle of the vector R . In the considered (idealized) case, the polygon, at the vertices of which there are oscillating weights of masses m, lies in the Z plane. multi-piston mechanism). In the considered multidimensional plane monoreactive oscillator, free harmonic linear oscillations of loads can occur. In this case, only kinetic energy is involved in the energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural oscillation frequency. The frequency depends on the initial speeds and positions of the weights. A regular polygon x1,x2,...,xn makes a double rotation – around the point 0 and around the point r. At the same time, the loads carry out linear harmonic oscillations with amplitude R. The use of a crank-slider or crank-and-rod mechanism will allow organizing the parallel movement of goods.

Keywords:

polygon, oscillating weight, free oscillations, monoreactive system, frequency

References

  1. Popov I.P. Trudy MAI, 2022, no. 126. URL: https://trudymai.ru/eng/published.php?ID=168986. DOI: 34759/trd-2022-126-01

  2. Popov I.P. Trudy MAI, 2023, no. 129. URL: https://trudymai.ru/eng/published.php?ID=173002. DOI: 10.34759/trd-2023-129-02

  3. Aleroeva Kh.T., Aleroev T.S. Trudy MAI, 2017, no. 94. URL: http://trudymai.ru/eng/published.php?ID=80904

  4. Dobryshkin A.Yu. Trudy MAI, 2020, no. 110. URL: https://trudymai.ru/eng/published.php?ID=112806. DOI: 10.34759/trd-2020-110-2

  5. Bykova T.V., Mogilevich L.I., Popov V.S., Popova A.A., Chernenko A.V. Trudy MAI, 2020, no. 110. URL: http://trudymai.ru/eng/published.php?ID=112836. DOI: 10.34759/trd-2020-110-6

  6. Aleroeva Kh.T. Trudy MAI, 2017, no. 92. URL: http://trudymai.ru/eng/published.php?ID=76821

  7. Kholostova O.V., Safonov A.I. Trudy MAI, 2018, no. 100. URL: http://trudymai.ru/eng/published.php?ID=93297

  8. Mukhametzyanova A.A. Trudy MAI, 2015, no. 84. URL: http://trudymai.ru/eng/published.php?ID=62975

  9. Semenov M.E., Solov’ev A.M., Popov M.A. Trudy MAI, 2017, no. 93. URL: http://trudymai.ru/eng/published.php?ID=80231

  10. Grushenkova E.D., Mogilevich L.I., Popov V.S., Popova A.A. Trudy MAI, 2019, no. 106. URL: http://trudymai.ru/eng/published.php?ID=105618

  11. Dobryshkin A.Yu., Sysoev O.E., Sysoev E.O. Trudy MAI, 2019, no. 109. URL: http://trudymai.ru/eng/published.php?ID=111349. DOI: 10.34759/trd-2019-109-4

  12. Petrukhin V.A., Mel’nikov V.E. Trudy MAI, 2017, no. 93. URL: http://trudymai.ru/eng/published.php?ID=80344

  13. Dobryshkin A.Yu., Sysoev O.E., Sysoev E.O. Trudy MAI, 2020, no. 113. URL: http://trudymai.ru/eng/published.php?ID=117957. DOI: 10.34759/trd-2020-113-01

  14. Sysoev O.E., Dobryshkin A.Yu., Nein S.N. Trudy MAI, 2018, no. 98. URL: http://trudymai.ru/eng/published.php?ID=90079

  15. Bardin B.S., Savin A.A. Trudy MAI, 2016, no, 85. URL: http://trudymai.ru/eng/published.php?ID=65212

  16. Blagodyreva O.V. Trudy MAI, 2017, no. 95. URL: http://trudymai.ru/eng/published.php?ID=84426

  17. Zagordan A.A., Zagordan N.L. Trudy MAI, 2019, no. 108. URL: http://trudymai.ru/eng/published.php?ID=109383. DOI: 10.34759/trd-2019-108-4

  18. Rybnikov S.I., Nguen T.Sh. Trudy MAI, 2017, no. 95. URL: http://trudymai.ru/eng/published.php?ID=84572

  19. Animitsa V.A., Borisov E.A., Kritskii B.S., Mirgazov R.M. Trudy MAI, 2016, no. 87. URL: http://trudymai.ru/eng/published.php?ID=69626

  20. Popov I.P. Trudy MAI, 2022, no. 122. URL: https://trudymai.ru/eng/published.php?ID=164101. DOI: 10.34759/trd-2022-122-03


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