Geodesic
Stabilized rotator and foundations of its theory
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 83 (2023), pp. 143-150 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The key circumstance for the possibility of generalizing cyclotron motion to mechanics is that the Lagrangian of an electron moving across a constant magnetic field is twice its kinetic energy. The aim of this work is to find a mechanical analog of the cyclotron motion and to determine the scheme of the corresponding device referred to as a stabilized rotator. At zero torque in the stationary mode, the rotational speed of the stabilized rotator cannot be arbitrary and takes on a single value. The features of the stabilized rotator are the identity of the formula for the frequency of rotation to the formula for the frequency of a spring pendulum, the equality of kinetic and potential energies, and the resulting equality of the radius of rotation of the load to the magnitude of the spring deformation. Just as the frequency does not coincide with the natural frequency during forced oscillations of the pendulum, the rotation frequency of the stabilized rotator under loading does not coincide with the natural rotation frequency. The stabilized rotator can be used to control the natural frequency of the radial oscillator, although in this capacity it may have a strong competition from mechatronic systems. On the contrary, as a rotation stabilizer, its competitive capabilities are undeniable and determined by the extreme simplicity of the design.
Keywords: rotator, pendulum, frequency, stabilization, run-out, energy, angular momentum, cyclotron motion. 
@article{VTGU_2023_83_a11,
     author = {I. P. Popov},
     title = {Stabilized rotator and foundations of its theory},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {143--150},
     year = {2023},
     number = {83},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_83_a11/}
}
TY  - JOUR
AU  - I. P. Popov
TI  - Stabilized rotator and foundations of its theory
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2023
SP  - 143
EP  - 150
IS  - 83
UR  - http://geodesic.mathdoc.fr/item/VTGU_2023_83_a11/
LA  - ru
ID  - VTGU_2023_83_a11
ER  - 
%0 Journal Article
%A I. P. Popov
%T Stabilized rotator and foundations of its theory
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2023
%P 143-150
%N 83
%U http://geodesic.mathdoc.fr/item/VTGU_2023_83_a11/
%G ru
%F VTGU_2023_83_a11
I. P. Popov. Stabilized rotator and foundations of its theory. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 83 (2023), pp. 143-150. http://geodesic.mathdoc.fr/item/VTGU_2023_83_a11/

[1] I. P. Popov, “Reaktansy i sasseptansy mekhanicheskikh sistem”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2021, no. 70, 64–75 | DOI

[2] Ya. R. Abdullaev, S. A. Khanakhmedova, “Issledovanie dinamicheskikh protsessov starter-generatora metodom elektromekhanicheskoi analogii”, Izvestiya vuzov. Elektromekhanika, 61:1 (2018), 32–39 | DOI

[3] Yu. S. Oparina, A. V. Savilov, “Spontannoe tsiklotronnoe izluchenie plotnogo elektronnogo sgustka”, Izvestiya Rossiiskoi akademii nauk. Ser. fizicheskaya, 82:12 (2018), 1771–1774 | DOI

[4] L. G. Askinazi, G. I. Abdullina, A. A. Belokurov, M. D. Blekhshtein, N. A. Zhubr, V. A. Kornev, S. V. Krikunov, S. V. Lebedev, D. V. Razumenko, A. I. Smirnov, A. S. Tukachinskii, “Spektr ionno-tsiklotronnogo izlucheniya iz plazmy tokamaka tuman-3m pri inzhektsionnom nagreve”, Pisma v Zhurnal tekhnicheskoi fiziki, 44:22 (2018), 48–56 | DOI

[5] P. V. Minashin, A. B. Kukushkin, “Spektralnaya intensivnost elektronnogo tsiklotronnogo izlucheniya, vykhodyaschego iz plazmy tokamaka-reaktora na pervuyu stenku”, Voprosy atomnoi nauki i tekhniki. Ser. Termoyadernyi sintez, 42:4 (2019), 14–20 | DOI

[6] I. P. Popov, “Application of the Symbolic (Complex) Method to Study Near-Resonance Phenomena”, Journal of Machinery Manufacture and Reliability, 42:19 (2020), 1053–1063 | DOI

[7] E. A. Antonov, I. V. Merkurev, V. V. Podalkov, “Vliyanie nelineinoi zhestkosti uprugikh elementov na dinamiku dvukhmassovogo mikromekhanicheskogo giroskopa L-L-tipa v rezhime vynuzhdennykh kolebanii”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2019, no. 57, 53–61 | DOI

[8] A. K. Tomilin, G. A. Baizakova, “Upravlenie chastotami kolebanii uprugikh elektromekhanicheskikh sistem”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2012, no. 3 (19), 87–92