Abstract
Consider a model shown in Fig. 3.1. An asynchronous motor is coupled to the elastic shaft with an unbalanced disk (rotator) and balancing sleeve (oscillator) elastically coupled to the disk that can oscillate along the shaft.
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References
Belykh, V.N., Verichev, N.N.: Dynamics of a rotator coupled with an oscillator. Radiophys. Quantum Electron. 31(8), 657 (1988)
Andronov, A.A., Vitt, A.A., Khaikin, S.E.: Theory of Oscillators. Dover Publications, New York (1987)
Alifov, A.A., Frolov K.V.: Interaction of Non-linear Oscillatory Systems with Energy Sources. Taylor & Francis (1990)
Butenin, N.V., Neimark, Yu.I., Fufaev, N.A.: Introduction to the Theory of Nonlinear. Oscillations, Nauka, Moscow, 1976 (in Russian)
Blekhman, I.I.: Vibrations in Engineering, V.2. Vibrations of Nonlinear Mechanical Systems. Mashinostroenie, Moscow (1979) (in Russian)
Verichev, N.N., Verichev, S.N., Erofeyev, V.I.: Chaotic dynamics of simple vibrational systems. Int. J. Sound Vib. 310, 755–767 (2008)
Verichev, N.N.: Study of systems with Josephson junctions by the method of a spinning phase. Radiotechnika i Elektronika 31(11), 2267–2274 (1986). (in Russian)
Afraimovich, V.S., Bykov, V.V., Shilnikov, L.P.: On structurally stable attracting limit sets of Lorenz-attractor type. Trudy Mosk. Mat. Obshch, 46, 153–216 (1983); English transl Trans. Moscow Math. Soc. 2 (1983)
Feigenbaum, M.J.: Quantitative universaliti for a class nonlinear trasformations. J. Stat. Phys. 19(1), 25–52 (1978)
Arnold, V.I., Gamkrelidze, R.V.: Progress in Science and Technology. Current Problems in Mathematics. Fundamental Directions 3 (Dynamical Systems III). VINITI AN SSSR, Moscow (1985)
Mintz, R.M.: Study of the trajectories of a system of three differential equations at the infinity. Collection of papers in memory of A.A. Andronov, M., izd. AN SSSR, 1955 (in Russian)
Belykh, V.N., Verichev, N.N.: On dynamics of coupled rotators. Izv. Vuzov Radiofizika XXXI(6), 688–697 (1988) (in Russian)
Belykh, V.N., Verichev, N.N.: On the complex dynamics of an autonomous system with Josephson junctions. Radiotekhnika i elektronika. 31(1), 140–147 (1987) (in Russian)
Akimov, N., Belyustina, L.N., Belykh, V.N., et al.: Phase Synchronization Systems (Radio Svyaz’, Moscow) (1982) (Russian)
Lorenz, E.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)
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Verichev, N., Verichev, S., Erofeev, V. (2020). Autonomous Systems with Two Degrees of Freedom. In: Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-36103-7_3
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