We consider a simplified model of a synchronous electric motor described by a second-order differential equation which is nonlinear with respect to the angular unknown, is linear with respect to its time derivative, and does not include electric currents. This equation plays the role of etalon equation in Leonov’s nonlocal reduction method which gives conditions where the global stability of such an equation implies the global stability of a multidimensional phase ODE system. It is exploiting in the reduction method that in the case of global stability of this equation, there exists an unbounded separatrix of each saddle point in its fourth quadrant. In the present work, regions of monotonicity and non-monotonicity are found for these unbounded separatrices and two-sided linear and nonlinear estimates are obtained for them.
Keywords: synchronous motor model, unbounded separatrix, critical value, global stability, nonlocal reduction method
Received October 14, 2025
Revised October 28, 2025
Accepted November 3, 2025
Funding Agency: The work was carried out within the framework of the development program of the regional Azov-Black Sea Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Grant Agreement no. 075-02-2025-1620).
Boris Ivanovich Konosevich, Dr. Phys.-Math. Sci., Institute of Applied Mathematics and Mechanics, Donetsk, 283048 Russia, e-mail: ipmm_mtt@mail.ru
Yuliya Borisovna Konosevich, Cand. Sci. (Phys.-Math.), Institute of Applied Mathematics and Mechanics, Donetsk, 283048 Russia, e-mail: konos.donetsk@yandex.ru
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Cite this article as: B.I. Konosevich, Yu.B. Konosevich. Estimates of the unbounded separatrices of the differential equation of the current-free model of a synchronous motor. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 4, pp. 188–202.
