Abstract—
This article is the second part of the work, published in the form of two articles. The case, which remained unexplored in the first part, is considered, when for an unperturbed value of the constant of the cyclic integral, the mechanical reduced potential energy is constant with respect to the internal cardan angle. It is proved that in this case, for the majority of device designs, instability of all stationary solutions of the equations of motion takes place. It follows from the results obtained that for most device designs the presence of an isolated minimum of the total reduced potential energy is a necessary and sufficient condition for the stability of any stationary solution of the equations of motion.
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REFERENCES
B. I. Konosevich and Y. B. Konosevich, “Stability criterion for stationary solutions of multi-current model equations for a synchronous gimbal-mounted gyroscope. Part 1,” Mech. Solids 55, 258–272 (2020). https://doi.org/10.3103/S0025654420020119
J. La Salle and S. Lefschetz, Stability by Lyapunov’s Direct Method (Academic Press, New York, London, 1961).
E. A. Barbashin and V. A. Tabueva, Dynamical Systems with Cylindrical Phase Space (Nauka, Moscow, 1969) [in Russian].
B. I. Konosevich and Yu. B. Konosevich, “Attraction property of a Gimbal gyro with an electric motor,” Mech. Solids 49 (4), 361–369 (2014). https://doi.org/10.3103/S0025654414040013
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Translated by M. Katuev
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Konosevich, B.I., Konosevich, Y.B. Stability Criterion for Stationary Solutions of the Equations of a Multi-Current Model of a Synchronous Gyroscope in a Gimbal. 2. Mech. Solids 56, 40–54 (2021). https://doi.org/10.3103/S0025654421010088
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DOI: https://doi.org/10.3103/S0025654421010088