We consider the motion of a symmetric gyroscope under the action of gravity and random influences that form a sequence of discrete events (the system parameters “jump” into some random values in the phase space at some random moments). To study the dynamic system, we construct a probabilistic model described by a Markov process that, in turn, is a solution of a differential equation with random parameters. Next, we consider the asymptotic situation where a discrete events becomes rarer, tending to vanish at infinity. This is ensured by replacing the transition function of the Markov process with a function that depends on a small parameter. After that, the behavior of the system as the parameter tends to zero and time tends to infinity is studied.
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Translated from Prykladna Mekhanika, Vol. 58, No. 6, pp. 18–28, November–December 2022.
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Degtyar, S.V., Shusharin, Y.V. & Zhuk, Y.O. Motion of a Symmetric Gyroscope Under Gravity with Discrete Random Change in the Parameters. Int Appl Mech 58, 634–644 (2022). https://doi.org/10.1007/s10778-023-01188-z
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DOI: https://doi.org/10.1007/s10778-023-01188-z