Sufficient technical stability conditions for oscillations of two coupled gyrostats moving flywheels (Q2714630)

The authors study nonlinear oscillations of two platforms interconnected by nonextensible threads. There are slowly rotating flywheels on the platforms that can move on the platform plane. The authors present the motion equations deduced earlier [see \textit{N. P. Plakhtienko}, Prikl. Mekh. 26, No. 6, 80--88 (1990; Zbl 0727.70009); Prikl. Mekh. 26, No. 7, 103--107 (1990)] and apply scalar comparison equation of the form NEWLINE\[NEWLINE \dot y = \gamma(t)(y+\sigma(t)),\qquad y(t_0)=y_0,\tag{1} NEWLINE\]NEWLINE the idea of which follows from the corollary of Theorem~1.6.1 from the monographs [\textit{V. Lakshmikantham} \textit{S. Leela} and \textit{A. A. Martynyuk}, Stability analysis of nonlinear systems. Pure Appl. Math. 125, New York etc.: Marcel Dekker (1989; Zbl 0676.34003)] and [\textit{J. Szarski}, Differential inequalities. Warszawa: PWN (1967; Zbl 0171.01502)]. Equation (1) is applied to obtain very rough conditions of technical stability of motion.