On Leonov's method for computing the linearization of transverse dynamics and analyzing Zhukovsky stability (Q2212400)

This paper complements and illustrates Leonov's well-known results from studying the Zhukovsky stability of nonlinear dynamical systems by linearization. The main result of this work is the justification of the analytical calculation of the auxiliary linear system of differential equations, which describes the linearization of the so-called transverse dynamics of the nonlinear system in the neighborhood of its solution. The result is illustrated with an exemplary analysis of the behavior of a nonlinear mechanical system with feedback.