Stability of unperturbed motion governed by the ternary differential system of Lyapunov-Darboux type with nonlinearities of degree four

Abstract

For the ternary differential system of Lyapunov-Darboux type with nonlinearities of degree four, using the Lie algebra admitted by this system, was obtained the analytic first integral, determined the Lyapunov function and the conditions of stability of the unperturbed motion.