Heteroclinic chaos detecting in dissipative mechanical systems: Chaotic regimes of compound nanosatellites dynamics

Abstract

The problem of heteroclinic chaos detecting is considered with the help of the Melnikov method. This paper presents the Melnikov method adaptation based on investigation of a nanosatellite attitude dynamics in the presence of internal dissipation properties. The need for this adaptation is determined by dynamical aspects of perturbing oscillations acting with damping amplitudes. In this case formal analytical exponential growth of perturbations values in reverse time takes place while the classical Melnikov integral does not converge.The adaptation of the Melnikov method allows investigating the heteroclinic chaos in mechanical systems with internal dissipation properties. As a prime example of this adaptation, the research presents the complete study of chaotic attitude dynamics of a nanosatellite with a slightly movable unit under action of its damped oscillations considered as perturbations. Moreover, the considered research of the nanosatellite attitude dynamics discovers a range of important tasks in the area of a rigid body dynamics under different perturbations with damping.