Chaotic Motion of an Electrodynamic Tethered Satellite System Under Oblateness Effect in a Circular Orbit

Ahmad, Ahmad Yousof; Abdelaziz, Ahmed Magdy; Abd El Naby, Abd El Hakeem; Abdel-Aziz, Yehia Ahmed

doi:10.21608/sjdfs.2025.399892.1240

Chaotic Motion of an Electrodynamic Tethered Satellite System Under Oblateness Effect in a Circular Orbit

Document Type : Original articles

Authors

¹ Mathematics department, faculty of science, Damietta university, new Damietta, Egypt.

² National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt

³ Department of mathematics, Faculty of science, Damietta University, Damietta, Egypt.

⁴ National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt.

10.21608/sjdfs.2025.399892.1240

Abstract

This paper investigates the chaotic behavior of an in-plane electrodynamic tethered satellite system (EDTSS) operating in a circular orbit under the influence of Earth's oblateness, represented by the J2 zonal harmonic. The system is modelled using the dumbbell model, consisting of two point masses connected by an inelastic tether. The equations of motion are derived through the Lagrangian formulation, incorporating the effects of the Lorentz force generated by the current interacting with Earth’s magnetic field and the radial acceleration due to the oblateness of Earth. To analyze the conditions under which chaos may arise, the Melnikov method is applied, leading to the identification of a necessary condition for the occurrence of chaotic motion. Based on this condition, the parameter domains that are likely to result in chaotic behavior are determined. To confirm the analytical findings, numerical simulations are conducted and discussed. The results highlight the critical role of the oblateness effect and its interaction with electrodynamic forces in governing the nonlinear dynamics of tethered satellite systems.

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