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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Hamiltonian View of the Nonlinear Stability of a Satellite with Variable Mass in Elliptical Orbit

Discontinuity, Nonlinearity, and Complexity 15(4) (2026) 541--551 | DOI:10.5890/DNC.2026.12.005

José Laudelino de Menezes Neto

Department of Exact Science, Federal University of Paraíba, Av. Santa Elizabeth, Rio Tinto, 58297-000, Paraíba, Brazil

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Abstract

The aim of this paper is to study the linear and nonlinear stability of four equilibrium positions of a satellite with variable mass distribution, performing an elliptical orbit around a Newtonian center of attraction. To do such research, we restrict to the plane of the orbit, and focuses in the Hamiltonian perspective of the problem, expanding its Hamiltonian function around the equilibrium positions up to terms of fourth order. Regions of linear stability are found in the plane of the parameters $K\times e$, where $e$ is the eccentricity of the orbit, and $K$ is a parameter associated with the tensor of inertia of the satellite. In the regions where linear stability happens, we perform the nonlinear analysis for arbitrary values of $e$ by using numerical methods, and for sufficiently small values of $e$ by analytical methods. We conclude about the nonlinear stability for the nonresonant case and in the case of parametric resonances of orders three and four.

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