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On the Periodic Solutions for the Perturbed Spatial Quantized Hill Problem

Author

Listed:
  • Elbaz I. Abouelmagd

    (Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt)

  • Sawsan Alhowaity

    (Department of Mathematics, College of Science & Humanities, Shaqra University, Shaqra 15551, Saudi Arabia)

  • Zouhair Diab

    (Department of Mathematics and Computer Science, Larbi Tebessi University, Tebessa 12002, Algeria)

  • Juan L. G. Guirao

    (Departamento de Matemáca Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
    Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Laboratory of Theoretical Cosmology, International Centre of Gravity and Cosmos, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050 Tomsk, Russia)

  • Mahmoud H. Shehata

    (Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt)

Abstract

In this work, we investigated the differences and similarities among some perturbation approaches, such as the classical perturbation theory, Poincaré–Lindstedt technique, multiple scales method, the KB averaging method, and averaging theory. The necessary conditions to construct the periodic solutions for the spatial quantized Hill problem—in this context, the periodic solutions emerging from the equilibrium points for the spatial Hill problem—were evaluated by using the averaging theory, under the perturbation effect of quantum corrections. This model can be used to develop a Lunar theory and the families of periodic orbits in the frame work for the spatial quantized Hill problem. Thereby, these applications serve to reinforce the obtained results on these periodic solutions and gain its own significance.

Suggested Citation

  • Elbaz I. Abouelmagd & Sawsan Alhowaity & Zouhair Diab & Juan L. G. Guirao & Mahmoud H. Shehata, 2022. "On the Periodic Solutions for the Perturbed Spatial Quantized Hill Problem," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:614-:d:751283
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    References listed on IDEAS

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    1. Singh, Jagadish & Perdiou, A.E. & Gyegwe, Jessica Mrumun & Perdios, E.A., 2018. "Periodic solutions around the collinear equilibrium points in the perturbed restricted three-body problem with triaxial and radiating primaries for binary HD 191408, Kruger 60 and HD 155876 systems," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 358-374.
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    Cited by:

    1. Vincent, Aguda Ekele & Abouelmagd, Elbaz I. & Perdios, Efstathios A. & Kalantonis, Vassilis S., 2024. "Numerical exploration of the quantized Hill problem dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Abdullah A. Ansari & Sawsan Alhowaity & Elbaz I. Abouelmagd & Shiv K. Sahdev, 2022. "Analysis of Equilibrium Points in Quantized Hill System," Mathematics, MDPI, vol. 10(13), pages 1-12, June.

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