Analysis of Equilibrium Points in Quantized Hill System

Abdullah A. Ansari, Sawsan Alhowaity, Elbaz I. Abouelmagd and Shiv K. Sahdev
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Abdullah A. Ansari: International Center for Advanced Interdisciplinary Research (ICAIR), Sangam Vihar, New Delhi 110062, India
Sawsan Alhowaity: Department of Mathematics, College of Science & Humanities, Shaqra University, Shaqra 15551, Saudi Arabia
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
Shiv K. Sahdev: Department of Mathematics, Shivaji College, University of Delhi, Delhi 110027, India

Mathematics, 2022, vol. 10, issue 13, 1-12

Abstract: In this work, the quantized Hill problem is considered in order for us to study the existence and stability of equilibrium points. In particular, we have studied three different cases which give all whole possible locations in which two points are emerging from the first case and four points from the second case, while the third case does not provide a realistic locations. Hence, we have obtained four new equilibrium points related to the quantum perturbations. Furthermore, the allowed and forbidden regions of motion of the first case are investigated numerically. We demonstrate that the obtained result in the first case is a generalization to the classical one and it can be reduced to the classical result in the absence of quantum perturbation, while the four new points will disappear. The regions of allowed motions decrease as the value of the Jacobian constant increases, and these regions will form three separate areas. Thus, the infinitesimal body can never move from one allowed region to another, and it will be trapped inside one of the possible regions of motion with the relative large values of the Jacobian constant .

Keywords: Hill problem; quantum correction; equilibrium points; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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