Journal
MATHEMATICS
Volume 10, Issue 4, Pages -Publisher
MDPI
DOI: 10.3390/math10040614
Keywords
quantized Hill problem; averaging theory; periodic solution
Categories
Funding
- National Research Institute of Astronomy
- GeophysicsNRIAG, 11421-Helwan, Cairo, Egypt
- NRIAG's technical
- National Natural Science Foundation of China (NSFC) [12172322]
- Ministerio de Ciencia, Innovacion y Universidades [PGC2018-097198-B-I00]
- Fundacion Seneca of Region de Murcia [20783/PI/18]
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In this work, we compared and analyzed several perturbation approaches, evaluated the necessary conditions for constructing periodic solutions under quantum corrections, and applied them to develop a Lunar theory and families of periodic orbits in the spatial quantized Hill problem.
In this work, we investigated the differences and similarities among some perturbation approaches, such as the classical perturbation theory, Poincare-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.
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