{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:43:27Z","timestamp":1772293407263,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,12,30]]},"abstract":"<jats:p> This paper presents analytical derivations to study periodic solutions for the two-body problem perturbed by the first zonal harmonic parameter. In particular, three different semianalytical approaches to solve this problem have been studied: (1) the classic perturbation theory, (2) the Lindstedt\u2013Poincar\u00e9 technique, and (3) the Krylov\u2013Bogoliubov\u2013Mitropolsky method. In addition, the numerical integration by Runge\u2013Kutta algorithm is established. However, the numerical comparison tests show that by increasing the value of angular momentum the solutions provided by Lindstedt\u2013Poincar\u00e9 and Krylov\u2013Bogoliubov\u2013Mitropolsky methods become similar, and they provide almost identical results using a smaller value for the perturbed parameter which quantify the dynamical flattening of the main body, the Krylov\u2013Bogoliubov\u2013Mitropolsky provides more accurate results to design elliptical periodic solutions than Lindstedt\u2013Poincar\u00e9 technique when the perturbed parameter has a relatively large value, regardless of the value of angular momentum. This study can be applied to equatorial orbits to obtain closed-form analytical solutions. <\/jats:p>","DOI":"10.1142\/s0218127415400404","type":"journal-article","created":{"date-parts":[[2016,1,14]],"date-time":"2016-01-14T14:17:31Z","timestamp":1452781051000},"page":"1540040","source":"Crossref","is-referenced-by-count":40,"title":["Analytical Study of Periodic Solutions on Perturbed Equatorial Two-Body Problem"],"prefix":"10.1142","volume":"25","author":[{"given":"Elbaz I.","family":"Abouelmagd","sequence":"first","affiliation":[{"name":"Celestial Mechanics Unit, Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo, Egypt"},{"name":"Department of Mathematics, Faculty of Scince, King Abdulaziz University, Jeddah, Saudi Arabia"}]},{"given":"Daniele","family":"Mortari","sequence":"additional","affiliation":[{"name":"Aerospace Engineering, Texas A&amp;M University, College Station, TX 77843-3141, USA"}]},{"given":"Hadia H.","family":"Selim","sequence":"additional","affiliation":[{"name":"National Research Institute of Astronomy and Geophysics, Cairo, Egypt"}]}],"member":"219","published-online":{"date-parts":[[2016,1,14]]},"reference":[{"key":"S0218127415400404BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s10509-012-1162-y"},{"key":"S0218127415400404BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s11038-013-9415-5"},{"key":"S0218127415400404BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s11012-013-9762-3"},{"key":"S0218127415400404BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s10509-014-2107-4"},{"key":"S0218127415400404BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2014.06.033"},{"key":"S0218127415400404BIB006","doi-asserted-by":"publisher","DOI":"10.2514\/4.861543"},{"key":"S0218127415400404BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/b137725"},{"key":"S0218127415400404BIB008","volume-title":"Asymptotic Methods in the Theory of Non-Linear Oscillations","author":"Bogoliubov N. 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