{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T08:59:51Z","timestamp":1775120391754,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,18]],"date-time":"2021-10-18T00:00:00Z","timestamp":1634515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Enhanced Seed Grant through Endowment fund","award":["EF\/2021-22\/QE04-07."],"award-info":[{"award-number":["EF\/2021-22\/QE04-07."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the approximated periodic solutions of the circular Sitnikov restricted four\u2013body problem (RFBP) were constructed using the Lindstedt\u2013Poincar\u00e9 method, by removing the secular terms, and compared with numerical solution. It can be observed that, in the numerical as well as approximated solutions patterns, the initial conditions are important. In the sense of a numerical solution, the motion is periodic in a certain interval, but beyond this interval, the motion is not periodic. But, the Lindstedt\u2013Poincar\u00e9 method constantly gives regular and periodic motion all time. Finally, we observed that the solution obtained by the Lindstedt\u2013Poincar\u00e9 method gives the true motion of the circular Sitnikov RFBP and the fourth approximate solution has more accuracy than the first, second, and third approximate solutions.<\/jats:p>","DOI":"10.3390\/sym13101966","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T22:07:04Z","timestamp":1634767624000},"page":"1966","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Approximation Solution of the Nonlinear Circular Sitnikov Restricted Four\u2013Body Problem"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2490-3787","authenticated-orcid":false,"given":"Reena","family":"Kumari","sequence":"first","affiliation":[{"name":"Department of Mathematics & Computing, IIT (ISM), Dhanbad 826004, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4445-1052","authenticated-orcid":false,"given":"Ashok Kumar","family":"Pal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2800-4527","authenticated-orcid":false,"given":"Elbaz I.","family":"Abouelmagd","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, India"},{"name":"Celestial Mechanics and Space Dynamics Research Group\u2014CMSDRG, Astronomy Department, National Research Institute of Astronomy and Geophysics\u2014NRIAG, Helwan 11421, Cairo, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2515-3762","authenticated-orcid":false,"given":"Sawsan","family":"Alhowaity","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science & Humanities, Shaqra University, Shaqra 11921, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,18]]},"reference":[{"key":"ref_1","first-page":"703","article-title":"Libration points in the restricted three-body problem: Euler angles, existence and stability","volume":"12","author":"Selim","year":"2019","journal-title":"Discret. 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