bb33ac8e2f229112a88e1cd23bd5610d universe_09_00149.pdf 4822256044c8b5ddf6b1df5f55624cf0c74eb7ac universe_09_00149.pdf fb16dba71801b79c6c98260484b661cfc2c6935c8aa34b081a320fe78708a384 universe_09_00149.pdf Title: Periodic Orbits of Quantised Restricted Three-Body Problem Subject: In this paper, perturbed third-body motion is considered under quantum corrections to analyse the existence of periodic orbits. These orbits are studied through two approaches to identify the first (second) periodic-orbit types. The essential conditions are given in order to prove that the circular (elliptical) periodic orbits of the rotating Kepler problem (RKP) can continue to the perturbed motion of the third body under quantum corrections where a massive primary body has excessive gravitational force over the smaller primary body. The primaries moved around each other in circular (elliptical) orbits, and the mass ratio was assumed to be sufficiently small. We prove the existence of the two types of orbits by using the terminologies of Poincaré for quantised perturbed motion. Keywords: periodic-orbit continuation; quantised three-body problem; first-kind periodic orbits; second-kind periodic orbits Author: Elbaz I. Abouelmagd, Juan Luis García Guirao, Jaume Llibre Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Wed Mar 15 06:23:00 2023 CET ModDate: Wed Mar 15 06:28:24 2023 CET Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 11 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 308265 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- ZRFLOK+URWPalladioL-Bold Type 1 Custom yes yes no 10 0 ZVKCAA+URWPalladioL-Roma Type 1 Custom yes yes no 15 0 ZPZEIZ+URWPalladioL-Ital Type 1 Custom yes yes no 19 0 WQBNLE+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 38 0 MJLFZM+PazoMath-Italic Type 1 Builtin yes yes no 60 0 TDULGJ+PazoMath-BoldItalic Type 1 Builtin yes yes no 64 0 XRJDFX+PazoMath Type 1 Builtin yes yes no 68 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 72 0 WEQDWC+CMSY10 Type 1 Builtin yes yes no 76 0 SWNAHA+CMEX10 Type 1 Builtin yes yes no 83 0 VHVABA+CMMI10 Type 1 Builtin yes yes no 90 0 MOTCQK+MSBM10 Type 1 Builtin yes yes no 94 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-06-23 02:26:40 CEST RepresentationInformation: universe_09_00149.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-06-21 01:34:38 CEST Size: 308265 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 277 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@44c8afef Item: Title: Model Description Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7b69c6ba Children: Item: Title: Equations of Motion for PCQRTBP Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@46daef40 Item: Title: Hamiltonian of PCQRTBP Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@12f41634 Item: Title: Periodic Orbits of First Kind Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@13c27452 Item: Title: Periodic Orbits of the Second Kind Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@262b2c86 Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@371a67ec Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@5ed828d Info: Title: Periodic Orbits of Quantised Restricted Three-Body Problem Author: Elbaz I. Abouelmagd, Juan Luis García Guirao, Jaume Llibre Subject: In this paper, perturbed third-body motion is considered under quantum corrections to analyse the existence of periodic orbits. These orbits are studied through two approaches to identify the first (second) periodic-orbit types. The essential conditions are given in order to prove that the circular (elliptical) periodic orbits of the rotating Kepler problem (RKP) can continue to the perturbed motion of the third body under quantum corrections where a massive primary body has excessive gravitational force over the smaller primary body. The primaries moved around each other in circular (elliptical) orbits, and the mass ratio was assumed to be sufficiently small. We prove the existence of the two types of orbits by using the terminologies of Poincaré for quantised perturbed motion. 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