45f81101768ab1327371e74459ac48e9 gal_a2023m4v11n2p58.pdf 925cef3c9492260e5b5bf85b706d7b587271f9f4 gal_a2023m4v11n2p58.pdf 3e246c7ebd409c13830e853b0cd22f51f0deb46c0abe517bbd8736cd1342ac64 gal_a2023m4v11n2p58.pdf Title: On the Periodic Orbits of the Perturbed Two- and Three-Body Problems Subject: In this work, a perturbed system of the restricted three-body problem is derived when the perturbation forces are conservative alongside the corresponding mean motion of two primaries bodies. Thus, we have proved that the first and second types of periodic orbits of the rotating Kepler problem can persist for all perturbed two-body and circular restricted three-body problems when the perturbation forces are conservative or the perturbed motion has its own extended Jacobian integral. Keywords: restricted 3-body problem; first- (second)-type periodic orbits; conservative forces; first integral of motion Author: Elbaz I. Abouelmagd, Juan Luis García Guirao, Jaume Llibre Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Wed Apr 19 04:45:22 2023 CEST ModDate: Wed Apr 19 04:47:44 2023 CEST 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: 303480 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- XGPRFM+URWPalladioL-Bold Type 1 Custom yes yes no 10 0 NWMQJX+URWPalladioL-Roma Type 1 Custom yes yes no 15 0 BGGPGA+URWPalladioL-Ital Type 1 Custom yes yes no 19 0 JXKYKS+CMSY10 Type 1 Builtin yes yes no 23 0 MYICIJ+PazoMath-Italic Type 1 Builtin yes yes no 27 0 VJBUQY+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 45 0 JHVSOB+CMEX10 Type 1 Builtin yes yes no 67 0 FWZAHR+PazoMath Type 1 Builtin yes yes no 71 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 75 0 HUPQFN+MSBM10 Type 1 Builtin yes yes no 79 0 DBCWHI+PazoMath-BoldItalic Type 1 Builtin yes yes no 89 0 QIELJB+CMMI10 Type 1 Builtin yes yes no 105 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-09-08 02:39:36 CEST RepresentationInformation: gal_a2023m4v11n2p58.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-09-07 19:52:46 CEST Size: 303480 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 275 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: Perturbation and Mean Motion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7b69c6ba Children: Item: Title: Perturbed Forces Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@46daef40 Item: Title: Perturbed Mean Motion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@12f41634 Item: Title: Restricted Three-Body Motion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@13c27452 Children: Item: Title: Unperturbed Restricted Three Body Motion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@262b2c86 Item: Title: Perturbed Restricted Three Body Motion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@371a67ec Item: Title: Hamiltonian of Perturbed Motion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@5ed828d Item: Title: Periodic Orbits of Perturbed Motion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@50d0686 Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7a3d45bd Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1e7c7811 Info: Title: On the Periodic Orbits of the Perturbed Two- and Three-Body Problems Author: Elbaz I. Abouelmagd, Juan Luis García Guirao, Jaume Llibre Subject: In this work, a perturbed system of the restricted three-body problem is derived when the perturbation forces are conservative alongside the corresponding mean motion of two primaries bodies. Thus, we have proved that the first and second types of periodic orbits of the rotating Kepler problem can persist for all perturbed two-body and circular restricted three-body problems when the perturbation forces are conservative or the perturbed motion has its own extended Jacobian integral. 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