51178e662c3de1fc75ee6a57eb1b22d1 dynamics-03-00032.pdf 3be0c551eef97e2131a30d4deea31e996555ebf2 dynamics-03-00032.pdf 264b68393d500b68722c1c59b1ec9a10c4128c0cb4d7df8230a727754bbe4667 dynamics-03-00032.pdf Title: The Free Euler Rigid Body Revisited Subject: We review from a different perspective the approach and solution to the torque-free Euler equations, also called the free asymmetric top equations. We aim to simplify and broaden the study of the asymmetric free rigid body. This is an old but important integrable problem that has two first integrals: the energy and the angular momentum. We reduce this problem by eliminating the time as the independent variable in the three autonomous Euler equations written in cylindrical dimensionless variables, which allows a geometric study of the solution as a function of the cylindrical angle variable , by means of continuous deformations dependent on the two independent parameters and e0. The parameter space is divided into six disjoint regions, whose boundaries are the separatices and degenerated cases. The solutions are given in terms of trigonometric functions of the independent cylindric angle . Keywords: free rigid body; Euler top; reduction; energy hyperboloid; global solution Author: Lidia Jiménez-Lara and Jaume Llibre Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Mon Sep 18 08:05:24 2023 CEST ModDate: Mon Sep 18 08:11:23 2023 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 19 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 412979 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- QKZANQ+URWPalladioL-Bold Type 1 Custom yes yes no 10 0 MKWZFK+URWPalladioL-Roma Type 1 Custom yes yes no 15 0 GXSDTP+URWPalladioL-Ital Type 1 Custom yes yes no 19 0 BPVKPL+PazoMath-Italic Type 1 Builtin yes yes no 23 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 65 0 DGHJJU+MSBM10 Type 1 Builtin yes yes no 69 0 KCDZCP+PazoMath-BoldItalic Type 1 Builtin yes yes no 76 0 CRUANN+URWPalladioL-BoldItal Type 1 Custom yes yes no 80 0 MZMCZL+CMSY10 Type 1 Builtin yes yes no 84 0 NVYHJQ+CMEX10 Type 1 Builtin yes yes no 91 0 QQXUPP+PazoMath Type 1 Builtin yes yes no 95 0 SYFPBV+CMMI10 Type 1 Builtin yes yes no 102 0 CEFWBA+Arial-ItalicMT TrueType WinAnsi yes yes yes 115 0 YXHHZX+ArialMT TrueType WinAnsi yes yes yes 121 0 NCSCZX+ArialMT TrueType WinAnsi yes yes yes 127 0 WSNNCM+MathematicaSans CID TrueType Identity-H yes yes yes 133 0 BUJQXR+ArialMT TrueType WinAnsi yes yes yes 140 0 NNVLYA+MathematicaSans TrueType WinAnsi yes yes yes 146 0 WSNNCM+MathematicaSans CID TrueType Identity-H yes yes yes 152 0 SHIBQR+ArialMT TrueType WinAnsi yes yes yes 159 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-11-15 02:38:38 CET RepresentationInformation: dynamics-03-00032.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-11-06 13:09:31 CET Size: 412979 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 400 FreeObjects: 17 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@4d3167f4 Item: Title: The Euler Equations Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@ed9d034 Item: Title: The Explicit Solution for the Trajectory Equation Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@6121c9d6 Item: Title: The Separatrices Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@87f383f Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@4eb7f003 Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@eafc191 Info: Title: The Free Euler Rigid Body Revisited Author: Lidia Jiménez-Lara and Jaume Llibre Subject: We review from a different perspective the approach and solution to the torque-free Euler equations, also called the free asymmetric top equations. We aim to simplify and broaden the study of the asymmetric free rigid body. This is an old but important integrable problem that has two first integrals: the energy and the angular momentum. We reduce this problem by eliminating the time as the independent variable in the three autonomous Euler equations written in cylindrical dimensionless variables, which allows a geometric study of the solution as a function of the cylindrical angle variable , by means of continuous deformations dependent on the two independent parameters and e0. The parameter space is divided into six disjoint regions, whose boundaries are the separatices and degenerated cases. The solutions are given in terms of trigonometric functions of the independent cylindric angle . 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