Academic Journal
Time-reversal symmetric quadratic differential systems having an invariant cylinder: global dynamics and mechanical application.
| Τίτλος: | Time-reversal symmetric quadratic differential systems having an invariant cylinder: global dynamics and mechanical application. |
|---|---|
| Συγγραφείς: | Messias, Marcelo, Reinol, Alisson C., Rodrigues de Lima, Camila A. B. |
| Πηγή: | International Journal of Dynamics & Control; Oct2026, Vol. 14 Issue 10, p1-15, 15p |
| Θεματικοί όροι: | Dynamical systems, Cylinder (Shapes), T-symmetry, Bifurcation theory, Autonomous differential equations, Applied mechanics, Limit cycles |
| Περίληψη: | This paper provides a comprehensive analysis of the global dynamics and an exact mechanical application for a class of time-reversal symmetric quadratic differential systems in R 3 having an elliptic cylinder as an invariant algebraic surface. A normal form for this family is first derived. When the polynomial defining the cylinder is a first integral, the phase space is foliated by a continuum of invariant cylinders. For fixed coefficients of the differential system, the initial condition selects a level of this first integral, and the vector fields restricted to the corresponding cylinders undergo pitchfork-type and degenerate topological transitions as the level crosses critical values. In the broader terminology used for systems with first integrals, these phenomena may be interpreted as initial-condition-induced bifurcations without parameters. The critical equilibrium collision is analyzed in regular coordinates and the resulting nilpotent singularities are classified. We also prove that every periodic orbit of the restricted flow on a nondegenerate invariant cylinder belongs to a local period annulus. Consequently, there are no limit cycles on the invariant cylinders, neither when they foliate the phase space nor when there is a single cylinder. Furthermore, we characterize all possible invariant parallels and meridians and describe the compactified flow at infinity, including the precise conditions under which invariant meridians form direct heteroclinic connections between the antipodal directions of the cylinder. Finally, we give an exact embedding into the classical problem of a bead sliding on a rotating hoop, showing that the same equilibrium-collision geometry is realized on the unit cylinder as the classical Hamiltonian pitchfork bifurcation when the angular velocity is varied. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Dynamics & Control is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://dx.doi.org/doi:10.1007/s40435-026-02300-0 Name: EDS - Springer Nature Journals (s7799221) Category: fullText Text: View record at Springer – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:edb&genre=article&issn=2195268X&ISBN=&volume=14&issue=10&date=20261001&spage=1&pages=1-15&title=International Journal of Dynamics & Control&atitle=Time-reversal%20symmetric%20quadratic%20differential%20systems%20having%20an%20invariant%20cylinder%3A%20global%20dynamics%20and%20mechanical%20application.&aulast=Messias%2C%20Marcelo&id=DOI:10.1007/s40435-026-02300-0 Name: Full Text Finder (for New FTF UI) (ns324271) Category: fullText Text: Full Text Finder MouseOverText: Full Text Finder |
|---|---|
| Header | DbId: edb DbLabel: Complementary Index An: 196689101 RelevancyScore: 1082 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1082.43029785156 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Time-reversal symmetric quadratic differential systems having an invariant cylinder: global dynamics and mechanical application. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Messias%2C+Marcelo%22">Messias, Marcelo</searchLink><br /><searchLink fieldCode="AR" term="%22Reinol%2C+Alisson+C%2E%22">Reinol, Alisson C.</searchLink><br /><searchLink fieldCode="AR" term="%22Rodrigues+de+Lima%2C+Camila+A%2E+B%2E%22">Rodrigues de Lima, Camila A. B.</searchLink> – Name: TitleSource Label: Source Group: Src Data: International Journal of Dynamics & Control; Oct2026, Vol. 14 Issue 10, p1-15, 15p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Cylinder+%28Shapes%29%22">Cylinder (Shapes)</searchLink><br /><searchLink fieldCode="DE" term="%22T-symmetry%22">T-symmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Autonomous+differential+equations%22">Autonomous differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Applied+mechanics%22">Applied mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Limit+cycles%22">Limit cycles</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper provides a comprehensive analysis of the global dynamics and an exact mechanical application for a class of time-reversal symmetric quadratic differential systems in R 3 having an elliptic cylinder as an invariant algebraic surface. A normal form for this family is first derived. When the polynomial defining the cylinder is a first integral, the phase space is foliated by a continuum of invariant cylinders. For fixed coefficients of the differential system, the initial condition selects a level of this first integral, and the vector fields restricted to the corresponding cylinders undergo pitchfork-type and degenerate topological transitions as the level crosses critical values. In the broader terminology used for systems with first integrals, these phenomena may be interpreted as initial-condition-induced bifurcations without parameters. The critical equilibrium collision is analyzed in regular coordinates and the resulting nilpotent singularities are classified. We also prove that every periodic orbit of the restricted flow on a nondegenerate invariant cylinder belongs to a local period annulus. Consequently, there are no limit cycles on the invariant cylinders, neither when they foliate the phase space nor when there is a single cylinder. Furthermore, we characterize all possible invariant parallels and meridians and describe the compactified flow at infinity, including the precise conditions under which invariant meridians form direct heteroclinic connections between the antipodal directions of the cylinder. Finally, we give an exact embedding into the classical problem of a bead sliding on a rotating hoop, showing that the same equilibrium-collision geometry is realized on the unit cylinder as the classical Hamiltonian pitchfork bifurcation when the angular velocity is varied. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of International Journal of Dynamics & Control is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edb&AN=196689101 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s40435-026-02300-0 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 1 Subjects: – SubjectFull: Dynamical systems Type: general – SubjectFull: Cylinder (Shapes) Type: general – SubjectFull: T-symmetry Type: general – SubjectFull: Bifurcation theory Type: general – SubjectFull: Autonomous differential equations Type: general – SubjectFull: Applied mechanics Type: general – SubjectFull: Limit cycles Type: general Titles: – TitleFull: Time-reversal symmetric quadratic differential systems having an invariant cylinder: global dynamics and mechanical application. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Messias, Marcelo – PersonEntity: Name: NameFull: Reinol, Alisson C. – PersonEntity: Name: NameFull: Rodrigues de Lima, Camila A. B. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 2195268X Numbering: – Type: volume Value: 14 – Type: issue Value: 10 Titles: – TitleFull: International Journal of Dynamics & Control Type: main |
| ResultId | 1 |