On Hopf bifurcation in the problem of motion of a heavy particle on a rotating sphere: the viscous friction case

Kuleshov, A. S.; Shalimova, E. S.; Steindl, Alois

doi:10.1007/s00707-019-02536-2

Datensatz Zitierlink:

https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-8063
http://hdl.handle.net/20.500.12708/757

Titel:

On Hopf bifurcation in the problem of motion of a heavy particle on a rotating sphere: the viscous friction case

Zitat:

Kuleshov, A. S., Shalimova, E. S., & Steindl, A. (2019). On Hopf bifurcation in the problem of motion of a heavy particle on a rotating sphere: the viscous friction case. Acta Mechanica, 4049–4060. https://doi.org/10.1007/s00707-019-02536-2

Verlags-DOI:

10.1007/s00707-019-02536-2

CatalogPlus:

AC15536715

Publikationstyp:

Artikel - Forschungsartikel

Sprache:

Englisch

Autor_innen:

Kuleshov, A. S.
Shalimova, E. S.
Steindl, Alois

Organisationseinheit:

E325 - Institut für Mechanik und Mechatronik

Zeitschrift:

Acta Mechanica

ISSN:

0001-5970

Datum (veröffentlicht):

2019

Umfang:

Verlag:

SPRINGER WIEN

Peer Reviewed:

Abstract:

We investigate the Hopf bifurcation of a mass on a rotating sphere under the influence of gravity and viscous friction. After determining the equilibria, we study their stability and calculate the first Lyapunov coefficient to determine the post-critical behavior. It is found that the bifurcating periodic branches are initially stable. For several inclination angles of the sphere’s rotation axis, the periodic solutions are calculated numerically, which shows that for large inclination angles turning points occur, at which the periodic solutions become unstable. We also investigate the limiting case of small friction coefficients, when the mass moves close to the equator of the rotating sphere.

Lizenz:

CC BY 4.0