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

Record link:

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

Title:

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

Citation:

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

Publisher DOI:

10.1007/s00707-019-02536-2

CatalogPlus:

AC15536715

Publication Type:

Article - Original Research Article

Language:

English

Authors:

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

Organisational Unit:

E325 - Institut für Mechanik und Mechatronik

Journal:

Acta Mechanica

ISSN:

0001-5970

Date (published):

2019

Number of Pages:

Publisher:

SPRINGER WIEN

Peer reviewed:

Yes

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.

License:

CC BY 4.0