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A. S. Kuleshov, E. S. Shalimova, A. Steindl:
"On Hopf bifurcation in the problem of motion of a heavy particle on a rotating sphere: the viscous friction case";
Acta Mechanica, 230 (2019), S. 4049 - 4060.

We investigate the Hopf bifurcation of a mass on a rotating sphere under the influence of gravityand viscous friction. After determining the equilibria, we study their stability and calculate the first Lyapunovcoefficient to determine the post-critical behavior. It is found that the bifurcating periodic branches are ini-tially stable. For several inclination angles of the sphere´s rotation axis, the periodic solutions are calculatednumerically, which shows that for large inclination angles turning points occur, at which the periodic solutionsbecome unstable. We also investigate the limiting case of small friction coefficients, when the mass movesclose to the equator of the rotating sphere.

Hopf bifurcation, Lyapunov coefficient, singular perturbation

http://dx.doi.org/10.1007/s00707-019-02536-2

https://doi.org/10.1007/s00707-019-02536-2