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- W2000823975 abstract "We study the Hess–Appelrot case of the Euler–Poisson system which describes dynamics of a rigid body around a fixed point. It is well known that in this case there is an invariant surface S in the phase space. In our previous paper (Lubowiecki and Żołądek, 2011 [6]) we proved that this surface is a torus and restricted to it dynamics is either hyperbolic or parabolic or elliptic quasi-periodic or elliptic periodic. We proved that the invariant torus is normally hyperbolic when the torus is close to a ‘critical circle’ and the motion is 1:q resonant. In this paper we consider perturbation of the Hess–Appelrot system (within the Euler–Poisson class) near the above situation. We prove existence of an invariant surface close to S and we study limit cycles on the perturbed surface. We estimate the number of such cycles by analysis of some non-standard Melnikov integrals." @default.
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- W2000823975 date "2012-01-01" @default.
- W2000823975 modified "2023-10-17" @default.
- W2000823975 title "The Hess–Appelrot system. II. Perturbation and limit cycles" @default.
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- W2000823975 doi "https://doi.org/10.1016/j.jde.2011.06.012" @default.
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