کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1896841 | 1044460 | 2012 | 7 صفحه PDF | دانلود رایگان |
For a gyrostat in a incompressible ideal fluid, by writing Kirchhoff’s equations as a Lie–Poisson system and using a non-canonical Hamiltonian formulation, we provide the expressions of the equilibria when the gyrostatic momentum is constant with the form l=(0,0,l) and present necessary and sufficient conditions for the stability of some of them via the energy–Casimir method and the study of the linearized equations of the motion. Finally, using a recent geometric method introduced by Hanssmann and Van der Meer, we give a sufficient condition for the existence of a non-degenerate Hamiltonian Hopf bifurcation at those equilibria when the gyrostat is symmetric.
► A gyrostat in a incompressible ideal fluid using a non-canonical Hamiltonian is considered.
► Expressions of the equilibria when the gyrostatic momentum is constant are obtained.
► Necessary and sufficient conditions for the stability are provided.
► When the gyrostat is symmetric a sufficient condition for Hamiltonian Hopf bifurcation is presented.
Journal: Physica D: Nonlinear Phenomena - Volume 241, Issue 19, 1 October 2012, Pages 1648–1654