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arXiv · 2501.07153

Bifurcations of MacLaurin spheroids. A Hamiltonian perspective

Miguel Rodríguez-Olmos
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Abstract

Dirichlet's problem for the dynamics of fluid bodies with ellipsoidal shape can be formulated as a Hamiltonian system invariant under the action of a symmetry Lie group. I apply methods from Hamiltonian bifurcation theory to the study of the branch of solutions known as MacLaurin spheroids. I show that all its bifurcations are into three types named I, $S$ and adjoint $S$ ellipsoids in agreement with previous necessary conditions obtained by Chandrasekhar by linearizing the hydrodynamic equations.

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Miguel Rodríguez-Olmos. 2025-01-13. Bifurcations of MacLaurin spheroids. A Hamiltonian perspective. https://doi.org/10.1016/j.geomphys.2026.105869

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