Bifurcations of MacLaurin spheroids. A Hamiltonian perspective
arXiv:2501.07153 · doi:10.1016/j.geomphys.2026.105869
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, and adjoint ellipsoids in agreement with previous necessary conditions obtained by Chandrasekhar by linearizing the hydrodynamic equations.
Article shortened and exposition improved. Minor errors fixed