2025/01/13 by Miguel Rodríguez-Olmos, Rodríguez-Olmos, Miguel
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2501.07153
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.