Bifurcations of MacLaurin spheroids. A Hamiltonian perspective
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909034350641152 |
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| author | Rodríguez-Olmos, Miguel |
| author_facet | Rodríguez-Olmos, Miguel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bifurcations of MacLaurin spheroids. A Hamiltonian perspective Rodríguez-Olmos, Miguel Symplectic Geometry Dynamical Systems 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. |
| title | Bifurcations of MacLaurin spheroids. A Hamiltonian perspective |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2501.07153 |