Poisson Structure and Reduction by Stages of the Full Gravitational $N$-Body Problem

DOI10.1137/21M1416783zbMath1505.70033OpenAlexW4285011683MaRDI QIDQ5095749

Edward A. Turner, Francisco Crespo

Publication date: 10 August 2022

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/21m1416783

zbMATH Keywords

Hamiltonian formalismrotational symmetryGalilean grouptranslational symmetrysemi-Lagrangian equilibrium

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) (n)-body problems (70F10) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (2)

Framework for the full N-body problem in \(\mathsf{SE}(3)\) and its reduction to the circular restricted full three-body problem ⋮ \(\textbf{(}\boldsymbol{\mathbb{R}}^{\textbf{3}} \boldsymbol{\times } \boldsymbol{SO(3)} \boldsymbol{\times } \boldsymbol{\mathbb{T}}^{\textbf{6}}\textbf{)}\)-Reduction, Relative Equilibria, and Bifurcations for the Full Averaged Model of Two Interacting Rigid Bodies

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