Symmetric constellations of satellites moving around a central body of large mass

DOI10.1007/s10884-021-10083-5arXiv2003.04580OpenAlexW3206597767WikidataQ115382972 ScholiaQ115382972MaRDI QIDQ6161077

Giovanni Federico Gronchi, M. Fenucci

Publication date: 2 June 2023

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.04580

zbMATH Keywords

symmetryperiodic solutionvariational methodgamma-convergenceLagrangian action functionaltopological constraint

Mathematics Subject Classification ID

Variational methods for problems in mechanics (70G75) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) (n)-body problems (70F10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Platonic polyhedra, periodic orbits and chaotic motions in the \(N\)-body problem with non-Newtonian forces
• Platonic polyhedra, topological constraints and periodic solutions of the classical \(N\)-body problem
• Periodic solutions for N-body type problems
• Hip-hop solutions of the \(2N\)-body problem
• Symmetric trajectories for the \(2N\)-body problem with equal masses
• Double collisions for a classical particle system with nongravitational interactions
• An introduction to \(\Gamma\)-convergence
• Binary decompositions for planar \(N\)-body problems and symmetric periodic solutions
• How the method of minimization of action avoids singularities
• On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
• Noncollision periodic solutions to some singular dynamical systems with very weak forces
• Entire minimal parabolic trajectories: the planar anisotropic Kepler problem
• Braids with the symmetries of Platonic polyhedra in the Coulomb (N+1)-body problem
• Transitive decomposition of symmetry groups for the \(n\)-body problem
• Symmetries and noncollision closed orbits for planar N-body-type problems
• On the Singularities of Generalized Solutions to n-Body-Type Problems
• A Minimizing Property of Keplerian Orbits
• On the stability of periodic N-body motions with the symmetry of Platonic polyhedra
• Minima of the action integral in the Newtonian problem of 4 bodies with equal masses: `Hip-hop' orbits
• A remarkable periodic solution of the three-body problem in the case of equal masses