Continuation of normal doubly symmetric orbits in conservative reversible systems

DOI10.1007/s10569-006-9048-3zbMath1162.37024OpenAlexW2099440500MaRDI QIDQ861353

Emilio Freire, Jorge Galan-Vioque, Francisco Javier Muñoz-Almaraz, André Vanderbauwhede

Publication date: 29 January 2007

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-006-9048-3

zbMATH Keywords

Boundary value problemPeriodic solutionsHamiltonian and conservative systemsNormal doubly symmetric solutionsNumerical continuationTime-reversibility

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) (n)-body problems (70F10) Approximation methods and numerical treatment of dynamical systems (37M99) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

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Uses Software

• AUTO2000

Cites Work

• On the variational approach to the periodic \(n\)-body problem
• Time-reversal symmetry in dynamical systems: a survey
• Continuation of periodic solutions in three dimensions
• Doubly-symmetric periodic solutions of the spatial restricted three-body problem
• Continuation of periodic orbits in conservative and Hamiltonian systems
• On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
• Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators
• The existence of simple choreographies for theN-body problem—a computer-assisted proof
• Braids in classical dynamics
• Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem
• Periodic solutions of the N-body problem
• A remarkable periodic solution of the three-body problem in the case of equal masses
• The family \(P_{12}\) of the three-body problem -- the simplest family of periodic orbits, with twelve symmetries per period

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