On action-angle coordinates and the Poincaré coordinates

DOI10.1134/S1560354713060105zbMath1290.01001MaRDI QIDQ2449297

Jacques Féjoz

Publication date: 7 May 2014

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

perturbation theoryintegrabilitytwo-body problemHamiltonian systemPoincaré coordinatesKepler problemfirst integralaction-angle coordinatesadiabatic invariantsLagrangian fibrationplanetary problemLiouville-Arnold theorem

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15) History of mechanics of particles and systems (70-03) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography (01-01) History of dynamical systems and ergodic theory (37-03)

Related Items

Periodic solutions of a perturbed Kepler problem in the plane: from existence to stability, Andoyer construction for Hill and Delaunay variables, Secular dynamics for curved two-body problems, Action-angle variables and a KAM theorem for \(b\)-Poisson manifolds, Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem, A conceptual approach to the problem of action-angle variables, Sharp Nekhoroshev estimates for the three-body problem around periodic orbits, New methods of isochrone mechanics, Global Kolmogorov tori in the planetary \(N\)-body problem. Announcement of result

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On ``Arnold's theorem on the stability of the solar system
• Weak Liouville-Arnol'd theorems and their implications
• The planetary \(N\)-body problem: symplectic foliation, reductions and invariant tori
• Elliptic two-dimensional invariant tori for the planetary three-body problem
• Corrigendum to: ``Elliptic two-dimensional invariant tori for the planetary three-body problem
• Symplectic manifolds and their Lagrangian submanifolds
• On global action-angle coordinates
• Generic Hamiltonian dynamical systems are neither integrable nor ergodic
• Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)
• Sur le théorème de Bertrand (d'après Michael Herman)