Periodic Solutions of the N-Body Problem (Lecture Notes in Mathematics, 1719, Band 1719) - Softcover

Meyer, Kenneth R.

Softcover

ISBN 10: 3540666303 ISBN 13: 9783540666301

Verlag: Springer, 2008

Inhaltsangabe

Equations of celestial mechanics.- Hamiltonian systems.- Central configurations.- Symmetries, integrals, and reduction.- Theory of periodic solutions.- Satellite orbits.- The restricted problem.- Lunar orbits.- Comet orbits.- Hill's lunar equations.- The elliptic problem.

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Über die Autorin bzw. den Autor

Ken Meyer has a long history of working in Hamiltonian differential equations and the N-body problem. He has over 100 papers published. Daniel Offin is an active researcher in the theory of Hamiltonian systems using variational methods. He has made some important contributions to celestial mechanics using the Maslov index.

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The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group and many first integrals. These lecture notes are an introduction to the theory of periodic solutions of such Hamiltonian systems. From a generic point of view the N-body problem is highly degenerate. It is invariant under the symmetry group of Euclidean motions and admits linear momentum, angular momentum and energy as integrals. Therefore, the integrals and symmetries must be confronted head on, which leads to the definition of the reduced space where all the known integrals and symmetries have been eliminated. It is on the reduced space that one can hope for a nonsingular Jacobian without imposing extra symmetries. These lecture notes are intended for graduate students and researchers in mathematics or celestial mechanics with some knowledge of the theory of ODE or dynamical system theory. The first six chapters develops the theory of Hamiltonian systems, symplectic transformations and coordinates, periodic solutions and their multipliers, symplectic scaling, the reduced space etc. The remaining six chapters contain theorems which establish the existence of periodic solutions of the N-body problem on the reduced space.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 3540666303
• ISBN 13: 9783540666301
• Einband: Taschenbuch
• Anzahl der Seiten: 168
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland