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Field name	Details
Dewey Class	514.74
Title	Periodic Solutions of the N-Body Problem ([EBook]) / by Kenneth R. Meyer.
Author	Meyer, Kenneth Ray , 1937-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer Berlin Heidelberg , 1999
Physical Details	XIV, 154 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1719
ISBN	9783540480730
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0094677
Links to Related Works	Subject References: Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Manifolds (Mathematics) . Mathematics . Authors: Meyer, Kenneth Ray 1937- . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 514.74 .

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Periodic Solutions of the N-Body Problem

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