# Periodic Solutions of the N-Body Problem

Part of the Lecture Notes in Mathematics book series (LNM, volume 1719)

Part of the Lecture Notes in Mathematics book series (LNM, volume 1719)

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.

Celestial Mechanics Hamiltonian Systems N-Body Problem Symmetries mechanics

- DOI https://doi.org/10.1007/BFb0094677
- Copyright Information Springer-Verlag Berlin Heidelberg 1999
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-66630-1
- Online ISBN 978-3-540-48073-0
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
- About this book