000 03158nam a22004575i 4500
001 978-3-540-48073-0
003 DE-He213
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007 cr nn 008mamaa
008 121227s1999 gw | s |||| 0|eng d
020 _a9783540480730
_9978-3-540-48073-0
024 7 _a10.1007/BFb0094677
_2doi
050 4 _aQA614-614.97
072 7 _aPBKS
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKS
_2thema
082 0 4 _a514.74
_223
100 1 _aMeyer, Kenneth R.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aPeriodic Solutions of the N-Body Problem
_h[electronic resource] /
_cby Kenneth R. Meyer.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1999.
300 _aXIV, 154 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1719
505 0 _aEquations 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.
520 _aThe 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.
650 0 _aGlobal analysis.
650 1 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662162637
776 0 8 _iPrinted edition:
_z9783540666301
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1719
856 4 0 _uhttps://doi.org/10.1007/BFb0094677
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10431
_d10431