000 | 03158nam a22004575i 4500 | ||
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001 | 978-3-540-48073-0 | ||
003 | DE-He213 | ||
005 | 20190213151351.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s1999 gw | s |||| 0|eng d | ||
020 |
_a9783540480730 _9978-3-540-48073-0 |
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024 | 7 |
_a10.1007/BFb0094677 _2doi |
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050 | 4 | _aQA614-614.97 | |
072 | 7 |
_aPBKS _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
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072 | 7 |
_aPBKS _2thema |
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082 | 0 | 4 |
_a514.74 _223 |
100 | 1 |
_aMeyer, Kenneth R. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aXIV, 154 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1719 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0094677 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c10431 _d10431 |