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008			100301s2008 xxu| s |||| 0|eng d
020			_a9780817645953
024	7		_a10.1007/978-0-8176-4595-3 _2doi
035			_a978-0-8176-4595-3
090			_amg
100	0		_aO Mathúna, Diarmuid _910751
245	1	0	_aIntegrable Systems in Celestial Mechanics _h[electronic resource]/ _cby Diarmuid Ó Mathúna.
260			_aBoston: _bBirkhäuser Boston, _c2008.
300			_bdigital.
490	0		_aProgress in Mathematical Physics; _v51
505	0		_aGeneral Introduction -- The Kepler Problem (Two-Body Problem): the central Newtonian potential -- Bernoulli solution -- Features of the central Newtonian potential -- The Non-Central Newtonian Potential -- The Euler problem: two fixed centers of attraction -- The Vinti problem: earth-satellite theory -- Implications for perturbation theories -- Relativistic context -- Index .
520			_aThis work presents a unified treatment of three important integrable problems relevant to both Celestial and Quantum Mechanics. Under discussion are the Kepler (two-body) problem and the Euler (two-fixed center) problem, the latter being the more complex and more instructive, as it exhibits a richer and more varied solution structure. Further, because of the interesting investigations by the 20th century mathematical physicist J.P. Vinti, the Euler problem is now recognized as being intimately linked to the Vinti (Earth-satellite) problem. Here the analysis of these problems is shown to follow a definite shared pattern yielding exact forms for the solutions. A central feature is the detailed treatment of the planar Euler problem where the solutions are expressed in terms of Jacobian elliptic functions, yielding analytic representations for the orbits over the entire parameter range. This exhibits the rich and varied solution patterns that emerge in the Euler problem, which are illustrated in the appendix. A comparably detailed analysis is performed for the Earth-satellite (Vinti) problem. Key features: * Highlights shared features in the unified treatment of the Kepler, Euler, and Vinti problems * Raises challenges in analysis and astronomy, placing this trio of problems in the modern context * Includes a full analysis of the planar Euler problem * Highlights the complex and surprising orbit patterns that arise from the Euler problem * Provides a detailed analysis and solution for the Earth-satellite problem The analysis and results in this work will be of interest to graduate students in mathematics and physics (including physical chemistry) and researchers concerned with the general areas of dynamical systems, statistical mechanics, and mathematical physics and has direct application to celestial mechanics, astronomy, orbital mechanics, and aerospace engineering .
650		0	_aMathematics _943458
650		0	_aDifferentiable dynamical systems. _943815
650		0	_aMathematical physics. _943632
650		0	_aStatistical physics _938204
650		0	_aMechanics. _943988
650		0	_aAstronomy. _937103
697			_aMatemáticas Gerais- _x(inclusive alguns textos elementares sobre assuntos específicos) _923752
710	1		_aSpringerLink (Online service). _98857
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817640965
830		0	_aProgress in mathematical physics; _v51 _914532
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4595-3
942			_2impa _cEBK
999			_aO MATHÚNA, Diarmuid. <b> Integrable Systems in Celestial Mechanics. </b> Boston: Birkhäuser Boston, 2008. (Progress in Mathematical Physics ; 51). ISBN 9780817645953. Disponível em: <http://dx.doi.org/10.1007/978-0-8176-4595-3 > _c38531 _d38531