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001 978-0-8176-4595-3
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007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780817645953
_9978-0-8176-4595-3
024 7 _a10.1007/978-0-8176-4595-3
_2doi
040 _aISI Library, Kolkata
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.1
_223
100 1 _aÓ Mathúna, Diarmuid.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aIntegrable Systems in Celestial Mechanics
_h[electronic resource] /
_cby Diarmuid Ó Mathúna.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2008.
300 _aX, 234 p. 24 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematical Physics,
_x1544-9998 ;
_v51
505 0 _aGeneral Introduction -- Lagrangian Mechanics -- The Kepler Problem -- The Euler Problem I — Planar Case -- The Euler Problem II — Three-dimensional Case -- The Earth Satellite — General Analysis -- The Earth Satellite — Some Special Orbits.
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 _aDifferentiable dynamical systems.
650 0 _aMechanics.
650 0 _aMathematical physics.
650 0 _aAstronomy.
650 1 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aClassical Mechanics.
_0http://scigraph.springernature.com/things/product-market-codes/P21018
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aAstronomy, Astrophysics and Cosmology.
_0http://scigraph.springernature.com/things/product-market-codes/P22006
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817671594
776 0 8 _iPrinted edition:
_z9780817640965
830 0 _aProgress in Mathematical Physics,
_x1544-9998 ;
_v51
856 4 0 _uhttps://doi.org/10.1007/978-0-8176-4595-3
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425802
_d425802