000 03231nam a22005175i 4500
001 978-3-540-85146-2
003 DE-He213
005 20140220084520.0
007 cr nn 008mamaa
008 100304s2010 gw | s |||| 0|eng d
020 _a9783540851462
_9978-3-540-85146-2
024 7 _a10.1007/978-3-540-85146-2
_2doi
050 4 _aQB495-500.269
072 7 _aTTDS
_2bicssc
072 7 _aSCI005000
_2bisacsh
082 0 4 _a520
_223
082 0 4 _a500.5
_223
100 1 _aCelletti, Alessandra.
_eauthor.
245 1 0 _aStability and Chaos in Celestial Mechanics
_h[electronic resource] /
_cby Alessandra Celletti.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Praxis Books
505 0 _aOrder and chaos -- Numerical dynamical methods -- Kepler’s problem -- The three-body problem and the Lagrangian solutions -- Rotational dynamics -- Perturbation theory -- Invariant tori -- Long-time stability -- Determination of periodic orbits -- Regularization theory.
520 _aThis book presents classical celestial mechanics and its interplay with dynamical systems in a way suitable for advance level undergraduate students as well as postgraduate students and researchers. First paradigmatic models are used to introduce the reader to the concepts of order, chaos, invariant curves, cantori. Next the main numerical methods to investigate a dynamical system are presented. Then the author reviews the classical two-body problem and proceeds to explore the three-body model in order to investigate orbital resonances and Lagrange solutions. In rotational dynamics the author details the derivation of the rigid body motion, and continues by discussing related topics, from spin-orbit resonances to dumbbell satellite dynamics. Perturbation theory is then explored in full detail including practical examples of its application to finding periodic orbits, computation of the libration in longitude of the Moon. The main ideas of KAM theory are provided including a presentation of long-term stability and converse KAM results. Celletti then explains the implementation of computer-assisted techniques, which allow the user to obtain rigorous results in good agreement with the astronomical expectations. Finally the study of collisions in the solar system is approached.
650 0 _aPhysics.
650 0 _aMathematical physics.
650 0 _aMechanics.
650 0 _aAstrophysics.
650 1 4 _aPhysics.
650 2 4 _aExtraterrestrial Physics, Space Sciences.
650 2 4 _aAstrophysics and Astroparticles.
650 2 4 _aMechanics.
650 2 4 _aStatistical Physics, Dynamical Systems and Complexity.
650 2 4 _aMathematical Methods in Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540851455
830 0 _aSpringer Praxis Books
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-540-85146-2
912 _aZDB-2-EES
999 _c111253
_d111253