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020 _a9783031722264
_9978-3-031-72226-4
024 7 _a10.1007/978-3-031-72226-4
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
100 1 _aCordani, Bruno.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_983347
245 1 0 _aGeography of Order and Chaos in Mechanics
_h[electronic resource] :
_bInvestigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools /
_cby Bruno Cordani.
250 _a2nd ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aXXV, 395 p. 77 illus., 16 illus. in color.
_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,
_x2197-1846 ;
_v64
505 0 _aIntroductory Survey -- Analytical Mechanics and Integrable Systems -- Perturbation Theory -- Numerical Tools I -- Numerical Tools II -- The Kepler Problem -- The KEPLER Program -- Some Perturbed Keplerian Systems -- The Multi Body Gravitational Problem -- But to What Extent is a Solar System Stable -- Final Remarks and Perspectives.
520 _aThis monograph explores the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems - such as the hydrogen atom and the solar system, with the associated Arnold web - through modern tools such as the frequency-modified Fourier transform, wavelets, and the frequency-modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems. Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novel ways, but perhaps its most useful feature is its inclusion of software to reproduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computer programming to visualize and experiment with the distribution of order, chaos and resonances in various Hamiltonian systems. This monograph will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, as well as an exceptional reference for PhD students with an interest in perturbation theory. The Second Edition includes a new chapter on theoretical and numerical results in the study of the solar system's (in)stability obtained since publication of the First Edition, clarifying the topological mechanism that causes the sudden increase in Mercury's eccentricity. An updated version of the companion software is also provided, which contains new features and better Graphical User Interfaces. Thanks to the compiled versions, all the software can be used even if the user does not have access to a MATLAB installation.
650 0 _aMathematical physics.
650 0 _aDynamical systems.
650 0 _aMechanics.
_968102
650 0 _aMathematics
_xData processing.
_965715
650 1 4 _aMathematical Physics.
650 2 4 _aMathematical Methods in Physics.
_970877
650 2 4 _aDynamical Systems.
650 2 4 _aClassical Mechanics.
_968103
650 2 4 _aComputational Science and Engineering.
_965717
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031722257
776 0 8 _iPrinted edition:
_z9783031722271
776 0 8 _iPrinted edition:
_z9783031722288
830 0 _aProgress in Mathematical Physics,
_x2197-1846 ;
_v64
_983348
856 4 0 _uhttps://doi.org/10.1007/978-3-031-72226-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c62933
_d62933