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020 _a9783540384274
_9978-3-540-38427-4
024 7 _a10.1007/BFb0094521
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aReithmeier, Eduard.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aPeriodic Solutions of Nonlinear Dynamical Systems
_h[electronic resource] :
_bNumerical Computation, Stability, Bifurcation and Transition to Chaos /
_cby Eduard Reithmeier.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1991.
300 _aVI, 174 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1483
520 _aLimit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations. The text addresses mathematicians interested in engineering problems as well as engineers working with nonlinear dynamics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aEngineering mathematics.
650 0 _aMechanics.
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aMathematical and Computational Engineering.
_0http://scigraph.springernature.com/things/product-market-codes/T11006
650 2 4 _aClassical Mechanics.
_0http://scigraph.springernature.com/things/product-market-codes/P21018
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662163498
776 0 8 _iPrinted edition:
_z9783540545125
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1483
856 4 0 _uhttps://doi.org/10.1007/BFb0094521
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11527
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