LEADER 03267nam 2200625 450 001 996466759603316 005 20220906113302.0 010 $a3-540-38427-8 024 7 $a10.1007/BFb0094521 035 $a(CKB)1000000000437083 035 $a(SSID)ssj0000325599 035 $a(PQKBManifestationID)12049796 035 $a(PQKBTitleCode)TC0000325599 035 $a(PQKBWorkID)10324064 035 $a(PQKB)10133505 035 $a(DE-He213)978-3-540-38427-4 035 $a(MiAaPQ)EBC5592576 035 $a(Au-PeEL)EBL5592576 035 $a(OCoLC)1066191057 035 $a(MiAaPQ)EBC6841950 035 $a(Au-PeEL)EBL6841950 035 $a(PPN)15518640X 035 $a(EXLCZ)991000000000437083 100 $a20220906d1991 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aPeriodic solutions of nonlinear dynamical systems $enumerical computation, stability, bifurcation, and transition to chaos /$fEduard Reithmeier 205 $a1st ed. 1991. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[1991] 210 4$dİ1991 215 $a1 online resource (VI, 174 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1483 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-54512-3 320 $aIncludes bibliographical references (pages [152]-162) and index. 330 $aLimit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations. The text addresses mathematicians interested in engineering problems as well as engineers working with nonlinear dynamics. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1483. 606 $aDifferential equations, Nonlinear$xNumerical solutions 606 $aDifferentiable dynamical systems 615 0$aDifferential equations, Nonlinear$xNumerical solutions. 615 0$aDifferentiable dynamical systems. 676 $a515.355 686 $a34C25$2msc 686 $a58F22$2msc 700 $aReithmeier$b Eduard$f1957-$059911 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466759603316 996 $aPeriodic solutions of nonlinear dynamical systems$978639 997 $aUNISA