03267nam 2200625 450 99646675960331620220906113302.03-540-38427-810.1007/BFb0094521(CKB)1000000000437083(SSID)ssj0000325599(PQKBManifestationID)12049796(PQKBTitleCode)TC0000325599(PQKBWorkID)10324064(PQKB)10133505(DE-He213)978-3-540-38427-4(MiAaPQ)EBC5592576(Au-PeEL)EBL5592576(OCoLC)1066191057(MiAaPQ)EBC6841950(Au-PeEL)EBL6841950(PPN)15518640X(EXLCZ)99100000000043708320220906d1991 uy 0engurnn#008mamaatxtccrPeriodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation, and transition to chaos /Eduard Reithmeier1st ed. 1991.Berlin, Germany ;New York, New York :Springer,[1991]©19911 online resource (VI, 174 p.)Lecture Notes in Mathematics,0075-8434 ;1483Bibliographic Level Mode of Issuance: Monograph3-540-54512-3 Includes bibliographical references (pages [152]-162) and index.Limit 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.Lecture notes in mathematics (Springer-Verlag) ;1483.Differential equations, NonlinearNumerical solutionsDifferentiable dynamical systemsDifferential equations, NonlinearNumerical solutions.Differentiable dynamical systems.515.35534C25msc58F22mscReithmeier Eduard1957-59911MiAaPQMiAaPQMiAaPQBOOK996466759603316Periodic solutions of nonlinear dynamical systems78639UNISA