LEADER 04246nam 22006855 450 001 9910746994503321 005 20230923093752.0 010 $a3-031-37788-5 024 7 $a10.1007/978-3-031-37788-4 035 $a(MiAaPQ)EBC30752341 035 $a(Au-PeEL)EBL30752341 035 $a(DE-He213)978-3-031-37788-4 035 $a(PPN)272740780 035 $a(CKB)28284167300041 035 $a(EXLCZ)9928284167300041 100 $a20230923d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOscillators and Oscillatory Signals from Smooth to Discontinuous $eGeometrical, Algebraic, and Physical Nature /$fby Valery N. Pilipchuk 205 $a2nd ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (461 pages) 311 08$aPrint version: Pilipchuk, Valery N. Oscillators and Oscillatory Signals from Smooth to Discontinuous Cham : Springer,c2023 9783031377877 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Smooth Oscillating Processes -- Nonsmooth Processes as Asymptotic Limits -- Nonsmooth Temporal Transformations (NSTT) -- Sawtooth Power Series -- NSTT for Linear and Piecewise-Linear Systems -- Periodic and Transient Nonlinear Dynamics under Discontinuous Loading -- Strongly Nonlinear Vibrations -- Strongly Nonlinear Waves -- Impact Modes and Parameter Variations -- Principal Trajectories of Forced Vibrations -- NSTT and Shooting Method for Periodic Motions -- Essentially Non-periodic Processes -- Spatially-Oscillating Structures. 330 $aThis updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford?s algebras, give rise to the essentially nonlinear ?quasi-impact? methodology based on the idea of non-smooth temporal substitutions. In the years since ?Nonlinear Dynamics: Between Linear and Impact Limits,? the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation j2 =± 1. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools. Presents an improved picture of non-smooth temporal transformations using impact systems as a basis for various analyses; Includes new examples of recent applications for problems in energy absorption/harvesting and resonance interactions; Describes a complementarity principle with a range of applications from smooth to discontinuous oscillatory processes. 606 $aMechanics 606 $aMultibody systems 606 $aVibration 606 $aMechanics, Applied 606 $aEngineering 606 $aDynamics 606 $aNonlinear theories 606 $aClassical Mechanics 606 $aMultibody Systems and Mechanical Vibrations 606 $aTechnology and Engineering 606 $aApplied Dynamical Systems 615 0$aMechanics. 615 0$aMultibody systems. 615 0$aVibration. 615 0$aMechanics, Applied. 615 0$aEngineering. 615 0$aDynamics. 615 0$aNonlinear theories. 615 14$aClassical Mechanics. 615 24$aMultibody Systems and Mechanical Vibrations. 615 24$aTechnology and Engineering. 615 24$aApplied Dynamical Systems. 676 $a530.416 700 $aPilipchuk$b V. N$g(Valerii? Nikolaevich),$01430246 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910746994503321 996 $aOscillators and Oscillatory Signals from Smooth to Discontinuous$93569959 997 $aUNINA