Oscillators and oscillatory signals from smooth to discontinuous : geometrical, algebraic, and physical nature / Valery N. Pilipchuk.
Pilipchuk, V. N. (Valeriĭ Nikolaevich), author.
2023
TK7872.O7
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Title Oscillators and oscillatory signals from smooth to discontinuous : geometrical, algebraic, and physical nature / Valery N. Pilipchuk.
Author Pilipchuk, V. N. (Valeriĭ Nikolaevich), author.
Edition Second edition.
ISBN 9783031377884 (electronic bk.)
3031377885 (electronic bk.)
9783031377877
DOI https://doi.org/10.1007/978-3-031-37788-4
Published Cham, Switzerland : Springer, [2023]
Language English
Description 1 online resource (xii, 456 pages) : illustrations
Item Number 10.1007/978-3-031-37788-4 doi
Call Number TK7872.O7
Dewey Decimal Classification 621.3815/33
Summary This 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed September 28, 2023).
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Introduction
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.

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