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Oscillators and Oscillatory Signals from Smooth to Discontinuous

Geometrical, Algebraic, and Physical Nature

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  • © 2023
  • Latest edition

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Overview

Authors:
  1. Valery N. Pilipchuk

    1. Mechanical Engineering Department, Wayne State University, Detroit, USA

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  • 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

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About this book

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 j</i>2 =± 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.



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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Valery N. Pilipchuk
    Pages 1-63
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  3. Smooth Oscillating Processes

    • Valery N. Pilipchuk
    Pages 65-88
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  4. Nonsmooth Processes as Asymptotic Limits

    • Valery N. Pilipchuk
    Pages 89-134
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  5. Nonsmooth Temporal Transformations (NSTT)

    • Valery N. Pilipchuk
    Pages 135-175
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  6. Periodic Power Series

    • Valery N. Pilipchuk
    Pages 177-198
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  7. NSTT for Linear and Piecewise-Linear Systems

    • Valery N. Pilipchuk
    Pages 199-234
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  8. Periodic and Transient Nonlinear Dynamics Under Discontinuous Loading

    • Valery N. Pilipchuk
    Pages 235-248
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  9. Strongly Nonlinear Vibrations

    • Valery N. Pilipchuk
    Pages 249-293
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  10. Strongly Nonlinear Waves

    • Valery N. Pilipchuk
    Pages 295-298
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  11. Impact Modes and Parameter Variations

    • Valery N. Pilipchuk
    Pages 299-340
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  12. Singular Trajectories of Forced Vibrations

    • Valery N. Pilipchuk
    Pages 341-349
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  13. NSTT and Shooting Method for Periodic Motions

    • Valery N. Pilipchuk
    Pages 351-368
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  14. Essentially Non-periodic Processes

    • Valery N. Pilipchuk
    Pages 369-378
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  15. Spatially Oscillating Structures

    • Valery N. Pilipchuk
    Pages 379-421
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  16. Back Matter

    Pages 423-456
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Authors and Affiliations

  • Mechanical Engineering Department, Wayne State University, Detroit, USA

    Valery N. Pilipchuk

About the author

Dr. Valery N. Pilipchuk is Associate professor of Mechanical Engineering at Wayne State University, Detroit, Michigan, USA.

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Bibliographic Information

  • Book Title: Oscillators and Oscillatory Signals from Smooth to Discontinuous

  • Book Subtitle: Geometrical, Algebraic, and Physical Nature

  • Authors: Valery N. Pilipchuk

  • DOI: https://doi.org/10.1007/978-3-031-37788-4

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-37787-7Published: 24 September 2023

  • Softcover ISBN: 978-3-031-37790-7Due: 07 October 2024

  • eBook ISBN: 978-3-031-37788-4Published: 23 September 2023

  • Edition Number: 2

  • Number of Pages: XII, 456

  • Number of Illustrations: 80 b/w illustrations, 89 illustrations in colour

  • Topics: Classical Mechanics, Vibration, Dynamical Systems, Control, Engineering, general, Complexity

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