Oscillators and Oscillatory Signals from Smooth to Discontinuous : Geometrical, Algebraic, and Physical Nature / by Valery N. Pilipchuk.

Format:

Book

Author/Creator:

Pilipchuk, V. N. (Valeriĭ Nikolaevich), author.

Language:

English

Subjects (All):

Mechanics.

Multibody systems.

Vibration.

Mechanics, Applied.

Engineering.

Dynamics.

Nonlinear theories.

Classical Mechanics.

Multibody Systems and Mechanical Vibrations.

Technology and Engineering.

Applied Dynamical Systems.

Local Subjects:

Classical Mechanics.

Multibody Systems and Mechanical Vibrations.

Technology and Engineering.

Applied Dynamical Systems.

Physical Description:

1 online resource (461 pages)

Edition:

2nd ed. 2023.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2023.

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 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. 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.

Contents:

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.

Notes:

Includes bibliographical references and index.

Other Format:

Print version: Pilipchuk, Valery N. Oscillators and Oscillatory Signals from Smooth to Discontinuous

ISBN:

3-031-37788-5