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Nonlinear Dynamics: Between Linear and Impact Limits

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Feldname	Details
Vorliegende Sprache	eng
Hinweise auf parallele Ausgaben	326057749 Buchausg. u.d.T.: ‡Pilipchuk, Valery N.: Nonlinear dynamics
ISBN	978-3-642-12798-4
Name	Pilipchuk, Valery N.
T I T E L	Nonlinear Dynamics
Zusatz zum Titel	Between Linear and Impact Limits
Verlagsort	Berlin, Heidelberg
Verlag	Springer-Verlag Berlin Heidelberg
Erscheinungsjahr	2010
Erscheinungsjahr	2010
Umfang	Online-Ressource (360p, digital)
Reihe	Lecture Notes in Applied and Computational Mechanics ; 52
Reihe	Lecture notes in applied and computational mechanics
Band	52
Notiz / Fußnoten	Description based upon print version of record
Weiterer Inhalt	Title Page; Preface; Contents; Introduction; Brief Literature Overview; Asymptotic Meaning of the Approach; Two Simple Limits of Lyapunov Oscillator; Oscillating Time and Hyperbolic Numbers, Standard and Idempotent Basis; Quick 'Tutorial'; Remarks on the Basic Functions; Viscous Dynamics under the Sawtooth Forcing; The Rectangular Cosine Input; Oscillatory Pipe Flow Model; Periodic Impulsive Loading; Strongly Nonlinear Oscillator; Geometrical Views on Nonlinearity; Geometrical Example; Nonlinear Equations and Nonlinear Phenomena; Rigid-Body Motions and Linear Systems. Remarks on the Multi-dimensional CaseElementary Nonlinearities; Example of Simplification in Nonsmooth Limit; Non-smooth Time Arguments; Further Examples and Discussion; Differential Equations of Motion and Distributions; Non-smooth Coordinate Transformations; Caratheodory Substitution; Transformation of Positional Variables; Transformation of State Variables; Smooth Oscillating Processes; Linear and Weakly Non-linear Approaches; A Brief Overview of Smooth Methods; Periodic Motions of Quasi Linear Systems; The Idea of Averaging; Averaging Algorithm for Essentially Nonlinear Systems. Averaging in Complex VariablesLie Group Approaches; Nonsmooth Processes as Asymptotic Limits; Lyapunov' Oscillator; Nonlinear Oscillators Solvable in Elementary Functions; Hardening Case; Localized Damping; Softening Case; Nonsmoothness Hiden in Smooth Processes; Nonlinear Beats Model; Nonlinear Beat Dynamics: The Standard Averaging Approach; Asymptotic of Equipartition; Asymptotic of Dominants; Necessary Condition of Energy Trapping; Sufficient Condition of Energy Trapping; Transition from Normal to Local Modes; System Description; Normal and Local Mode Coordinates. Local Mode Interaction DynamicsAuto-localized Modes in Nonlinear Coupled Oscillators; Nonsmooth Temporal Transformations (NSTT); Non-smooth Time Transformations; Positive Time; 'Single-Tooth' Substitution; 'Broken Time' Substitution; Sawtooth Sine Transformation; Links between NSTT and Matrix Algebras; Differentiation and Integration Rules; NSTT Averaging; Generalizations on Asymmetrical Sawtooth Wave; Multiple Frequency Case; Idempotent Basis Generated by the Triangular Sine-Wave; Definitions and Algebraic Rules; Time Derivatives in the Idempotent Basis. Idempotent Basis Generated by Asymmetric Triangular WaveDefinition and Algebraic Properties; Differentiation Rules; Oscillators in the Idempotent Basis; Integration in the Idempotent Basis; Discussions, Remarks and Justifications; Remarks on Nonsmooth Solutions in the Classical Dynamics; Caratheodory Equation; Other Versions of Periodic Time Substitutions; General Case of Non-invertible Time and Its Physical Meaning; NSTT and Cnoidal Waves; Sawtooth Power Series; Manipulations with the Series; Smoothing Procedures; Sawtooth Series for Normal Modes; Periodic Version of Lie Series. Lie Series of Transformed Systems
Titelhinweis	Buchausg. u.d.T.: ‡Pilipchuk, Valery N.: Nonlinear dynamics
ISBN	ISBN 978-3-642-12799-1
Klassifikation	TGMD4
	TEC009070
	SCI018000
	*37-02
	70-02
	70Kxx
	37N20
	70-08
	37N05
	531.11
	530.15
	TA355
	TA352-356
	SK 955
Kurzbeschreibung	Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of "unusual" physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and too
1. Schlagwortkette	Nichtlineare Dynamik
1. Schlagwortkette ANZEIGE DER KETTE	Nichtlineare Dynamik
2. Schlagwortkette	Nichtlineare Dynamik
ANZEIGE DER KETTE	Nichtlineare Dynamik
SWB-Titel-Idn	323615910
Signatur	Springer E-Book
Bemerkungen	Elektronischer Volltext - Campuslizenz
Elektronische Adresse	$uhttp://dx.doi.org/10.1007/978-3-642-12799-1
Internetseite / Link	Volltext
Siehe auch	Volltext
Siehe auch	Inhaltstext

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