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Nonlinear Dynamics: Between Linear and Impact Limits
Kategorie	Beschreibung
036a	XA-DE
037b	eng
077a	326057749 Buchausg. u.d.T.: ‡Pilipchuk, Valery N.: Nonlinear dynamics
087q	978-3-642-12798-4
100	Pilipchuk, Valery N.
331	Nonlinear Dynamics
335	Between Linear and Impact Limits
410	Berlin, Heidelberg
412	Springer-Verlag Berlin Heidelberg
425	2010
425a	2010
433	Online-Ressource (360p, digital)
451	Lecture Notes in Applied and Computational Mechanics ; 52
454	Lecture notes in applied and computational mechanics
455	52
501	Description based upon print version of record
517	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
527	Buchausg. u.d.T.: ‡Pilipchuk, Valery N.: Nonlinear dynamics
540a	ISBN 978-3-642-12799-1
700	\|TGMD4
700	\|TEC009070
700	\|SCI018000
700	\|*37-02
700	\|70-02
700	\|70Kxx
700	\|37N20
700	\|70-08
700	\|37N05
700b	\|531.11
700b	\|530.15
700c	\|TA355
700c	\|TA352-356
700g	1270715054 SK 955
750	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
902s	209582588 Nichtlineare Dynamik
907s	209582588 Nichtlineare Dynamik
012	323615910
081	Pilipchuk, Valery N.: Nonlinear Dynamics
100	Springer E-Book
125a	Elektronischer Volltext - Campuslizenz
655e	$uhttp://dx.doi.org/10.1007/978-3-642-12799-1