Applied Non-Linear Dynamical Systems

✍ Scribed by Jan Awrejcewicz (eds.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 535
• Series: Springer Proceedings in Mathematics & Statistics 93
• Edition: 1
• Category: Library

✦ Synopsis

The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the International Conference on Dynamical Systems: Theory and Applications, held in Łódź, Poland on December 2-5, 2013. The studies give deep insight into both the theory and applications of non-linear dynamical systems, emphasizing directions for future research. Topics covered include: constrained motion of mechanical systems and tracking control; diversities in the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic solutions to the problem of vortex structure around a cylinder; investigation of the regular and chaotic dynamics; rare phenomena and chaos in power converters; non-holonomic constraints in wheeled robots; exotic bifurcations in non-smooth systems; micro-chaos; energy exchange of coupled oscillators; HIV dynamics; homogenous transformations with applications to off-shore slender structures; novel approaches to a qualitative study of a dissipative system; chaos of postural sway in humans; oscillators with fractional derivatives; controlling chaos via bifurcation diagrams; theories relating to optical choppers with rotating wheels; dynamics in expert systems; shooting methods for non-standard boundary value problems; automatic sleep scoring governed by delay differential equations; isochronous oscillations; the aerodynamics pendulum and its limit cycles; constrained N-body problems; nano-fractal oscillators and dynamically-coupled dry friction.

✦ Table of Contents

Front Matter....Pages i-xiv
Duffing-Type Oscillators with Amplitude-Independent Period....Pages 1-10
Asymptotic of “Rigid-Body” Motions for Nonlinear Dynamics: Physical Insight and Methodologies....Pages 11-22
Non-linear Phenomena Exhibited by Flexible Cylindrical and Sector Shells....Pages 23-35
Gear Shift Patterns in Uncertain Terrestrial Locomotion Systems....Pages 37-48
Turbulent Phenomena in Flexible Plates and Shells....Pages 49-76
Using Bifurcation Diagrams for Controlling Chaos....Pages 77-84
Shear Waves Dispersion in Cylindrically Structured Cancellous Viscoelastic Bones....Pages 85-101
Quasi-regular and Chaotic Dynamics of Postural Sway in Human....Pages 103-114
Modelling of Ropes with Consideration of Large Deformations and Friction by Means of the Rigid Finite Element Method....Pages 115-137
Dynamical Response of a Van der Pol–Duffing System with an External Harmonic Excitation and Fractional Derivative....Pages 139-150
Vortex Structure Around the Cylinder at a Flow of Viscous Fluid....Pages 151-159
Asymptotic Analysis and Limiting Phase Trajectories in the Dynamics of Spring Pendulum....Pages 161-173
Vibration Surveillance System with Variable Stiffness Holder for Milling Flexible Details....Pages 175-184
Diversities in the Inverse Dynamics Problem for Underactuated Mechanical Systems Subject to Servo-constraints....Pages 185-201
Rare Phenomena and Chaos in Switching Power Converters....Pages 203-211
Constrained Motion of Mechanical Systems and Tracking Control of Nonlinear Systems....Pages 213-244
The General Conception of the Intellectual Investigation of the Regular and Chaotic Behavior of the Dynamical System Hamiltonian Structure....Pages 245-254
Dynamic Properties of Two-Axle Freight Wagon with UIC Double-Link Suspension as a Non-smooth System with Dry Friction....Pages 255-268
Dynamics of Mechanical Systems with Mecanum Wheels....Pages 269-279
Reliability Analysis of the Dynamics of a Horizontal Drill-String....Pages 281-293
Transition in Oscillatory Behavior in Mouse Oocyte and Mouse Embryo Through Oscillatory Spherical Net Model of Mouse Zona Pellucida....Pages 295-303
Constrained n -Body Problems....Pages 305-317
Hunting French Ducks in Population Dynamics....Pages 319-335
Model of Nonlinear Fractal Oscillator in Nanosystem....Pages 337-350
Dynamical Statement Networks....Pages 351-361
The Shooting Method for Non-standard Boundary Value Problem....Pages 363-370
Automatic Sleep Scoring from a Single Electrode Using Delay Differential Equations....Pages 371-382
Methods for the Quick Analysis of Micro-chaos....Pages 383-395
Bouncing Ball Dynamics: Simple Motion of the Table Approximating the Sinusoidal Motion....Pages 397-405
Periodic Motions of Coupled Oscillators Excited by Dry Friction and Harmonic Force....Pages 407-414
Limit Cycle Oscillations of an Aerodynamic Pendulum....Pages 415-427
Vibratory Energy Localization by Non-smooth Energy Sink with Time-Varying Mass....Pages 429-442
Coordinate-Free Formulation of Nonholonomic Constraints for Wheeled Robots....Pages 443-455
Optomechatronic Choppers with Rotating Elements: Design Programs....Pages 457-464
A Delay Mathematical Model for HIV Dynamics in HIV-Specific Helper Cells....Pages 465-472
The Application of Parametric Excitation in Resonant MEMS Gyroscopes....Pages 473-492
Influence of Smart Material on the Dynamical Response of Mechanical Oscillator....Pages 493-502
Dynamical Pendulum-Like Nonconservative Systems....Pages 503-525
Back Matter....Pages 527-538

✦ Subjects

Dynamical Systems and Ergodic Theory; Ordinary Differential Equations; Partial Differential Equations