Perspectives in Dynamical Systems III: Control and Stability: DSTA, Łódź, Poland December 2–5, 2019

Preface
Contents
On the Spinning Motion of a Disc under the Influence a Gyrostatic Moment
	1 Introduction
	2 Modeling of the Problem
	3 Construction of Periodic Solutions
	4 Discussion of the Results
	5 Conclusion
	References
Suppression of Impact Oscillations in a Railway Current Collection System with an Additional Oscillatory System
	1 Introduction
	2 Experiments
		2.1 Experimental Apparatus
		2.2 Experimental Results
	3 Theoretical Analysis
		3.1 Analytical Model and Basic Equation
		3.2 Theoretical Results
	4 Conclusions
	References
On Qualitative Analysis of Lattice Dynamical System of Two- and Three-Dimensional Biopixels Array: Bifurcations and Transition to ``Chaos''
	1 Introduction
	2 Lattice Model of Antibody-Antigen Interaction for Two-Dimensional Biopixels Array
		2.1 Stability Investigation
		2.2 Persistence of the Solutions
		2.3 Extinction Research
		2.4 Numerical Simulation of Square 44 Pixels Array
	3 Three-Dimensional Biopixels Array
		3.1 Persistence and Extinction of the Solutions
		3.2 Numerical Study
	4 Conclusions
	References
Response Sensitivity of Damper-connected Adjacent Structural Systems Subjected to Fully Non-stationary Random Excitations
	1 Introduction
	2 Equations of Motion
	3 Dynamic Response Sensitivity for Fully Non-stationary Stochastic Load Processes
		3.1 Closed Form Solutions for the Time-frequency Varying Response Vector Function
		3.2 Closed Form Solutions for the Sensitivity of Time-Frequency Varying Response Vector Function
		3.3 Sensitivity of Frequency Response Vector Function for Stationary Excitations
	4 Numerical Results
	5 Conclusions
	References
Analysis of Switching Strategies for the Optimization of Periodic Chemical Reactions with Controlled Flow-Rate
	1 Introduction
	2 Optimization Problem
	3 Computation of the Switching Controls
	4 Simulation Results
	5 Conclusions
	References
Quaternion Based Free-Floating Space Manipulator Dynamics Modeling Using the Dynamically Equivalent Manipulator Approach
	1 Introduction
	2 Space Manipulator Dynamics Modeling Using the DEM Method Modified for Quaternion Parameterization
		2.1 Quaternion Parameterization Properties for Attitude Dynamics Description
		2.2 The DEM Method for Space Manipulators Modeling
	3 Space Manipulator Reorientation Using the Quaternion Based DEM Method
	4 Conclusions
	References
Slosh Analyzes of a Full Vehicle-Tank Model with SDRE Control with a Hydraulic Damper
	1 Introduction
	2 Mathematical Model
		2.1 Truck Dynamics with Pendulum
		2.2 Pendulum Slosh
		2.3 Tire Dynamics
		2.4 Damper Dynamics
		2.5 Spring Dynamics
		2.6 Road Profile and External Forces
		2.7 Simplified Controllers
		2.8 State-Dependent Riccati Equation Control
	3 Methodology
	4 Results and Conclusions
	5 Conclusions
	References
A Comparison of the Common Types of Nonlinear Energy Sinks
	1 Introduction
	2 System Description and Governing Equations
	3 Results and Discussion
	4 Conclusions
	References
Stability of Three Wheeled Narrow Vehicle
	Nomenclature
	1 Introduction
	2 Narrow Vehicle Stability
	3 Vehicle Dynamics Model
	4 Preliminary Simulations
	5 Controller Design
	6 Simulations and Road Tests
	7 Conclusion
	References
Testing and Analysis of Vibration of a Tension Transmission with a Thermally Sealed Belt
	1 Introduction
	2 Research Methodology
	3 Broadband Analysis of the Point Measures
	4 Results of the Analysis of the Influence of the Change in the Belt Tension on Selected Point Measures
	5 Determining the Vibration Frequency Generated by the Belt Drive
	6 Analysis of the Spectra of the Vibration Signal
	7 Analysis of the Spectra in the Envelope of the Vibration Signal
	8 Conclusions
	References
Modeling and Experimental Tests on Motion Resistance of Double-Flanged Rollers of Rubber Track Systems Due to Sliding Friction Between the Rollers and Guide Lugs of Rubber Tracks
	1 Introduction
	2 Model Assumptions
	3 Experimental Tests and Model Verification
		3.1 Course of the Experiment
		3.2 A Method for Estimation of Model Parameters
		3.3 Verification of the Model and Model Computations
	4 Summary and Conclusions
	References
Structural Dynamic Response of Coupling Between Transmission Line and Tower Under Random Excitation
	1 Introduction
	2 Spectral Element Theory
		2.1 Beam Spectral Element with Axial Load
		2.2 Bar Elementar Spectral Element
		2.3 Spectral Elements in Global Coordinate
	3 Wind Force and Random Spectra
	4 Numerical Analysis
		4.1 Effect of the Wind Random Excitation in the Transmission Line
	5 Conclusion
	References
Experimental Assessment of the Test Station Support Structure Rigidity by the Vibration Diagnostics Method
	1 Testing Station for Dynamic Testing of Toothed and Belt Gear Drives
		1.1 Functional Testing of the Test Station and Verification of the Proposed Methodology for Dynamic Testing
		1.2 Verification Test Results Evaluation
	2 Solving Adverse Resonance Events
	3 Impact Test (Bump Test)
		3.1 Description of the Bump Test Conditions
		3.2 Measurement Procedure
		3.3 Bump Test – Measurements Results
	4 Evaluation of Natural Frequency Measurement Results
	5 Conclusions
	References
Experimental Dynamical Analysis of a Mechatronic Analogy of the Human Circulatory System
	1 Introduction
		1.1 Mechanical Operation of the Heart
		1.2 The Time History of Blood Pressure
	2 Concepts and Implementation of Model Circulatory Systems
	3 Laboratory Station
		3.1 Analogy to Reality
		3.2 Construction and Components
	4 Control System
	5 Measurements and Analysis of Time Characteristics of Dynamic Responses
		5.1 Sensor Characteristics and Signal Processing
		5.2 Measurement Method
		5.3 Results
	6 Conclusions
	References
Robust Design of Inhibitory Neuronal Networks Displaying Rhythmic Activity
	1 Introduction
	2 Model System
	3 Network Configuration and Dynamics
	4 PRCs Determine Network Dynamics
	5 Stable Modes Correspond to Specific PRC Shapes
	6 Parameter Estimation Procedure
	7 Application to ECG Recordings
	8 Conclusion
	References
Nonlinear Dynamics of the Industrial City's Atmospheric Ventilation: New Differential Equations Model and ChaoticVentilation
	1 Introduction
	2 Nonlinear Dynamics of Chaotic Atmospheric Ventilation
	3 Some Numerical Results and Conclusions
	References
Biomechanical Analysis of Different Foot Morphology During Standing on a Dynamic Support Surface
	1 Introduction
	2 Methods
	3 Results and Discussion
	4 Conclusions
	References
Comparison of Various Fractional Order Controllers on a Poorly Damped System
	1 Introduction
	2 Fractional Order Proportional Integral Control
	3 Fractional Order Internal Model Control
	4 The Poorly Damped Case Study
		4.1 Process Description
		4.2 Tuning of the Fractional Order Controllers
		4.3 Experimental Results and Comparisons
	5 Conclusions
	References
AsymptoticAnalysisofSubmergedSpringPendulumMotion inLiquid
	1 Introduction
	2 Dynamical Model Description
	3 The Proposed Method
	4 Stability of the System
	5 Steady-State Solutions
	6 Conclusion
	References
Parametric Identification of Nonlinear Structures Using Particle Swarm Optimization Based on Power Flow Balance Criteria
	1 Introduction
	2 Objective Functions
		2.1 Substructure Acceleration Matching
		2.2 Instantaneous Power Flow Balance
	3 Numerical Modeling
	4 Parameter Identification
	5 Conclusions
	References
Vibration and Buckling of Laminated Plates of Complex Form under in-Plane Uniform and Non-uniform Loading
	1 Introduction
	2 Problem Formulation
	3 Method of Solution
	4 Numerical Results
		4.1 Problem 1
		4.2 Problem 2
		4.3 Problem 3
	5 Conclusions
	References
Dynamical Systems and Stability in Fractional Solid Mechanics
	1 Introduction
	2 Non-locality in Space and Time
		2.1 Eringen's Approach to Non-locality
		2.2 Gradient Materials
		2.3 Visco-Elastic Materials
	3 Elements of Fractional Calculus
		3.1 Two Important Functions
		3.2 Integral Operators and Classical Fractional Derivatives
		3.3 Generalized Fractional Derivatives
	4 Fractional Derivatives in Non-local Mechanics
		4.1 Dynamical Systems Approach
		4.2 Stability and Bifurcation for Conventional Derivatives
		4.3 Non-local Strain
		4.4 Fractional Gradient Material
	5 Conclusions
	References
Stability of Coupled Systems of Stochastic Cohen-Grossberg Neural Networks with Time Delays, Impulsesand Markovian Switching
	1 Introduction
	2 Formulation of the Problem and Preliminary Results
	3 General Decay Stability
	4 Numerical Example (General Decay Stability)
	5 Conclusions
	References
Stability of Steady States with Complex Behavior in Time
	1 Introduction
	2 The Ince Algebraization of Equations in Variations for Nonlinear Normal Modes and Traveling Waves
		2.1 Stability of Nonlinear Normal Modes
		2.2 Stability of Traveling Waves in the Klein-Gordon Equation
	3 Analytical-Numerical Criterion of Stability for Nonlinear Normal Modes and Traveling Waves
		3.1 Stability of Nonlinear Normal Mode with Complex Behavior in Time
		3.2 Stability of Localized Standing Waves in the Peyard-Bishop-Doksua DNA Model
	4 Conclusions
	References
Modelling of Torsional Vibrations in a Motorcycle Steering System
	1 Introduction
	2 Mathematical Model and Its Application in Sensitivity Analysis
	3 The Reduced Model and Its Application in the Synthesis of the Algorithm by a Vibration Damper
	4 Conclusion
	References
Free Vibration Frequencies of Simply Supported Bars with Variable Cross Section
	1 Introduction
	2 Materials and Methods
		2.1 Truncated Cone Beam – Deflection and First Natural Frequency
		2.2 Truncated Cone Beam – The Second Natural Frequency
		2.3 Truncated Cone Beam – Higher Natural Frequencies
		2.4 Truncated Wedge Beam
	3 Validation of Results
	4 Conclusions
	References
On Dynamics of a Rigid Block on Visco-Elastic Foundation
	1 Introduction
	2 Equations of Motion
	3 Stability and Free Oscillations
	4 Response to Excitation
	5 Conclusions
	References
Preface
Contents
On the Spinning Motion of a Disc under the Influence a Gyrostatic Moment
	1 Introduction
	2 Modeling of the Problem
	3 Construction of Periodic Solutions
	4 Discussion of the Results
	5 Conclusion
	References
Suppression of Impact Oscillations in a Railway Current Collection System with an Additional Oscillatory System
	1 Introduction
	2 Experiments
		2.1 Experimental Apparatus
		2.2 Experimental Results
	3 Theoretical Analysis
		3.1 Analytical Model and Basic Equation
		3.2 Theoretical Results
	4 Conclusions
	References
On Qualitative Analysis of Lattice Dynamical System of Two- and Three-Dimensional Biopixels Array: Bifurcations and Transition to ``Chaos''
	1 Introduction
	2 Lattice Model of Antibody-Antigen Interaction for Two-Dimensional Biopixels Array
		2.1 Stability Investigation
		2.2 Persistence of the Solutions
		2.3 Extinction Research
		2.4 Numerical Simulation of Square 44 Pixels Array
	3 Three-Dimensional Biopixels Array
		3.1 Persistence and Extinction of the Solutions
		3.2 Numerical Study
	4 Conclusions
	References
Response Sensitivity of Damper-connected Adjacent Structural Systems Subjected to Fully Non-stationary Random Excitations
	1 Introduction
	2 Equations of Motion
	3 Dynamic Response Sensitivity for Fully Non-stationary Stochastic Load Processes
		3.1 Closed Form Solutions for the Time-frequency Varying Response Vector Function
		3.2 Closed Form Solutions for the Sensitivity of Time-Frequency Varying Response Vector Function
		3.3 Sensitivity of Frequency Response Vector Function for Stationary Excitations
	4 Numerical Results
	5 Conclusions
	References
Analysis of Switching Strategies for the Optimization of Periodic Chemical Reactions with Controlled Flow-Rate
	1 Introduction
	2 Optimization Problem
	3 Computation of the Switching Controls
	4 Simulation Results
	5 Conclusions
	References
Quaternion Based Free-Floating Space Manipulator Dynamics Modeling Using the Dynamically Equivalent Manipulator Approach
	1 Introduction
	2 Space Manipulator Dynamics Modeling Using the DEM Method Modified for Quaternion Parameterization
		2.1 Quaternion Parameterization Properties for Attitude Dynamics Description
		2.2 The DEM Method for Space Manipulators Modeling
	3 Space Manipulator Reorientation Using the Quaternion Based DEM Method
	4 Conclusions
	References
Slosh Analyzes of a Full Vehicle-Tank Model with SDRE Control with a Hydraulic Damper
	1 Introduction
	2 Mathematical Model
		2.1 Truck Dynamics with Pendulum
		2.2 Pendulum Slosh
		2.3 Tire Dynamics
		2.4 Damper Dynamics
		2.5 Spring Dynamics
		2.6 Road Profile and External Forces
		2.7 Simplified Controllers
		2.8 State-Dependent Riccati Equation Control
	3 Methodology
	4 Results and Conclusions
	5 Conclusions
	References
A Comparison of the Common Types of Nonlinear Energy Sinks
	1 Introduction
	2 System Description and Governing Equations
	3 Results and Discussion
	4 Conclusions
	References
Stability of Three Wheeled Narrow Vehicle
	Nomenclature
	1 Introduction
	2 Narrow Vehicle Stability
	3 Vehicle Dynamics Model
	4 Preliminary Simulations
	5 Controller Design
	6 Simulations and Road Tests
	7 Conclusion
	References
Testing and Analysis of Vibration of a Tension Transmission with a Thermally Sealed Belt
	1 Introduction
	2 Research Methodology
	3 Broadband Analysis of the Point Measures
	4 Results of the Analysis of the Influence of the Change in the Belt Tension on Selected Point Measures
	5 Determining the Vibration Frequency Generated by the Belt Drive
	6 Analysis of the Spectra of the Vibration Signal
	7 Analysis of the Spectra in the Envelope of the Vibration Signal
	8 Conclusions
	References
Modeling and Experimental Tests on Motion Resistance of Double-Flanged Rollers of Rubber Track Systems Due to Sliding Friction Between the Rollers and Guide Lugs of Rubber Tracks
	1 Introduction
	2 Model Assumptions
	3 Experimental Tests and Model Verification
		3.1 Course of the Experiment
		3.2 A Method for Estimation of Model Parameters
		3.3 Verification of the Model and Model Computations
	4 Summary and Conclusions
	References
Structural Dynamic Response of Coupling Between Transmission Line and Tower Under Random Excitation
	1 Introduction
	2 Spectral Element Theory
		2.1 Beam Spectral Element with Axial Load
		2.2 Bar Elementar Spectral Element
		2.3 Spectral Elements in Global Coordinate
	3 Wind Force and Random Spectra
	4 Numerical Analysis
		4.1 Effect of the Wind Random Excitation in the Transmission Line
	5 Conclusion
	References
Experimental Assessment of the Test Station Support Structure Rigidity by the Vibration Diagnostics Method
	1 Testing Station for Dynamic Testing of Toothed and Belt Gear Drives
		1.1 Functional Testing of the Test Station and Verification of the Proposed Methodology for Dynamic Testing
		1.2 Verification Test Results Evaluation
	2 Solving Adverse Resonance Events
	3 Impact Test (Bump Test)
		3.1 Description of the Bump Test Conditions
		3.2 Measurement Procedure
		3.3 Bump Test – Measurements Results
	4 Evaluation of Natural Frequency Measurement Results
	5 Conclusions
	References
Experimental Dynamical Analysis of a Mechatronic Analogy of the Human Circulatory System
	1 Introduction
		1.1 Mechanical Operation of the Heart
		1.2 The Time History of Blood Pressure
	2 Concepts and Implementation of Model Circulatory Systems
	3 Laboratory Station
		3.1 Analogy to Reality
		3.2 Construction and Components
	4 Control System
	5 Measurements and Analysis of Time Characteristics of Dynamic Responses
		5.1 Sensor Characteristics and Signal Processing
		5.2 Measurement Method
		5.3 Results
	6 Conclusions
	References
Robust Design of Inhibitory Neuronal Networks Displaying Rhythmic Activity
	1 Introduction
	2 Model System
	3 Network Configuration and Dynamics
	4 PRCs Determine Network Dynamics
	5 Stable Modes Correspond to Specific PRC Shapes
	6 Parameter Estimation Procedure
	7 Application to ECG Recordings
	8 Conclusion
	References
Nonlinear Dynamics of the Industrial City's Atmospheric Ventilation: New Differential Equations Model and ChaoticVentilation
	1 Introduction
	2 Nonlinear Dynamics of Chaotic Atmospheric Ventilation
	3 Some Numerical Results and Conclusions
	References
Biomechanical Analysis of Different Foot Morphology During Standing on a Dynamic Support Surface
	1 Introduction
	2 Methods
	3 Results and Discussion
	4 Conclusions
	References
Comparison of Various Fractional Order Controllers on a Poorly Damped System
	1 Introduction
	2 Fractional Order Proportional Integral Control
	3 Fractional Order Internal Model Control
	4 The Poorly Damped Case Study
		4.1 Process Description
		4.2 Tuning of the Fractional Order Controllers
		4.3 Experimental Results and Comparisons
	5 Conclusions
	References
AsymptoticAnalysisofSubmergedSpringPendulumMotion inLiquid
	1 Introduction
	2 Dynamical Model Description
	3 The Proposed Method
	4 Stability of the System
	5 Steady-State Solutions
	6 Conclusion
	References
Parametric Identification of Nonlinear Structures Using Particle Swarm Optimization Based on Power Flow Balance Criteria
	1 Introduction
	2 Objective Functions
		2.1 Substructure Acceleration Matching
		2.2 Instantaneous Power Flow Balance
	3 Numerical Modeling
	4 Parameter Identification
	5 Conclusions
	References
Vibration and Buckling of Laminated Plates of Complex Form under in-Plane Uniform and Non-uniform Loading
	1 Introduction
	2 Problem Formulation
	3 Method of Solution
	4 Numerical Results
		4.1 Problem 1
		4.2 Problem 2
		4.3 Problem 3
	5 Conclusions
	References
Dynamical Systems and Stability in Fractional Solid Mechanics
	1 Introduction
	2 Non-locality in Space and Time
		2.1 Eringen's Approach to Non-locality
		2.2 Gradient Materials
		2.3 Visco-Elastic Materials
	3 Elements of Fractional Calculus
		3.1 Two Important Functions
		3.2 Integral Operators and Classical Fractional Derivatives
		3.3 Generalized Fractional Derivatives
	4 Fractional Derivatives in Non-local Mechanics
		4.1 Dynamical Systems Approach
		4.2 Stability and Bifurcation for Conventional Derivatives
		4.3 Non-local Strain
		4.4 Fractional Gradient Material
	5 Conclusions
	References
Stability of Coupled Systems of Stochastic Cohen-Grossberg Neural Networks with Time Delays, Impulsesand Markovian Switching
	1 Introduction
	2 Formulation of the Problem and Preliminary Results
	3 General Decay Stability
	4 Numerical Example (General Decay Stability)
	5 Conclusions
	References
Stability of Steady States with Complex Behavior in Time
	1 Introduction
	2 The Ince Algebraization of Equations in Variations for Nonlinear Normal Modes and Traveling Waves
		2.1 Stability of Nonlinear Normal Modes
		2.2 Stability of Traveling Waves in the Klein-Gordon Equation
	3 Analytical-Numerical Criterion of Stability for Nonlinear Normal Modes and Traveling Waves
		3.1 Stability of Nonlinear Normal Mode with Complex Behavior in Time
		3.2 Stability of Localized Standing Waves in the Peyard-Bishop-Doksua DNA Model
	4 Conclusions
	References
Modelling of Torsional Vibrations in a Motorcycle Steering System
	1 Introduction
	2 Mathematical Model and Its Application in Sensitivity Analysis
	3 The Reduced Model and Its Application in the Synthesis of the Algorithm by a Vibration Damper
	4 Conclusion
	References
Free Vibration Frequencies of Simply Supported Bars with Variable Cross Section
	1 Introduction
	2 Materials and Methods
		2.1 Truncated Cone Beam – Deflection and First Natural Frequency
		2.2 Truncated Cone Beam – The Second Natural Frequency
		2.3 Truncated Cone Beam – Higher Natural Frequencies
		2.4 Truncated Wedge Beam
	3 Validation of Results
	4 Conclusions
	References
On Dynamics of a Rigid Block on Visco-Elastic Foundation
	1 Introduction
	2 Equations of Motion
	3 Stability and Free Oscillations
	4 Response to Excitation
	5 Conclusions
	References