Melnikov s Method Applied to a MultiDOF Ship Model


 Valentine Thompson
 11 months ago
 Views:
Transcription
1 Proceedings of the th International Ship Staility Workshop Melnikov s Method Applied to a MultiDOF Ship Model Wan Wu, Leigh S. McCue, Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksurg, VA, USA ABSTRACT In this paper, a coupled rollswayheave model derived y Chen et al (999) is studied. In order to address the small damping constraint, the etended Melnikov s method for slowly varying system is used y assuming the damping term is large. Using the etended Melnikov s method, the critical wave amplitudes are calculated. A phase space transport method has een applied. The ratios of erosion safe asin areas have een calculated ased on the Melnikov s method and were compared with the results from numerical simulations. KEYWORDS MultiDOF Melnikov; Slowlyvarying; Ship; Staility. INTRODUCTION Si degree of freedom (DOF) vessel motion prolems ehiit numerous compleities, particularly when studied analytically. Most previous work on multidof vessel motions either reduced the prolems to lower (one or two) DOF prolems or used numerical simulations. In the work of ship motion analysis, compared to DOF prolems, relatively little work have een done using analytical methods for multidof ship motion prolems. In this paper, the etended Melnikov s method (Salam, 987) is applied to a rollswayheave coupled ship model derived y Chen et al. (999). By changing the coordinates and applying the singular perturation technique, Chen showed the model can e simplified to a slowly varying system with three variales, which contain roll displacement and roll velocity as the fast varying variales and a slowly varying variale. This kind of system can e manageale using the Melnikov's method discussed y Wiggins and Holmes (987, 988). But similar to the planar Melnikov s method, the constraint of this method is the small perturation assumption. In order to address this constraint, the etended Melnikov s method for slowly varying systems is applied. The etended Melnikov s method developed in the literature y Salam (987) has een recently applied to ship motions prolems such as capsize (Wu and McCue, 007, 008, Wu, 009) and surfriding (Wu et al. 00 and Wu 009). The purpose of this work is to show the possiility of applying the etended Melnikov s method to multidof ship models. MATHEMATICAL MODEL The equations of motion for the coupled rollswayheave model in the earthfied coordinate system can e epressed in Eq.() my mz '' c '' c Y Z () '' I44 K in which, m is the mass of the ship, yc, zcand are sway displacement, heave displacement and
2 Proceedings of the th International Ship Staility Workshop roll displacement, respectively. YZand, K are generalized forces. The prime denotes the derivative with respect to time t. Chen et al. (999) transformed the model to a wavefied coordinate, in which the ship is viewed as a particle riding on the surface of the wave. The sway motion is now parallel to the local wave surface and the heave motion is perpendicular to the local wave surface. The equations of motion now can e epressed as in Eq.().. f, y g z z a y g z (,, y, z, z, ) (,, y, z, z, ) f ( z, z ) g (,, y, z, z, ) c () where, ', z z / h 0 in which h is the draft of the ship. y is a transformed coordinate which contains sway velocity and other variales. z 0 is small compared to h. (.) is the derivative relative to, where. r is the natural frequency of roll. In Eq.(), the heave motion is considered to ehiit fast dynamics compared to roll and y. Chen et al. (999) used the singular perturation theory to this system to show that z and z can e solved from the steady state equation and can e sustituted into the slow dynamics. The dynamics of the whole system Eq.() can e represented y the reduced system Eq.(3). f, y ga y g (,, y,, ) (,, y,, ) r t (3) Chen et al. found that for the reduced system in Eq.(3), roll motions are the fast varying variales while y is the slowly varying variale. Systems like this are called slowly varying systems. When 0, this is simply the planar roll motion with zero forcing and zero damping. When is a small positive numer, the y motion (which includes sway and other motions) ecomes relevant. Because the sway motion is stale, the system will trend towards the invariant manifold of roll dynamics. THEORETICAL BACKGROUND Melnikov s Method for Slowly Varying Systems Melnikov s method is one of few analytical methods that can e used to predict the occurrence of chaotic motions in nonlinear dynamic systems. Melnikov s method has een applied to a numer of ship dynamics prolems, such as capsize in eam seas (Falzarano, 990) and surfriding in following seas (Spyrou, 006). Most of these are treated as single DOF prolems. Melnikov s method for multidof prolems has een introduced in several references including the works of Wiggins and Holmes (987, 988), who derived the Melnikov s function for slowly varying system in Eq.(3). When 0, the unpertured system in Eq.(3) has a planar Hamiltonian, which contains a homoclinic (or heteroclinic) orit. The Melnikov s function for this system is M ( t ) ( H g)( q ( t), t t ) dt H ( ( z )) g ( q ( t), t t ) dt z (4) g [0, g, g ]. H is the Hamiltonian for the a unpertured system. q0( t) (, ) is the coordinates of the homoclinic orit for the unpertured system. And is the dot product. Melnikov s Method for Slowly Varying Systems with Large Damping When the damping term is assumed to e large, it is grouped in the unpertured system.
3 Proceedings of the th International Ship Staility Workshop 3 Therefore, the unpertured system is no longer Hamiltonian due to the presence of in f. f,, y (5) The homoclinic orit, which is essential in the formation of Melnikov s function, disappears as well. Since the homoclinic orit does not arise naturally, it has to e created artificially. Eq.(3) is then written in the form of Eq.(6)., a f, y g (,, y,, ) y g (,, y,, ) The Melnikov s function for this system is t M ( t0) ga ( q0, t t0) ep a( s) dsdt 0 t t f g( s t0) ds ep a( s) dsdt y 0 0 (7) in which, q0( t) (, ) is the coordinates of the new homoclinic orit of Eq.(5). as () is the trace of the Jacoian matri of Eq.(5). If the unpertured system in Eq.(5) is Hamiltonian, as ( ) 0. Eq.(7) can e reduced to the same form as Eq.(4). Phase Space Transport (6) As mentioned earlier, the unpertured system of Eq.(3) has a planar homoclinic orit, which contains a stale manifold and a unstale manifold. Wiggins and Holmes (987) pointed out that when is small enough, the pertured system is close to the local unpertured manifolds in a small neighorhood. Outside of this region, the pertured manifold is close to the unpertured manifold in finite time. The theory of phase space transport for planar systems is applied here to predict the safe region erosion in finite time. For the unpertured system, the inside of the homoclinic orit is the safe region. When the homoclinic orit is pertured, the manifolds will intersect resulting in loes. And some initial conditions initially inside the safe region may e outside the safe region for the pertured system (pseudoseparatri) after some time. This phenomenon corresponds to a special loe called turnstile loe (Wiggins, 99). The area of this loe is given in Eq.(8) (Wiggins, 99). T ( L0 ) M ( t0, 0) dt0 ( ) 0 O (8) in which M ( t0, 0) is the positive part of the Melnikov s function, L0 represents the loe, t 0 is the parameter in the homoclinic orit q0( t 0) denoting different time in the Poincaré map. 0 is the phase difference with the eternal forcing. T is the period of the eternal forcing. Phase space transport refers to the initial conditions transporting outside the safe region after several periods of eternal forcing. The amount of the transported phase space can e used to show the rate of safe area erosion. Chen and Shaw (997) derived the estimate of erosion ratio as shown in Eq.(9). 3 ( L ) 3 T 0 e M ( t0, 0) dt0 ( ) As A O (9) s 0 where As is the area of the unpertured safe region, e is the ratio erosion area divided y the original safe region, and ecause is a small positive numer, O( ) term can e ignored. In this work, Eq.(9) is used to show the erosion of safe asin for the capsize prolem. APPLICATIONS The data from twice capsized fishing oat PattiB are used here for numerical investigation. Chen et al. (999) proposed this model shown in Eq.(0).
4 Proceedings of the th International Ship Staility Workshop 4 f k k k 3 3 ga 4 cos 4 cos 4 y 44 (0) f ( )cos sin 44q 4 g cos y sin 4 f is the restoring moment in the roll motion, which includes the effect of ias. is the nonlinear roll 44 44q damping. is the nondimensional wave frequency. Other coefficients come from hydrodynamic forces, wind forces and wave forces. Melnikov s Function The etended Melnikov s method is applied here y assuming the roll damping terms are large. For the slowly varying system, it is essential to have a homoclinic orit in order to calculate the Melnikov s function (Wiggins, 987). If the linear damping term is assumed to e large, the center in the unpertured system will ecome a sink, which makes it impossile to have a homoclinic orit. In this work, the following damping term is assumed for roll B( ) c () 3 44 where and c are coefficients. Although it is physically unrealistic to have quadratic damping term in roll, it is used here to show the possiility of using the etended Melnikov s method to multidof prolems. In order to form the homoclinic orit for the unpertured system, the quadratic damping term is assumed to e large. The unpertured system is now 3 k k k3 where y cos 4 y () is the sway variale otained from averaging. is the coordinate of the saddle point, which can e calculated y setting 0 and 0. Eq() contains a homoclinic orit starting from a saddle connecting to itself, as shown in Figure. The solid line in the figure is the homoclinic orit for Eq.(), while the dashed line is the homoclinic orit for the unpertured system in Eq.(3) without the quadratic damping term. These two homoclinic orits start from the same saddle point, and are close to each other. The Melnikov s function can e calculated using Eq.(7). Numerical integration can e carried out without difficulty. Fig. : Homoclinic orit for the unpertured system Numerical Results Chen et al. (999) have found the hydrodynamic and hydrostatic coefficients in Eq.(0) for PattiB at wave frequency w 0.6 rad / s. In this work, the simulation is carried out for the case when the center of gravity has slight ias yg The wind forces are assumed to e zero. The quadratic damping coefficient is set to 0.. Melnikov s functions for oth the standard and etended methods can e calculated using Eqs (4) and (7), respectively. When Mt ( 0) 0, this corresponds to the critical wave amplitude a eyond which the chaotic motion and capsize may occur. The critical wave amplitude a has een calculated for oth Melnikov s methods listed in Tale. As shown in the tale, the etended Melnikov s method predicted the critical wave amplitude slightly higher than the standard Melnikov s method for the case studied here.
5 Proceedings of the th International Ship Staility Workshop 5 Tale : Critical wave amplitude for two Melnikov s methods Method a (m) Standard Melnikov 0.79 Etended Melnikov 0.86 Numerical simulations are carried out to otain safe asins of the 3DOF system with the damping terms shown Eq.() and with original damping term. The safe asins are calculated y integrating a grid of 0000 points in roll plane with yz, and z initial conditions equal to. Every initial condition is integrated until a roll angle is greater than the angle of vanishing staility ( rad ), thus capsize occurs or through 0 cycles of eternal forcing, thus deemed safe. Capsize was checked every dt 0.0s. Figure (a) is the system with quadratic damping and Figure () is the original system. In oth cases, the wave amplitude a 0. The ratio of erosion area has een calculated using Eq.(9) for oth Melnikov s function defined y Eqs.(4) and (7). Numerical simulations are also carried out for the 3DOF system to compare the results. Chen and Shaw (997) pointed out that in order to implement phase space transport methods, the dynamics should e studied on the invariant manifold where loes can e defined. Therefore, similar to their work, the initial conditions for the numerical simulations have een chosen as 70 points on the invariant manifold of roll dynamics, which are otained y numerically calculated the safe points for the unpertured system (asically the homoclinic orit). Two points are picked on every direction of yzand, z. A grid of (70 ) points are used as the initial conditions. For the numerical data, the ratio of erosion area is calculated using the points capsized in 0 cycles of eternal forcing divided y the total numer of points. (a) Fig. 3: The ratio of erosion area for different methods. () Fig. : Safe asins for different models (The white areas are the safe asins, and the dark areas are capsize area.) (a). Safe asin for system with quadratic damping included. (). Safe asin for original system. Figure 3 shows the ratio of erosion areas for different methods. The results from oth Melnikov s methods are conservative compared to the numerical simulation results. And the results from the etended Melnikov s method are more accurate than those from the standard Melnikov s method, especially for larger wave amplitudes. Compared to the time consuming 3DOF numerical simulations, the method of phase space transport ased on the etended Melnikov s method provides a fast way to estimate ratio of erosion with
6 Proceedings of the th International Ship Staility Workshop 6 reasonale accuracy. CONCLUSIONS REMARKS In this paper, the etended Melnikov s method has een used to a rollswayheave coupled model which can e reduced to a slowly varying system. In order to otain the homoclinic orit, a quadratic damping term is treated as large. Although it is physically unrealistic to have a quadratic term in roll damping, it is used here just to demonstrate the feasiility of the method. Coupled with the method of phase space transport, this results in a fast and effective way to estimate the ratio of erosion with apparently conservative accuracy. This work is the first step of applying the etended Melnikov s method to a special form of multidof dynamical systems. It provides the possiility of applying the method to other multidof prolems in ship dynamics. ACKNOWLEDMENTS This work has een supported y Dr. Patrick Purtell under ONR Grant N and Dr. Eduardo Misawa under NSF Grant CMMI References Chen, S.L.; Shaw, S.W. and Troesch, A.W.: A Systematic Approach to Modelling Nonlinear MultiDOF Ship Motions in Regular Seas. In: Journal of Ship Research. 43 (999) Chen, S.L. and Shaw,S.W.: Phase Space Transport in a Class of MultiDegreeofFreedom Systems. In: Proceedings of 997 ASME Design Engineering Technical Conferences (DETC97) Falzarano, J.M.: Predicting Complicated Dynamics Leading to Vessel Capsizing. PhD dissertation, University of Michigan, Ann Aror, 990. Salam, F.M.: The Melnikov Technique for Highly Dissipative Systems.In: SIAM Jounal on Applied Mathematics.47 (987) Spyrou, K.J.: Asymmetric Surging of Ships in Following Seas and its Repercussions for Safety. In: Nonlinear Dynamics. 43 (006) Wiggins, S.; Holms, P.: Homoclinic Orits in Slowly Varying Oscillators. In: SIAM Journal of Mathematical Analysis. 8(3) (987) Wiggins, S.: Chaotic Transport in Dynamical Systems. (99) SpringerVerlag, New York. Wiggins, S.; Holms, P.: Errata: Homoclinic Orits in Slowly Varying Oscillators. In: SIAM Journal of Mathematical Analysis. 5(9) (988) Wu, W. and McCue, L.S.: Melnikov's Method for Ship Motions Without the Constraint of Small Linear Damping. In: Proceedings of IUTAM Symposium on FluidStructure Interaction in Ocean Engineering, (007), Hamurg, Germany. Wu, W. and McCue, L.S.: Application of the etended Melnikov's Method for Singledegreeoffreedom Vessel Roll Motion. In: Ocean Engineering. 35 (008) Wu, W., Spyrou, K.J. and McCue, L.S.: Improved Prediction of the Threshold of Surfriding of a Ship in Steep Following Seas. In: Ocean Engineering. (00) doi:0.06/j.oceaneng Wu, W.: Analytical and numerical methods applied to nonlinear vessel dynamics and code verification for chaotic systems. PhD dissertation, Virginia Tech, Blacksurg, 009.
EnergyRate Method and Stability Chart of Parametric Vibrating Systems
Reza N. Jazar Reza.Jazar@manhattan.edu Department of Mechanical Engineering Manhattan College New York, NY, A M. Mahinfalah Mahinfalah@msoe.edu Department of Mechanical Engineering Milwaukee chool of Engineering
More informationPROOF COPY [EM/2004/023906] QEM
Coupled SurgeHeave Motions of a Moored System. II: Stochastic Analysis and Simulations Solomon C. S. Yim, M.ASCE 1 ; and Huan Lin, A.M.ASCE Abstract: Analyses and simulations of the coupled surgeandheave
More informationDYNAMIC CHARACTERISTICS OF OFFSHORE TENSION LEG PLATFORMS UNDER HYDRODYNAMIC FORCES
International Journal of Civil Engineering (IJCE) ISSN(P): 22789987; ISSN(E): 22789995 Vol. 3, Issue 1, Jan 214, 716 IASET DYNAMIC CHARACTERISTICS OF OFFSHORE TENSION LEG PLATFORMS UNDER HYDRODYNAMIC
More informationExperimental Analysis of Roll Damping in Small Fishing Vessels for Large Amplitude Roll Forecasting
International Ship Stability Workshop 213 1 Experimental Analysis of Roll Damping in Small Fishing Vessels for Large Amplitude Roll Forecasting Marcos Míguez González, Vicente Díaz Casás, Fernando López
More informationInfluence of moving breathers on vacancies migration
Influence of moving reathers on vacancies migration J Cuevas a,1, C Katerji a, JFR Archilla a, JC Eileck, FM Russell a Grupo de Física No Lineal. Departamento de Física Aplicada I. ETSI Informática. Universidad
More informationResponse of square tension leg platforms to hydrodynamic forces
Ocean Systems Engineering, Vol., No. (01) 000000 1 Response of square tension leg platforms to hydrodynamic forces A.M. AbouRayan 1, Ayman A. Seleemah* and Amr R. Elgamal 1 1 Civil Engineering Tec.
More informationReview Article Modeling of Ship Roll Dynamics and Its Coupling with Heave and Pitch
Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 21, Article ID 934714, 32 pages doi:1.1155/21/934714 Review Article Modeling of Ship Roll Dynamics and Its Coupling with Heave
More informationEffect of Tethers Tension Force in the Behavior of a Tension Leg Platform Subjected to Hydrodynamic Force Amr R. ElGamal, Ashraf Essa, Ayman Ismail
Vol:7, No:1, 13 Effect of Tethers Tension Force in the Behavior of a Tension Leg Platform Subjected to Hydrodynamic Force Amr R. ElGamal, Ashraf Essa, Ayman Ismail International Science Index, Bioengineering
More informationab is shifted horizontally by h units. ab is shifted vertically by k units.
Algera II Notes Unit Eight: Eponential and Logarithmic Functions Sllaus Ojective: 8. The student will graph logarithmic and eponential functions including ase e. Eponential Function: a, 0, Graph of an
More informationCALCULATION OF NONLINEAR VIBRATIONS OF PIECEWISELINEAR SYSTEMS USING THE SHOOTING METHOD
Vietnam Journal of Mechanics, VAST, Vol. 34, No. 3 (2012), pp. 157 167 CALCULATION OF NONLINEAR VIBRATIONS OF PIECEWISELINEAR SYSTEMS USING THE SHOOTING METHOD Nguyen Van Khang, Hoang Manh Cuong, Nguyen
More informationModelling and Gain Scheduled Control of a Tailless Fighter
Modelling and Gain Scheduled Control of a Tailless Fighter Nico G. M. Rademakers a, Rini kmeliawati, Roin Hill, Cees Bil c, Henk Nijmeijer a a Department of Mechanical Engineering Mathematics and Statistics
More informationCoupled HeavePitch Motions and Froude Krylov Excitation Forces
Coupled HeavePitch Motions and Froude Krylov Excitation Forces 13.42 Lecture Notes; Spring 2004; c A.H. Techet 1. Coupled Equation of Motion in Heave and Pitch Once we have set up the simple equation
More informationThe basic principle to be used in mechanical systems to derive a mathematical model is Newton s law,
Chapter. DYNAMIC MODELING Understanding the nature of the process to be controlled is a central issue for a control engineer. Thus the engineer must construct a model of the process with whatever information
More informationModeling of Water Flows around a Circular Cylinder with the SPH Method
Archives of HydroEngineering and Environmental Mechanics Vol. 61 (2014), No. 1 2, pp. 39 60 DOI: 10.1515/heem20150003 IBW PAN, ISSN 1231 3726 Modeling of Water Flows around a Circular Cylinder with
More informationObject Impact on the Free Surface and Added Mass Effect Laboratory Fall 2005 Prof. A. Techet
Object Impact on the Free Surface and Added Mass Effect.016 Laboratory Fall 005 Prof. A. Techet Introduction to Free Surface Impact Free surface impact of objects has applications to ocean engineering
More informationThe Non Linear Behavior of the Microplane Model in COMSOL
The on Linear Behavior of the Microplane Model in COMSOL A. Frigerio 1 1 RSE S.p.A. *via Ruattino, 54 20134 Milan (Italy), antonella.frigerio@rsewe.it Astract: umerical models ased on the Finite Element
More informationGround and Excited States of Bipolarons in Two and Three Dimensions
Commun. Theor. Phys. Beijing, China 8 007 pp. 169 17 c International Academic Pulishers Vol. 8, No. 1, July 15, 007 Ground and Excited States of Bipolarons in Two and Three Dimensions RUAN YongHong and
More informationarxiv: v1 [cs.fl] 24 Nov 2017
(Biased) Majority Rule Cellular Automata Bernd Gärtner and Ahad N. Zehmakan Department of Computer Science, ETH Zurich arxiv:1711.1090v1 [cs.fl] 4 Nov 017 Astract Consider a graph G = (V, E) and a random
More informationApplication of Viscous Vortex Domains Method for Solving FlowStructure Problems
Application of Viscous Vortex Domains Method for Solving FlowStructure Problems Yaroslav Dynnikov 1, Galina Dynnikova 1 1 Institute of Mechanics of Lomonosov Moscow State University, Michurinskiy pr.
More informationProceedings of the ASME st International Conference on Ocean, Offshore and Arctic Engineering OMAE2012 July 16, 2012, Rio de Janeiro, Brazil
Proceedings of the ASME 3st International Conference on Ocean, Offshore and Arctic Engineering OMAE July 6,, Rio de Janeiro, Brazil OMAE84 Stability Analysis Hinged Vertical Flat Plate Rotation in a
More informationTarek S. Ellaithy 1, Alexander Prexl 1, Nicolas Daynac 2. (1) DEA Egypt Branches, (2) Eliis SAS, France. Introduction
Methodology and results of Nile Delta MessinianPliocene Holistic 3D seismic interpretation A case study from the Disouq area, Onshore Nile Delta, Egypt Tarek S. Ellaithy 1, Alexander Prexl 1, Nicolas
More informationPrediction of SemiSubmersible s Motion Response by Using Diffraction Potential Theory and Heave Viscous Damping Correction
Jurnal Teknologi Full paper Prediction of SemiSubmersible s Motion Response by Using Diffraction Potential Theory and Heave Viscous Damping Correction C. L. Siow a, Jaswar Koto a,b*, Hassan Abby c, N.
More informationA MULTIBODY ALGORITHM FOR WAVE ENERGY CONVERTERS EMPLOYING NONLINEAR JOINT REPRESENTATION
Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering OMAE2014 June 813, 2014, San Francisco, California, USA OMAE201423864 A MULTIBODY ALGORITHM FOR WAVE
More informationSafetrans Safe design and operation of marine transports
Safetrans Safe design and operation of marine transports CONTENTS General Voyage Motion Climate Monte Carlo Simulations Calculation of Ship Motions Weather Databases User Group References 2 SAFETRANS Safetrans
More informationLab M5: Hooke s Law and the Simple Harmonic Oscillator
M5.1 Lab M5: Hooke s Law and the Simple Harmonic Oscillator Most springs obey Hooke s Law, which states that the force exerted by the spring is proportional to the extension or compression of the spring
More informationSurface Fitting. Moving Least Squares. Preliminaries (Algebra & Calculus) Preliminaries (Algebra & Calculus) Preliminaries (Algebra & Calculus) ( )(
Preliminaries Algebra Calculus Surface Fitting Moving Least Squares Gradients If F is a function assigning a real value to a D point the gradient of F is the vector: Preliminaries Algebra Calculus Extrema
More informationRobot Position from Wheel Odometry
Root Position from Wheel Odometry Christopher Marshall 26 Fe 2008 Astract This document develops equations of motion for root position as a function of the distance traveled y each wheel as a function
More informationOn NonIdeal Simple Portal Frame Structural Model: Experimental Results Under A NonIdeal Excitation
On NonIdeal Simple Portal Frame Structural Model: Experimental Results Under A NonIdeal Excitation J M Balthazar 1,a, RMLRF Brasil,b and FJ Garzeri 3, c 1 State University of São Paulo at Rio Claro,
More informationNonchaotic random behaviour in the second order autonomous system
Vol 16 No 8, August 2007 c 2007 Chin. Phys. Soc. 10091963/2007/1608)/228506 Chinese Physics and IOP Publishing Ltd Nonchaotic random behaviour in the second order autonomous system Xu Yun ) a), Zhang
More information8.1 Bifurcations of Equilibria
1 81 Bifurcations of Equilibria Bifurcation theory studies qualitative changes in solutions as a parameter varies In general one could study the bifurcation theory of ODEs PDEs integrodifferential equations
More informationTHE EFFECT OF MEMORY IN PASSIVE NONLINEAR OBSERVER DESIGN FOR A DP SYSTEM
DYNAMIC POSIIONING CONFERENCE October 113, 1 DESIGN SESSION HE EFFEC OF MEMORY IN PASSIVE NONLINEAR OBSERVER DESIGN FOR A DP SYSEM By A. Hajivand & S. H. Mousavizadegan (AU, ehran, Iran) ABSRAC he behavior
More informationGlobal Analysis of Dynamical Systems Festschrift dedicated to Floris Takens for his 60th birthday
Global Analysis of Dynamical Systems Festschrift dedicated to Floris Takens for his 6th birthday Edited by Henk W. Broer, Bernd Krauskopf and Gert Vegter January 6, 3 Chapter Global Bifurcations of Periodic
More informationThe Breakdown of KAM Trajectories
The Breakdown of KAM Trajectories D. BENSIMONO ~t L. P. KADANOFF~ OAT& T Bell Laboraiories Murray Hill,New Jersey 07974 bthe James Franck Insrirure Chicago, Illinois 60637 INTRODUCl'ION Hamiltonian systems
More informationTorus Doubling Cascade in Problems with Symmetries
Proceedings of Institute of Mathematics of NAS of Ukraine 4, Vol., Part 3, 11 17 Torus Doubling Cascade in Problems with Symmetries Faridon AMDJADI School of Computing and Mathematical Sciences, Glasgow
More informationYanlin Shao 1 Odd M. Faltinsen 2
Yanlin Shao 1 Odd M. Faltinsen 1 Ship Hydrodynamics & Stability, Det Norsk Veritas, Norway Centre for Ships and Ocean Structures (CeSOS), NTNU, Norway 1 The stateoftheart potential flow analysis: Boundary
More informationMeasuring the Universal Gravitational Constant, G
Measuring the Universal Gravitational Constant, G Introduction: The universal law of gravitation states that everything in the universe is attracted to everything else. It seems reasonable that everything
More informationConceptual Discussion on Free Vibration Analysis of Tension Leg Platforms
Development and Applications of Oceanic Engineering (DAOE) Volume Issue, ay 3 Conceptual Discussion on Free Vibration Analysis of Tension Leg Platforms ohammad Reza Tabeshpour Center of Ecellence in Hydrodynamics
More informationCOMPUTATION OF ADDED MASS AND DAMPING COEFFICIENTS DUE TO A HEAVING CYLINDER
J. Appl. Math. & Computing Vol. 3(007), No. 1 , pp. 17140 Website: http://jamc.net COMPUTATION OF ADDED MASS AND DAMPING COEFFICIENTS DUE TO A HEAVING CYLINDER DAMBARU D BHATTA Abstract. We present the
More informationBuoyancy and Stability of Immersed and Floating Bodies
Buoyancy and Stability of Immersed and Floating Bodies 9. 12. 2016 Hyunse Yoon, Ph.D. Associate Research Scientist IIHRHydroscience & Engineering Review: Pressure Force on a Plane Surface The resultant
More informationA Comparative Study of f B within QCD Sum Rules with Two Typical Correlators up to NexttoLeading Order
Commun. Theor. Phys. 55 (2011) 635 639 Vol. 55, No. 4, April 15, 2011 A Comparative Study of f B within QCD Sum Rules with Two Typical Correlators up to NexttoLeading Order WU XingGang ( ), YU Yao (ß
More informationInteraction between heat dipole and circular interfacial crack
Appl. Math. Mech. Engl. Ed. 30(10), 1221 1232 (2009) DOI: 10.1007/s104830091002x c Shanghai University and SpringerVerlag 2009 Applied Mathematics and Mechanics (English Edition) Interaction etween
More informationPOLITECNICO DI TORINO. Dipartimento di Ingegneria Elettrica. Dottorato di Ricerca in Ingegneria Elettrica XX Ciclo (DOTTORATO EUROPEO) DOCTORAL THESIS
POLTECNCO D TORNO Dipartimento di ngegneria Elettrica Dottorato di Ricerca in ngegneria Elettrica XX Ciclo DOTTORATO EUROPEO DOCTORAL THESS CURRENT DECOMPOSTONBASED LOSS PARTTONNG AND LOSS ALLOCATON N
More informationstatus solidi Stability of elastic material with negative stiffness and negative Poisson s ratio
physica pss www.pss.com status solidi asic solid state physics Editor s Choice Staility of elastic material with negative stiffness and negative Poisson s ratio Shang Xinchun 1, and Roderic S. Lakes,
More informationGeneralized ReedSolomon Codes
Chapter 5 Generalized ReedSolomon Codes In 1960, I.S. Reed and G. Solomon introduced a family of errorcorrecting codes that are douly lessed. The codes and their generalizations are useful in practice,
More informationUpperbound limit analysis based on the natural element method
Acta Mechanica Sinica (2012) 28(5):1398 1415 DOI 10.1007/s1040901201499 RESEARCH PAPER Upperound limit analysis ased on the natural element method ShuTao Zhou YingHua Liu Received: 14 Novemer 2011
More informationStability Analysis of UzawaLucas Endogenous Growth Model
Abstract: Stability Analysis of UzawaLucas Endogenous Growth Model William A. Barnett* University of Kansas, Lawrence and Center for Financial Stability, NY City and Taniya Ghosh Indira Gandhi Institute
More informationNonlinear Stability of a Delayed Feedback Controlled Container Crane
Nonlinear Stability of a Delayed Feedback Controlled Container Crane THOMAS ERNEUX Université Libre de Bruxelles Optique Nonlinéaire Théorique Campus Plaine, C.P. 231 1050 Bruxelles, Belgium (terneux@ulb.ac.be)
More informationVered RomKedar a) The Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel
CHAOS VOLUME 9, NUMBER 3 SEPTEMBER 1999 REGULAR ARTICLES Islands of accelerator modes and homoclinic tangles Vered RomKedar a) The Department of Applied Mathematics and Computer Science, The Weizmann
More informationChapter 1 Dynamical Models of Extreme Rolling of Vessels in Head Waves
Chapter 1 Dynamical Models of Extreme Rolling of Vessels in Head Waves Claude Archer 1 Ed F.G. van Daalen 2 Sören Dobberschütz 3 MarieFrance Godeau 1 Johan Grasman 4 Michiel Gunsing 2 Michael Muskulus
More informationPiecewise Smooth Solutions to the BurgersHilbert Equation
Piecewise Smooth Solutions to the BurgersHilbert Equation Alberto Bressan and Tianyou Zhang Department of Mathematics, Penn State University, University Park, Pa 68, USA emails: bressan@mathpsuedu, zhang
More informationDESIGN SUPPORT FOR MOTION CONTROL SYSTEMS Application to the Philips Fast Component Mounter
DESIGN SUPPORT FOR MOTION CONTROL SYSTEMS Application to the Philips Fast Component Mounter Hendri J. Coelingh, Theo J.A. de Vries and Jo van Amerongen Dreel Institute for Systems Engineering, ELRT, University
More informationOSCILLATORS WITH DELAY COUPLING
Proceedings of DETC'99 1999 ASME Design Engineering Technical Conferences September 115, 1999, Las Vegas, Nevada, USA D E T C 9 9 / V IB 8 3 1 8 BIFURCATIONS IN THE DYNAMICS OF TWO COUPLED VAN DER POL
More informationParametric Study of Magnetic Pendulum
Parametric Study of Magnetic Pendulum Author: Peter DelCioppo Persistent link: http://hdl.handle.net/2345/564 This work is posted on escholarship@bc, Boston College University Libraries. Boston College
More informationThe linear equations can be classificed into the following cases, from easier to more difficult: 1. Linear: u y. u x
Week 02 : Method of C haracteristics From now on we will stu one by one classical techniques of obtaining solution formulas for PDEs. The first one is the method of characteristics, which is particularly
More informationDYNAMICS OF AN UMBILICAL CABLE FOR UNDERGROUND BOREWELL APPLICATIONS
DYNAMICS OF AN UMBILICAL CABLE FOR UNDERGROUND BOREWELL APPLICATIONS 1 KANNAN SANKAR & 2 JAYA KUMAR.V.K Engineering and Industrial Services, TATA Consultancy Services, Chennai, India Email: sankar.kannan@tcs.com,
More informationKink, singular soliton and periodic solutions to class of nonlinear equations
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1939466 Vol. 10 Issue 1 (June 015 pp. 1  Applications and Applied Mathematics: An International Journal (AAM Kink singular soliton and periodic
More informationDynamics of vibrating systems with tuned liquid column dampers and limited power supply
Journal of Sound and Vibration 289 (2006) 987 998 JOURNAL OF SOUND AND VIBRATION www.elsevier.com/locate/jsvi Dynamics of vibrating systems with tuned liquid column dampers and limited power supply S.L.T.
More informationarxiv:physics/ v1 [physics.plasmph] 7 Apr 2006
Europhysics Letters PREPRINT arxiv:physics/6455v [physics.plasmph] 7 Apr 26 Olique electromagnetic instailities for an ultra relativistic electron eam passing through a plasma A. Bret ETSI Industriales,
More informationStable Manifolds of Saddle Equilibria for Pendulum Dynamics on S 2 and SO(3)
2011 50th IEEE Conference on Decision and Control and European Control Conference (CDCECC) Orlando, FL, USA, December 1215, 2011 Stable Manifolds of Saddle Equilibria for Pendulum Dynamics on S 2 and
More informationThe Performance Comparison among Common Struts of Heavyduty Gas Turbine
5th International Conference on Information Engineering for Mechanics and Materials (ICIMM 2015) The Performance Comparison among Common Struts of Heavyduty Gas Turbine Jian Li 1, a, Jian Zhou 1, b, Guohui
More informationSTATIONARY AND TRANSIENT VIBRATIONS OF DAVI VIBROINSULATION SYSTEM.
STTIONRY ND TRNSIENT VIBRTIONS OF DVI VIBROINSULTION SYSTEM. Jerzy Michalczyk, ul.zagorze c, 3 398 Cracow, Poland Piotr Czuak, ul. Szujskiego /4, 33 Cracow, Poland address for correspondence Grzegorz
More informationReview on VortexInduced Vibration for Wave Propagation Class
Review on VortexInduced Vibration for Wave Propagation Class By Zhibiao Rao What s VortexInduced Vibration? In fluid dynamics, vortexinduced vibrations (VIV) are motions induced on bodies interacting
More informationSection 0.4 Inverse functions and logarithms
Section 0.4 Inverse functions and logarithms (5/3/07) Overview: Some applications require not onl a function that converts a numer into a numer, ut also its inverse, which converts ack into. In this section
More informationSwash Zone Dynamics: Modeling and Data Analysis
Swash Zone Dynamics: Modeling and Data Analysis Donald N. Slinn Department of Civil and Coastal Engineering University of Florida Gainesville, FL 326116590 phone: (352) 3921436 x 1431 fax: (352) 3923466
More informationComputational Analysis of Added Resistance in Short Waves
13 International Research Exchange Meeting of Ship and Ocean Engineering in Osaka 1 December, Osaka, Japan Computational Analysis of Added Resistance in Short Waves Yonghwan Kim, KyungKyu Yang and MinGuk
More informationDEPARTMENT OF ECONOMICS
ISSN 08964 ISBN 978 0 7340 405 THE UNIVERSITY OF MELBOURNE DEPARTMENT OF ECONOMICS RESEARCH PAPER NUMBER 06 January 009 Notes on the Construction of Geometric Representations of Confidence Intervals of
More informationThe Variants of Energy Integral Induced by the Vibrating String
Applied Mathematical Sciences, Vol. 9, 15, no. 34, 16551661 HIKARI td, www.mhikari.com http://d.doi.org/1.1988/ams.15.5168 The Variants of Energy Integral Induced by the Vibrating String Hwajoon Kim
More informationRoll dynamics of a ship sailing in large amplitude head waves
J Eng Math DOI 10.1007/s1066501496874 Roll dynamics of a ship sailing in large amplitude head waves E. F. G. van Daalen M. Gunsing J. Grasman J. Remmert Received: 8 January 2013 / Accepted: 18 January
More informationSuperelements and GlobalLocal Analysis
10 Superelements and GloalLocal Analysis 10 1 Chapter 10: SUPERELEMENTS AND GLOBALLOCAL ANALYSIS TABLE OF CONTENTS Page 10.1 Superelement Concept................. 10 3 10.1.1 Where Does the Idea Come
More informationAn introduction to Birkhoff normal form
An introduction to Birkhoff normal form Dario Bambusi Dipartimento di Matematica, Universitá di Milano via Saldini 50, 0133 Milano (Italy) 19.11.14 1 Introduction The aim of this note is to present an
More informationA NEW AND SIMPLE CHAOS TOY
International Journal of Bifurcation and Chaos, Vol. 1, No. 8 (00) 1843 1857 c World Scientific Publishing Company A NEW AND SIMPLE CHAOS TOY ERIK M. BOLLT Department of Mathematics and Computer Science,
More information3 Stability and Lyapunov Functions
CDS140a Nonlinear Systems: Local Theory 02/01/2011 3 Stability and Lyapunov Functions 3.1 Lyapunov Stability Denition: An equilibrium point x 0 of (1) is stable if for all ɛ > 0, there exists a δ > 0 such
More informationExamination paper for TMA4195 Mathematical Modeling
Department of Mathematical Sciences Examination paper for TMA4195 Mathematical Modeling Academic contact during examination: Elena Celledoni Phone: 48238584, 73593541 Examination date: 11th of December
More informationSU(N) representations
Appendix C SU(N) representations The group SU(N) has N 2 1 generators t a which form the asis of a Lie algera defined y the commutator relations in (A.2). The group has rank N 1 so there are N 1 Casimir
More informationDistributed Structural Stabilization and Tracking for Formations of Dynamic MultiAgents
CDC02REG0736 Distributed Structural Stabilization and Tracking for Formations of Dynamic MultiAgents Reza OlfatiSaber Richard M Murray California Institute of Technology Control and Dynamical Systems
More informationPerioddoubling cascades of a Silnikov equation
Perioddoubling cascades of a Silnikov equation Keying Guan and Beiye Feng Science College, Beijing Jiaotong University, Email: keying.guan@gmail.com Institute of Applied Mathematics, Academia Sinica,
More informationGeneration of undular bores and solitary wave trains in fully nonlinear shallow water theory
Generation of undular bores and solitary wave trains in fully nonlinear shallow water theory Gennady El 1, Roger Grimshaw 1 and Noel Smyth 2 1 Loughborough University, UK, 2 University of Edinburgh, UK
More informationSTABILITY AND TRIM OF MARINE VESSELS. Massachusetts Institute of Technology, Subject 2.017
STABILITY AND TRIM OF MARINE VESSELS Concept of Mass Center for a Rigid Body Centroid the point about which moments due to gravity are zero: 6 g m i (x g x i )= 0 Æ x = 6m i x i / 6m i = 6m i x i / M g
More informationOn Vertical Variations of WaveInduced Radiation Stress Tensor
Archives of HydroEngineering and Environmental Mechanics Vol. 55 (2008), No. 3 4, pp. 83 93 IBW PAN, ISSN 1231 3726 On Vertical Variations of WaveInduced Radiation Stress Tensor Włodzimierz Chybicki
More informationSIGNATURE OF HYDRODYNAMIC PRESSURE FIELD JAN BIELA SKI
SIGNATURE OF HYDRODYNAMIC PRESSURE FIELD JAN BIELA SKI Gdansk University of Technology Narutowicza 11/12, 8233 Gdansk, Poland jbielan@pg.gda.pl The article presents the results of calculations of the
More information2. Preliminaries. x 2 + y 2 + z 2 = a 2 ( 1 )
x 2 + y 2 + z 2 = a 2 ( 1 ) V. Kumar 2. Preliminaries 2.1 Homogeneous coordinates When writing algebraic equations for such geometric objects as planes and circles, we are used to writing equations that
More informationis represented by a convolution of a gluon density in the collinear limit and a universal
. On the k? dependent gluon density in hadrons and in the photon J. Blumlein DESY{Zeuthen, Platanenallee 6, D{15735 Zeuthen, Germany Abstract The k? dependent gluon distribution for protons, pions and
More informationAdvanced hydrodynamic analysis of LNG terminals
Advanced hydrodynamic analysis of LNG terminals X.B. Chen ), F. Rezende ), S. Malenica ) & J.R. Fournier ) ) Research Department, Bureau Veritas Paris La Défense, France ) Single Buoy Moorings, INC Monaco,
More informationA Classical Approach to the StarkEffect. Mridul Mehta Advisor: Prof. Enrique J. Galvez Physics Dept., Colgate University
A Classical Approach to the StarkEffect Mridul Mehta Advisor: Prof. Enrique J. Galvez Physics Dept., Colgate University Abstract The state of an atom in the presence of an external electric field is known
More informationq HYBRID CONTROL FOR BALANCE 0.5 Position: q (radian) q Time: t (seconds) q1 err (radian)
Hybrid Control for the Pendubot Mingjun Zhang and TzyhJong Tarn Department of Systems Science and Mathematics Washington University in St. Louis, MO, USA mjz@zach.wustl.edu and tarn@wurobot.wustl.edu
More informationMATHEMATICS PAPER IB COORDINATE GEOMETRY(2D &3D) AND CALCULUS. Note: This question paper consists of three sections A,B and C.
MATHEMATICS PAPER IB COORDINATE GEOMETRY(D &3D) AND CALCULUS. TIME : 3hrs Ma. Marks.75 Note: This question paper consists of three sections A,B and C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS. 0X =0.
More informationIntroduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.
Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. BernoulliEuler Beams.
More informationShafts. Fig.(4.1) Dr. Salah Gasim Ahmed YIC 1
Shafts. Power transmission shafting Continuous mechanical power is usually transmitted along and etween rotating shafts. The transfer etween shafts is accomplished y gears, elts, chains or other similar
More informationUniversit at Fachbereich Stuttgart Mathematik Preprint 2005/006
Universität Stuttgart Fachereich Mathematik Spatially nondecaying solutions of 2D NavierStokes equation in a strip Sergey Zelik Preprint 25/6 Universität Stuttgart Fachereich Mathematik Spatially nondecaying
More informationCopyright 2009, August E. Evrard.
Unless otherwise noted, the content of this course material is licensed under a Creative Commons BY 3.0 License. http://creativecommons.org/licenses/by/3.0/ Copyright 2009, August E. Evrard. You assume
More informationVertical chaos and horizontal diffusion in the bouncingball billiard
Vertical chaos and horizontal diffusion in the bouncingball billiard Astrid S. de Wijn and Holger Kantz MaxPlanckInstitute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
More informationTHE CONVECTION DIFFUSION EQUATION
3 THE CONVECTION DIFFUSION EQUATION We next consider the convection diffusion equation ɛ 2 u + w u = f, (3.) where ɛ>. This equation arises in numerous models of flows and other physical phenomena. The
More informationSelfExcited Vibration in Hydraulic Ball Check Valve
SelfExcited Vibration in Hydraulic Ball Check Valve L. Grinis, V. Haslavsky, U. Tzadka Abstract This paper describes an experimental, theoretical model and numerical study of concentrated vortex flow
More informationAn MCSCF Study of the Thermal Cycloaddition of Two Ethylenes
~~~ ~ 2260 J. Am. Chem. SOC. 1985, 107, 22602264 stale species on the potential energy surface of C302+. dications is not questioned y the result. It should also e mentioned that in line with the theoretical
More informationAn Unscented Kalman Filter Based Wave Filtering Algorithm for Dynamic Ship Positioning
Proceeding of the IEEE International Conference on Automation and Logistics Chongqing, China, August An Unscented Kalman Filter Based Wave Filtering Algorithm for Dynamic Ship Positioning Xiaocheng Shi,
More informationIrregular Wave Forces on Monopile Foundations. Effect af Full Nonlinearity and Bed Slope
Downloaded from orbit.dtu.dk on: Dec 04, 2017 Irregular Wave Forces on Monopile Foundations. Effect af Full Nonlinearity and Bed Slope Schløer, Signe; Bredmose, Henrik; Bingham, Harry B. Published in:
More informationQuasiPeriodic Orbits of the Restricted ThreeBody Problem Made Easy
QuasiPeriodic Orbits of the Restricted ThreeBody Problem Made Easy Egemen Kolemen, N. Jeremy Kasdin and Pini Gurfil Mechanical and Aerospace Engineering, Princeton, NJ 08544, ekolemen@princeton.edu Mechanical
More informationLikewise, any operator, including the most generic Hamiltonian, can be written in this basis as H11 H
Finite Dimensional systems/ilbert space Finite dimensional systems form an important subclass of degrees of freedom in the physical world To begin with, they describe angular momenta with fixed modulus
More informationIm + α α. β + I 1 I 1< 0 I 1= 0 I 1 > 0
ON THE HAMILTONIAN ANDRONOVHOPF BIFURCATION M. Olle, J. Villanueva 2 and J. R. Pacha 3 2 3 Departament de Matematica Aplicada I (UPC), Barcelona, Spain In this contribution, we consider an specic type
More informationQuaternion Feedback Regulation of Underwater Vehicles OlaErik FJELLSTAD and Thor I. FOSSEN Abstract: Position and attitude setpoint regulation of au
Quaternion Feedback Regulation of Underwater Vehicles OlaErik Fjellstad Dr.Ing. EE Seatex AS Trondheim NORWAY Thor I. Fossen Dr.Ing EE, M.Sc Naval Architecture Assistant Professor Telephone: +7 7 9 6
More information