LEADER 05772nam 2200721 a 450 001 9910139032503321 005 20200520144314.0 010 $a1-118-60408-3 010 $a1-118-60404-0 010 $a1-299-40244-5 010 $a1-118-60432-6 035 $a(CKB)2550000001017884 035 $a(EBL)1157400 035 $a(SSID)ssj0000884297 035 $a(PQKBManifestationID)11475941 035 $a(PQKBTitleCode)TC0000884297 035 $a(PQKBWorkID)10940578 035 $a(PQKB)11747338 035 $a(Au-PeEL)EBL1157400 035 $a(CaPaEBR)ebr10677258 035 $a(CaONFJC)MIL471494 035 $a(OCoLC)831115115 035 $a(MiAaPQ)EBC1157400 035 $a(PPN)183762401 035 $a(EXLCZ)992550000001017884 100 $a20130403d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNon-smooth deterministic or stochastic discrete dynamical systems$b[electronic resource] $eapplications to models with friction or impact /$fJe?ro?me Bastien, Fre?de?ric Bernardin, Claude-Henri Lamarque 210 $aLondon $cISTE ;$aHoboken, N.J. $cWiley$d2013 215 $a1 online resource (514 p.) 225 0 $aMechanical engineering and solid mechanics series 300 $aDescription based upon print version of record. 311 $a1-84821-525-8 320 $aIncludes bibliographical references and index. 327 $aTitle Page; Contents; Introduction; Chapter 1. Some Simple Examples; 1.1. Introduction; 1.2. Frictions; 1.2.1. Coulomb's law; 1.2.2. Differential equation with univalued operator and usual sign; 1.2.3. Differential equation with multivalued term: differential inclusion; 1.2.4. Other friction laws; 1.3. Impact; 1.3.1. Difficulties with writing the differential equation; 1.3.2. Ill-posed problems; 1.4. Probabilistic context; Chapter 2. Theoretical Deterministic Context; 2.1. Introduction; 2.2. Maximal monotone operators and first result on differential inclusions (in R) 327 $a2.2.1. Graphs (operators) definitions2.2.2. Maximal monotone operators; 2.2.3. Convex function, sub-differentials and operators; 2.2.4. Resolvent and regularization; 2.2.5. Taking the limit; 2.2.6. First result of existence and uniqueness for a differential inclusion; 2.3. Extension to any Hilbert space; 2.4. Existence and uniqueness results in Hilbert space; 2.5. Numerical scheme in a Hilbert space; 2.5.1. The numerical scheme; 2.5.2. State of the art summary and results shown in this publication; 2.5.3. Convergence (general results and order 1/2); 2.5.4. Convergence (order one) 327 $a2.5.5. Change of scalar product2.5.6. Resolvent calculation; 2.5.7. More regular schemes; Chapter 3. Stochastic Theoretical Context; 3.1. Introduction; 3.2. Stochastic integral; 3.2.1. The stochastic processes background; 3.2.2. Stochastic integral; 3.3. Stochastic differential equations; 3.3.1. Existence and uniqueness of strong solution; 3.3.2. Existence and uniqueness of weak solution; 3.3.3. Kolmogorov and Fokker-Planck equations; 3.4. Multivalued stochastic differential equations; 3.4.1. Problem statement; 3.4.2. Uniqueness and existence results; 3.5. Numerical scheme 327 $a3.5.1. Which convergence: weak or strong?3.5.2. Strong convergence results; 3.5.3. Weak convergence results; Chapter 4. Riemannian Theoretical Context; 4.1. Introduction; 4.2. First or second order; 4.3. Differential geometry; 4.3.1. Sphere case; 4.3.2. General case; 4.4. Dynamics of the mechanical systems; 4.4.1. Definition of mechanical system; 4.4.2. Equation of the dynamics; 4.5. Connection, covariant derivative, geodesics and parallel transport; 4.6. Maximal monotone term; 4.7. Stochastic term; 4.8. Results on the existence and uniqueness of a solution; Chapter 5. Systems with Friction 327 $a5.1. Introduction5.2. Examples of frictional systems with a finite number of degrees of freedom; 5.2.1. General framework; 5.2.2. Two elementary models; 5.2.3. Assembly and results in finite dimensions; 5.2.4. Conclusion; 5.2.5. Examples of numerical simulation; 5.2.6. Identification of the generalized Prandtl model (principles and simulation); 5.3. Another example: the case of a pendulum with friction; 5.3.1. Formulation of the problem, existence and uniqueness; 5.3.2. Numerical scheme; 5.3.3. Numerical estimation of the order; 5.3.4. Example of numerical simulations 327 $a5.3.5. Free oscillations 330 $a This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities.The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal monotone operators (graphs) in order to describe models of impact or friction. The authors of this book master the mathematical, numerical and modeling tools in a particular way so that they can propose all aspects of the approach, in both a deterministic 410 0$aISTE 606 $aDynamics$xMathematical models 606 $aFriction$xMathematical models 606 $aImpact$xMathematical models 615 0$aDynamics$xMathematical models. 615 0$aFriction$xMathematical models. 615 0$aImpact$xMathematical models. 676 $a620.00151539 700 $aBastien$b Je?ro?me$0958558 701 $aBernardin$b Fre?de?ric$0958559 701 $aLamarque$b Claude-Henri$0739265 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139032503321 996 $aNon-smooth deterministic or stochastic discrete dynamical systems$92171955 997 $aUNINA