Vor Ort
Merkzettel Warenkorb
Produktbild: Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems

Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems Applications to Models with Friction or Impact

Aus der Reihe ISTE

262,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

25.02.2013

Verlag

John Wiley & Sons

Seitenzahl

512

Maße (L/B/H)

23,4/15,7/3,3 cm

Gewicht

885 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-84821-525-2

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

25.02.2013

Verlag

John Wiley & Sons

Seitenzahl

512

Maße (L/B/H)

23,4/15,7/3,3 cm

Gewicht

885 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-84821-525-2

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

Noch keine Bewertungen vorhanden

Verfassen Sie die erste Bewertung zu diesem Artikel

Helfen Sie anderen Kundinnen und Kunden durch Ihre Meinung.

Kundinnen und Kunden meinen

Bewertungen (0)
Die Leseprobe wird geladen.
  • Produktbild: Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems
  • Introduction xi
     
    Chapter 1. Some Simple Examples 1
     
    1.1. Introduction 1
     
    1.2. Frictions 1
     
    1.2.1. Coulomb's law 1
     
    1.2.2. Differential equation with univalued operator and usual sign 3
     
    1.2.3. Differential equation with multivalued term: differential inclusion 11
     
    1.2.4. Other friction laws 12
     
    1.3. Impact 16
     
    1.3.1. Difficulties with writing the differential equation 16
     
    1.3.2. Ill-posed problems 19
     
    1.4. Probabilistic context 22
     
    Chapter 2. Theoretical Deterministic Context 27
     
    2.1. Introduction 27
     
    2.2. Maximal monotone operators and first result on differential inclusions (in R) 27
     
    2.2.1. Graphs (operators) definitions 28
     
    2.2.2. Maximal monotone operators 29
     
    2.2.3. Convex function, subdifferentials and operators 33
     
    2.2.4. Resolvent and regularization 38
     
    2.2.5. Taking the limit 40
     
    2.2.6. First result of existence and uniqueness for a differential inclusion 40
     
    2.3. Extension to any Hilbert space 45
     
    2.4. Existence and uniqueness results in Hilbert space 57
     
    2.5. Numerical scheme in a Hilbert space 59
     
    2.5.1. The numerical scheme 59
     
    2.5.2. State of the art summary and results shown in this publication 60
     
    2.5.3. Convergence (general results and order 1/2) 61
     
    2.5.4. Convergence (order one) 67
     
    2.5.5. Change of scalar product 72
     
    2.5.6. Resolvent calculation 74
     
    2.5.7. More regular schemes 76
     
    Chapter 3. Stochastic Theoretical Context 79
     
    3.1. Introduction 79
     
    3.2. Stochastic integral 79
     
    3.2.1. The stochastic processes background 80
     
    3.2.2. Stochastic integral 84
     
    3.3. Stochastic differential equations 90
     
    3.3.1. Existence and uniqueness of strong solution 91
     
    3.3.2. Existence and uniqueness of weak solution 92
     
    3.3.3. Kolmogorov and Fokker-Planck equations 95
     
    3.4. Multivalued stochastic differential equations 101
     
    3.4.1. Problem statement 101
     
    3.4.2. Uniqueness and existence results 103
     
    3.5. Numerical scheme 104
     
    3.5.1. Which convergence: weak or strong? 106
     
    3.5.2. Strong convergence results 108
     
    3.5.3. Weak convergence results 122
     
    Chapter 4. Riemannian Theoretical Context 129
     
    4.1. Introduction 129
     
    4.2. First or second order 129
     
    4.3. Differential geometry 131
     
    4.3.1. Sphere case 131
     
    4.3.2. General case 132
     
    4.4. Dynamics of the mechanical systems 139
     
    4.4.1. Definition of mechanical system 139
     
    4.4.2. Equation of the dynamics 141
     
    4.5. Connection, covariant derivative, geodesics and parallel transport 144
     
    4.6. Maximal monotone term 148
     
    4.7. Stochastic term 149
     
    4.8. Results on the existence and uniqueness of a solution 151
     
    Chapter 5. Systems with Friction 155
     
    5.1. Introduction 155
     
    5.2. Examples of frictional systems with a finite number of degrees of freedom 155
     
    5.2.1. General framework 155
     
    5.2.2. Two elementary models 156
     
    5.2.3. Assembly and results in finite dimensions 165
     
    5.2.4. Conclusion 193
     
    5.2.5. Examples of numerical simulation 194
     
    5.2.6. Identification of the generalized Prandtl model (principles and simulation) 205
     
    5.3. Another example: the case of a pendulum with friction 215
     
    5.3.1. Formulation of the problem, existence and uniqueness 215
     
    5.3.2. Numerical scheme 218
     
    5.3.3. Numerical estimation of the order 219
     
    5.3.4. Exampl