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Non-smooth deterministic or stochastic discrete dynamical systems [[electronic resource] ] : applications to models with friction or impact / / Jérôme Bastien, Frédéric Bernardin, Claude-Henri Lamarque
| Non-smooth deterministic or stochastic discrete dynamical systems [[electronic resource] ] : applications to models with friction or impact / / Jérôme Bastien, Frédéric Bernardin, Claude-Henri Lamarque |
| Autore | Bastien Jérôme |
| Pubbl/distr/stampa | London, : ISTE |
| Descrizione fisica | 1 online resource (514 p.) |
| Disciplina | 620.00151539 |
| Altri autori (Persone) |
BernardinFrédéric
LamarqueClaude-Henri |
| Collana | Mechanical engineering and solid mechanics series |
| Soggetto topico |
Dynamics - Mathematical models
Friction - Mathematical models Impact - Mathematical models |
| ISBN |
1-118-60408-3
1-118-60404-0 1-299-40244-5 1-118-60432-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Title 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)
2.2.1. 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) 2.5.5. 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 3.5.1. 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 5.1. 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 5.3.5. Free oscillations |
| Record Nr. | UNINA-9910139032503321 |
Bastien Jérôme
|
||
| London, : ISTE | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Non-smooth deterministic or stochastic discrete dynamical systems : applications to models with friction or impact / / Jérôme Bastien, Frédéric Bernardin, Claude-Henri Lamarque
| Non-smooth deterministic or stochastic discrete dynamical systems : applications to models with friction or impact / / Jérôme Bastien, Frédéric Bernardin, Claude-Henri Lamarque |
| Autore | Bastien Jérôme |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | London, : ISTE |
| Descrizione fisica | 1 online resource (514 p.) |
| Disciplina | 620.00151539 |
| Altri autori (Persone) |
BernardinFrédéric
LamarqueClaude-Henri |
| Collana | Mechanical engineering and solid mechanics series |
| Soggetto topico |
Dynamics - Mathematical models
Friction - Mathematical models Impact - Mathematical models |
| ISBN |
1-118-60408-3
1-118-60404-0 1-299-40244-5 1-118-60432-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Title 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)
2.2.1. 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) 2.5.5. 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 3.5.1. 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 5.1. 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 5.3.5. Free oscillations |
| Record Nr. | UNINA-9910818175103321 |
|
Bastien Jérôme
|
||
| London, : ISTE | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||