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Biblioteca

MARC Lista (tabellare)
3D discrete element workbench for highly dynamic thermo-mechanical analysis : GranOO. Volume 3 / / Damien André, Jean-Luc Charles, Ivan Iordanoff ; coordinated by Ivan Iordanoff
3D discrete element workbench for highly dynamic thermo-mechanical analysis : GranOO. Volume 3 / / Damien André, Jean-Luc Charles, Ivan Iordanoff ; coordinated by Ivan Iordanoff
Autore André Damien
Pubbl/distr/stampa Hoboken, NJ : , : Wiley, , 2015
Descrizione fisica 1 online resource (175 p.)
Collana Numerical methods in engineering series : discrete element model and simulation of continuous materials behavior set
Soggetto topico Materials - Dynamic testing
Discrete element method
Object-oriented methods (Computer science)
UML (Computer science)
Soggetto genere / forma Electronic books.
ISBN 1-119-23979-6
1-119-11635-X
1-119-23978-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Table of Contents; Title; Copyright; List of Figures; List of Tables; Introduction; I.1. The black box problem; I.2. A numerical tool to study a tribological problem; I.3. Why have we chosen a free license?; I.4. Discrete element methods; I.5. Application to tribological problems; I.6. A brief history of the workbench GranOO; I.7. A design to serve versatility; I.8. Choice of the programming language; I.9. Book organization; 1: Object Oriented Approach and UML; 1.1. Object Oriented (OO) paradigms; 1.2. OO analysis and design; 1.3. UML diagrams; 2: Operating Architecture
2.1. The GranOO package2.2. Compilation process of the executable file; 2.3. Launching a GranOO executable; 2.4. The input files; 2.5. The magic world of the plugins; 2.6. The output files; 3: Focus on Libraries; 3.1. The geometrical library; 3.2. The DEM library; 3.3. The libMySandbox library; 3.4. Conclusion; 4: Tools and Practical Examples of Use of GranOO.; 4.1. Tool overview; 4.2. Granular simulation: the bluewave example; 4.3. The continuous discrete element model; 4.4. Conclusion; Conclusion; Appendices; Appendix 1: Using Quaternions; A1.1. Introduction; A1.2. Norm transformation
A1.3. Direction transformationA1.4. Quaternion definition; A1.5. Mathematical properties; A1.6. Quaternion and attitude; A1.7. Quaternion and angular velocity; A1.8. Application to dynamics; A1.9. Numerical integration; A1.10. Conclusion; Appendix 2: Pendulum Problem Complete Code; Bibliography; Index; End User License Agreement
Record Nr. UNINA-9910131529003321
André Damien  
Hoboken, NJ : , : Wiley, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
3D discrete element workbench for highly dynamic thermo-mechanical analysis : GranOO. Volume 3 / / Damien André, Jean-Luc Charles, Ivan Iordanoff ; coordinated by Ivan Iordanoff
3D discrete element workbench for highly dynamic thermo-mechanical analysis : GranOO. Volume 3 / / Damien André, Jean-Luc Charles, Ivan Iordanoff ; coordinated by Ivan Iordanoff
Autore André Damien
Pubbl/distr/stampa Hoboken, NJ : , : Wiley, , 2015
Descrizione fisica 1 online resource (175 p.)
Disciplina 005.117
Collana Numerical methods in engineering series : discrete element model and simulation of continuous materials behavior set
Soggetto topico Materials - Dynamic testing
Discrete element method
Object-oriented methods (Computer science)
UML (Computer science)
ISBN 1-119-23979-6
1-119-11635-X
1-119-23978-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Table of Contents; Title; Copyright; List of Figures; List of Tables; Introduction; I.1. The black box problem; I.2. A numerical tool to study a tribological problem; I.3. Why have we chosen a free license?; I.4. Discrete element methods; I.5. Application to tribological problems; I.6. A brief history of the workbench GranOO; I.7. A design to serve versatility; I.8. Choice of the programming language; I.9. Book organization; 1: Object Oriented Approach and UML; 1.1. Object Oriented (OO) paradigms; 1.2. OO analysis and design; 1.3. UML diagrams; 2: Operating Architecture
2.1. The GranOO package2.2. Compilation process of the executable file; 2.3. Launching a GranOO executable; 2.4. The input files; 2.5. The magic world of the plugins; 2.6. The output files; 3: Focus on Libraries; 3.1. The geometrical library; 3.2. The DEM library; 3.3. The libMySandbox library; 3.4. Conclusion; 4: Tools and Practical Examples of Use of GranOO.; 4.1. Tool overview; 4.2. Granular simulation: the bluewave example; 4.3. The continuous discrete element model; 4.4. Conclusion; Conclusion; Appendices; Appendix 1: Using Quaternions; A1.1. Introduction; A1.2. Norm transformation
A1.3. Direction transformationA1.4. Quaternion definition; A1.5. Mathematical properties; A1.6. Quaternion and attitude; A1.7. Quaternion and angular velocity; A1.8. Application to dynamics; A1.9. Numerical integration; A1.10. Conclusion; Appendix 2: Pendulum Problem Complete Code; Bibliography; Index; End User License Agreement
Record Nr. UNINA-9910830547503321
André Damien  
Hoboken, NJ : , : Wiley, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Discrete element model and simulation of continuous materials behavior set . Volume 1 Discrete element method to model 3D continuous materials / / Mohamed Jebahi [and three others]
Discrete element model and simulation of continuous materials behavior set . Volume 1 Discrete element method to model 3D continuous materials / / Mohamed Jebahi [and three others]
Autore Jebahi Mohamed
Pubbl/distr/stampa London, England ; ; Hoboken, New Jersey : , : iSTE : , : Wiley, , 2015
Descrizione fisica 1 online resource (198 p.)
Disciplina 620.11015118
Collana Numerical Methods in Engineering Series
Soggetto topico Materials - Mathematical models
Discrete element method
ISBN 1-119-10275-8
1-119-10304-5
1-119-10291-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover; Title Page; Copyright; Contents; List of Figures; List of Tables; Preface; Introduction; I.1. Toward discrete element modeling of continuous materials; I.2. Scope and objective; I.3. Organization; 1: State of the Art: Discrete Element Modeling; 1.1. Introduction; 1.2. Classification of discrete methods; 1.2.1. Quantum mechanical methods; 1.2.2. Atomistic methods; 1.2.3. Mesoscopic discrete methods; 1.2.3.1. Lattice methods; 1.2.3.2. Smooth contact particle methods; 1.2.3.3. Non-smooth contact particle models; 1.2.3.4. Hybrid lattice-particle models
1.3. Discrete element method for continuous materials1.4. Discrete-continuum transition: macroscopic variables; 1.4.1. Stress tensor for discrete systems; 1.4.2. Strain tensor for discrete systems; 1.4.2.1. Equivalent continuum strains; 1.4.2.2. Best-fit strains; 1.4.2.3. Satake strain; 1.5. Conclusion; 2: Discrete Element Modeling of Mechanical Behavior of Continuous Materials; 2.1. Introduction; 2.2. Explicit dynamic algorithm; 2.3. Construction of the discrete domain; 2.3.1. The cooker compaction algorithm; 2.3.1.1. Stopping criterion of compaction process; 2.3.1.2. Filling process
2.3.1.3. Overlapping removing2.3.2. Geometrical characterization of the discrete domain; 2.3.2.1. Geometrical isotropy and granulometry; 2.3.2.2. Average coordination number; 2.3.2.3. Discrete domain fineness; 2.4. Mechanical behavior modeling; 2.4.1. Cohesive beam model; 2.4.1.1. Analytical model; 2.4.1.2. Strain energy computation; 2.4.2. Calibration of the cohesive beam static parameters; 2.4.2.1. Quasistatic tensile test description; 2.4.2.1.1. From discrete to continuous geometry; 2.4.2.1.2. Loading; 2.4.2.1.3. EM and νM computation; 2.4.2.2. Parametric study
2.4.2.2.1. Microscopic Poisson's ratio influence2.4.2.2.2. Microscopic Young's modulus influence; 2.4.2.2.3. Microscopic radius ratio influence; 2.4.2.3. Calibration method for static parameters; 2.4.2.4. Convergence study; 2.4.2.5. Validation; 2.4.3. Calibration of the cohesive beam dynamic parameters; 2.4.3.1. Calibration method for dynamic parameters; 2.4.3.2. Validation; 2.5. Conclusion; 3: Discrete Element Modeling of Thermal Behavior of Continuous Materials; 3.1. Introduction; 3.2. General description of the method; 3.2.1. Characterization of field variable variation in discrete domain
3.2.2. Application to heat conduction3.3. Thermal conduction in 3D ordered discrete domains; 3.4. Thermal conduction in 3D disordered discrete domains; 3.4.1. Determination of local parameters for each discrete element; 3.4.2. Calculation of discrete element transmission surface; 3.4.3. Calculation of local volume fraction; 3.4.4. Interactions between each discrete element and its neighbors; 3.5. Validation; 3.5.1. Cylindrical beam in contact with a hot plane; 3.5.2. Dynamically heated sheet; 3.6. Conclusion; 4: Discrete Element Modeling of Brittle Fracture; 4.1. Introduction
4.2. Fracture model based on the cohesive beam bonds
Record Nr. UNINA-9910132269503321
Jebahi Mohamed  
London, England ; ; Hoboken, New Jersey : , : iSTE : , : Wiley, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Discrete element model and simulation of continuous materials behavior set . Volume 1 Discrete element method to model 3D continuous materials / / Mohamed Jebahi [and three others]
Discrete element model and simulation of continuous materials behavior set . Volume 1 Discrete element method to model 3D continuous materials / / Mohamed Jebahi [and three others]
Autore Jebahi Mohamed
Pubbl/distr/stampa London, England ; ; Hoboken, New Jersey : , : iSTE : , : Wiley, , 2015
Descrizione fisica 1 online resource (198 p.)
Disciplina 620.11015118
Collana Numerical Methods in Engineering Series
Soggetto topico Materials - Mathematical models
Discrete element method
ISBN 1-119-10275-8
1-119-10304-5
1-119-10291-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover; Title Page; Copyright; Contents; List of Figures; List of Tables; Preface; Introduction; I.1. Toward discrete element modeling of continuous materials; I.2. Scope and objective; I.3. Organization; 1: State of the Art: Discrete Element Modeling; 1.1. Introduction; 1.2. Classification of discrete methods; 1.2.1. Quantum mechanical methods; 1.2.2. Atomistic methods; 1.2.3. Mesoscopic discrete methods; 1.2.3.1. Lattice methods; 1.2.3.2. Smooth contact particle methods; 1.2.3.3. Non-smooth contact particle models; 1.2.3.4. Hybrid lattice-particle models
1.3. Discrete element method for continuous materials1.4. Discrete-continuum transition: macroscopic variables; 1.4.1. Stress tensor for discrete systems; 1.4.2. Strain tensor for discrete systems; 1.4.2.1. Equivalent continuum strains; 1.4.2.2. Best-fit strains; 1.4.2.3. Satake strain; 1.5. Conclusion; 2: Discrete Element Modeling of Mechanical Behavior of Continuous Materials; 2.1. Introduction; 2.2. Explicit dynamic algorithm; 2.3. Construction of the discrete domain; 2.3.1. The cooker compaction algorithm; 2.3.1.1. Stopping criterion of compaction process; 2.3.1.2. Filling process
2.3.1.3. Overlapping removing2.3.2. Geometrical characterization of the discrete domain; 2.3.2.1. Geometrical isotropy and granulometry; 2.3.2.2. Average coordination number; 2.3.2.3. Discrete domain fineness; 2.4. Mechanical behavior modeling; 2.4.1. Cohesive beam model; 2.4.1.1. Analytical model; 2.4.1.2. Strain energy computation; 2.4.2. Calibration of the cohesive beam static parameters; 2.4.2.1. Quasistatic tensile test description; 2.4.2.1.1. From discrete to continuous geometry; 2.4.2.1.2. Loading; 2.4.2.1.3. EM and νM computation; 2.4.2.2. Parametric study
2.4.2.2.1. Microscopic Poisson's ratio influence2.4.2.2.2. Microscopic Young's modulus influence; 2.4.2.2.3. Microscopic radius ratio influence; 2.4.2.3. Calibration method for static parameters; 2.4.2.4. Convergence study; 2.4.2.5. Validation; 2.4.3. Calibration of the cohesive beam dynamic parameters; 2.4.3.1. Calibration method for dynamic parameters; 2.4.3.2. Validation; 2.5. Conclusion; 3: Discrete Element Modeling of Thermal Behavior of Continuous Materials; 3.1. Introduction; 3.2. General description of the method; 3.2.1. Characterization of field variable variation in discrete domain
3.2.2. Application to heat conduction3.3. Thermal conduction in 3D ordered discrete domains; 3.4. Thermal conduction in 3D disordered discrete domains; 3.4.1. Determination of local parameters for each discrete element; 3.4.2. Calculation of discrete element transmission surface; 3.4.3. Calculation of local volume fraction; 3.4.4. Interactions between each discrete element and its neighbors; 3.5. Validation; 3.5.1. Cylindrical beam in contact with a hot plane; 3.5.2. Dynamically heated sheet; 3.6. Conclusion; 4: Discrete Element Modeling of Brittle Fracture; 4.1. Introduction
4.2. Fracture model based on the cohesive beam bonds
Record Nr. UNINA-9910823353003321
Jebahi Mohamed  
London, England ; ; Hoboken, New Jersey : , : iSTE : , : Wiley, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Discrete-continuum coupling method to simulate highly dynamic multi-scale problems . Volume 2 : simulation of laser-induced damage in silica glass / / Mohamed Jebahi [and three others]
Discrete-continuum coupling method to simulate highly dynamic multi-scale problems . Volume 2 : simulation of laser-induced damage in silica glass / / Mohamed Jebahi [and three others]
Autore Jebahi Mohamed
Pubbl/distr/stampa London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2015
Descrizione fisica 1 online resource (195 p.)
Disciplina 514.325
Collana Numerical Methods in Engineering Series
Soggetto topico Continuum (Mathematics)
Discrete element method
Multiscale modeling
ISBN 1-119-11928-6
1-119-11929-4
1-119-11527-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910131353103321
Jebahi Mohamed  
London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Discrete-continuum coupling method to simulate highly dynamic multi-scale problems . Volume 2 : simulation of laser-induced damage in silica glass / / Mohamed Jebahi [and three others]
Discrete-continuum coupling method to simulate highly dynamic multi-scale problems . Volume 2 : simulation of laser-induced damage in silica glass / / Mohamed Jebahi [and three others]
Autore Jebahi Mohamed
Pubbl/distr/stampa London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2015
Descrizione fisica 1 online resource (195 p.)
Disciplina 514.325
Collana Numerical Methods in Engineering Series
Soggetto topico Continuum (Mathematics)
Discrete element method
Multiscale modeling
ISBN 1-119-11928-6
1-119-11929-4
1-119-11527-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910822441503321
Jebahi Mohamed  
London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Matrix discrete element analysis of geological and geotechnical engineering / / Chun Liu
Matrix discrete element analysis of geological and geotechnical engineering / / Chun Liu
Autore Liu Chun
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Singapore : , : Springer, , [2021]
Descrizione fisica 1 online resource (XXIII, 294 p. 349 illus., 117 illus. in color.)
Disciplina 624.1510151352
Soggetto topico Geotechnical engineering - Mathematics
Discrete element method
ISBN 981-334-524-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1 Principles and Implementation of DEM -- Chapter 2 The Basic Structure of MatDEM -- Chapter 3 Geometric Modeling and Material Setup -- Chapter 4　Load Settings and Numerical Calculations -- Chapter 5 Postprocessing and System Functions -- Chapter 6 Basic Application of Geotechnical Engineering -- Chapter 7 Rock-Soil Body Discrete Element Test -- Chapter 8　Modeling of Complex 3D Models -- Chapter 9 Numerical Simulations of Dynamic Action -- Chapter 10 Multi-field Coupled Numerical Simulation -- Appendix　Properties, Functions and Frequently Asked Questions.
Record Nr. UNINA-9910483722003321
Liu Chun  
Singapore : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Siku sea ice discrete element method model / / principal investigator: Anton Kulchitsky ; co-investigators: Jennifer Hutchings, Jerome Johnson ; graduate student: Benjamin Lewis
Siku sea ice discrete element method model / / principal investigator: Anton Kulchitsky ; co-investigators: Jennifer Hutchings, Jerome Johnson ; graduate student: Benjamin Lewis
Autore Kulchitsky Anton
Pubbl/distr/stampa Fairbanks, AK : , : Coastal Marine Institute, College of Fisheries and Ocean Sciences, University of Alaska Fairbanks, , 2017
Descrizione fisica 1 online resource (v, 40 pages) : illustrations (chiefly color), maps (chiefly color)
Collana OCS study
Soggetto topico Sea ice drift - Computer simulation
Sea ice drift - Forecasting
Discrete element method
Sea ice drift - Beaufort Sea
Sea ice drift - Chukchi Sea
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910706154803321
Kulchitsky Anton  
Fairbanks, AK : , : Coastal Marine Institute, College of Fisheries and Ocean Sciences, University of Alaska Fairbanks, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Understanding the discrete element method : simulation of non-spherical particles for granular and multi-body systems / / Hans-Georg Matuttis, Jian Chen
Understanding the discrete element method : simulation of non-spherical particles for granular and multi-body systems / / Hans-Georg Matuttis, Jian Chen
Autore Matuttis Hans-Georg
Pubbl/distr/stampa Singapore : , : Wiley, , 2014
Descrizione fisica 1 online resource (480 p.)
Disciplina 531/.163
Soggetto topico Granular flow
Discrete element method
Multibody systems
Mechanics, Applied - Computer simulation
ISBN 1-118-56728-5
1-118-56722-6
1-118-56721-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto UNDERSTANDING THE DISCRETE ELEMENT METHOD SIMULATION OF NON-SPHERICAL PARTICLES FOR GRANULARAND MULTI-BODY SYSTEMS; Copright; Contents; Exercises; About the Authors; Preface; Acknowledgements; List of Abbreviations; 1 Mechanics; 1.1 Degrees of freedom; 1.1.1 Particle mechanics and constraints; 1.1.2 From point particles to rigid bodies; 1.1.3 More context and terminology; 1.2 Dynamics of rectilinear degrees of freedom; 1.3 Dynamics of angular degrees of freedom; 1.3.1 Rotation in two dimensions; 1.3.2 Moment of inertia; 1.3.3 From two to three dimensions
1.3.4 Rotation matrix in three dimensions1.3.5 Three-dimensional moments of inertia; 1.3.6 Space-fixed and body-fixed coordinate systems andequations of motion; 1.3.7 Problems with Euler angles; 1.3.8 Rotations represented using complex numbers; 1.3.9 Quaternions; 1.3.10 Derivation of quaternion dynamics; 1.4 The phase space; 1.4.1 Qualitative discussion of the time dependence of linear oscillations; 1.4.2 Resonance; 1.4.3 The flow in phase space; 1.5 Nonlinearities; 1.5.1 Harmonic balance; 1.5.2 Resonance in nonlinear systems; 1.5.3 Higher harmonics and frequency mixing
1.5.4 The van der Pol oscillator1.6 From higher harmonics to chaos; 1.6.1 The bifurcation cascade; 1.6.2 The nonlinear frictional oscillator and Poincar ́e maps; 1.6.3 The route to chaos; 1.6.4 Boundary conditions and many-particle systems; 1.7 Stability and conservationlaws; 1.7.1 Stability in statics; 1.7.2 Stability in dynamics; 1.7.3 Stable axes of rotation around the principal axis; 1.7.4 Noether's theorem and conservation laws; 1.8 Further reading; Exercises; References; 2Numerical Integration of OrdinaryDifferential Equations; 2.1 Fundamentals of numerical analysis
2.1.1 Floating point numbers2.1.2 Big-O notation; 2.1.3 Relative and absolute error; 2.1.4 Truncation error; 2.1.5 Local and global error; 2.1.6 Stability; 2.1.7 Stable integrators for unstable problems; 2.2 Numerical analysis for ordinary differential equations; 2.2.1 Variable notation and transformation of the order of adifferential equation; 2.2.2 Differences in the simulation of atoms and molecules,as compared to macroscopic particles; 2.2.3 Truncation error for solutions of ordinary differential equations; 2.2.4 Fundamental approaches; 2.2.5 Explicit Euler method
2.2.6 Implicit Euler method2.3 Runge-Kutta methods; 2.3.1 Adaptive step-size control; 2.3.2 Dense output and event location; 2.3.3 Partitioned Runge-Kutta methods; 2.4 Symplectic methods; 2.4.1 The classical Verlet method; 2.4.2 Velocity-Verlet methods; 2.4.3 Higher-order velocity-Verlet methods; 2.4.4 Pseudo-symplectic methods; 2.4.5 Order, accuracy and energy conservation; 2.4.6 Backward error analysis; 2.4.7 Case study: the harmonic oscillator with andwithout viscous damping; 2.5 Stiff problems; 2.5.1 Evaluating computational costs; 2.5.2 Stiff solutions and error as noise
2.5.3 Order reduction
Record Nr. UNINA-9910132498003321
Matuttis Hans-Georg  
Singapore : , : Wiley, , 2014
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Understanding the discrete element method : simulation of non-spherical particles for granular and multi-body systems / / Hans-Georg Matuttis, Jian Chen
Understanding the discrete element method : simulation of non-spherical particles for granular and multi-body systems / / Hans-Georg Matuttis, Jian Chen
Autore Matuttis Hans-Georg
Pubbl/distr/stampa Singapore : , : Wiley, , 2014
Descrizione fisica 1 online resource (480 p.)
Disciplina 531/.163
Soggetto topico Granular flow
Discrete element method
Multibody systems
Mechanics, Applied - Computer simulation
ISBN 1-118-56728-5
1-118-56722-6
1-118-56721-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto UNDERSTANDING THE DISCRETE ELEMENT METHOD SIMULATION OF NON-SPHERICAL PARTICLES FOR GRANULARAND MULTI-BODY SYSTEMS; Copright; Contents; Exercises; About the Authors; Preface; Acknowledgements; List of Abbreviations; 1 Mechanics; 1.1 Degrees of freedom; 1.1.1 Particle mechanics and constraints; 1.1.2 From point particles to rigid bodies; 1.1.3 More context and terminology; 1.2 Dynamics of rectilinear degrees of freedom; 1.3 Dynamics of angular degrees of freedom; 1.3.1 Rotation in two dimensions; 1.3.2 Moment of inertia; 1.3.3 From two to three dimensions
1.3.4 Rotation matrix in three dimensions1.3.5 Three-dimensional moments of inertia; 1.3.6 Space-fixed and body-fixed coordinate systems andequations of motion; 1.3.7 Problems with Euler angles; 1.3.8 Rotations represented using complex numbers; 1.3.9 Quaternions; 1.3.10 Derivation of quaternion dynamics; 1.4 The phase space; 1.4.1 Qualitative discussion of the time dependence of linear oscillations; 1.4.2 Resonance; 1.4.3 The flow in phase space; 1.5 Nonlinearities; 1.5.1 Harmonic balance; 1.5.2 Resonance in nonlinear systems; 1.5.3 Higher harmonics and frequency mixing
1.5.4 The van der Pol oscillator1.6 From higher harmonics to chaos; 1.6.1 The bifurcation cascade; 1.6.2 The nonlinear frictional oscillator and Poincar ́e maps; 1.6.3 The route to chaos; 1.6.4 Boundary conditions and many-particle systems; 1.7 Stability and conservationlaws; 1.7.1 Stability in statics; 1.7.2 Stability in dynamics; 1.7.3 Stable axes of rotation around the principal axis; 1.7.4 Noether's theorem and conservation laws; 1.8 Further reading; Exercises; References; 2Numerical Integration of OrdinaryDifferential Equations; 2.1 Fundamentals of numerical analysis
2.1.1 Floating point numbers2.1.2 Big-O notation; 2.1.3 Relative and absolute error; 2.1.4 Truncation error; 2.1.5 Local and global error; 2.1.6 Stability; 2.1.7 Stable integrators for unstable problems; 2.2 Numerical analysis for ordinary differential equations; 2.2.1 Variable notation and transformation of the order of adifferential equation; 2.2.2 Differences in the simulation of atoms and molecules,as compared to macroscopic particles; 2.2.3 Truncation error for solutions of ordinary differential equations; 2.2.4 Fundamental approaches; 2.2.5 Explicit Euler method
2.2.6 Implicit Euler method2.3 Runge-Kutta methods; 2.3.1 Adaptive step-size control; 2.3.2 Dense output and event location; 2.3.3 Partitioned Runge-Kutta methods; 2.4 Symplectic methods; 2.4.1 The classical Verlet method; 2.4.2 Velocity-Verlet methods; 2.4.3 Higher-order velocity-Verlet methods; 2.4.4 Pseudo-symplectic methods; 2.4.5 Order, accuracy and energy conservation; 2.4.6 Backward error analysis; 2.4.7 Case study: the harmonic oscillator with andwithout viscous damping; 2.5 Stiff problems; 2.5.1 Evaluating computational costs; 2.5.2 Stiff solutions and error as noise
2.5.3 Order reduction
Record Nr. UNINA-9910821695203321
Matuttis Hans-Georg  
Singapore : , : Wiley, , 2014
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui