Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
The calculus of variations and functional analysis [[electronic resource] ] : with optimal control and applications in mechanics / / Leonid P. Lebedev, Michael J. Cloud
| The calculus of variations and functional analysis [[electronic resource] ] : with optimal control and applications in mechanics / / Leonid P. Lebedev, Michael J. Cloud |
| Autore | Lebedev L. P |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (435 p.) |
| Disciplina | 515.7 |
| Altri autori (Persone) | CloudMichael J |
| Collana | Series on stability, vibration, and control of systems. Series A |
| Soggetto topico |
Functional analysis
Mechanics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-93546-8
9786611935467 981-279-499-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Preface; Contents; 1. Basic Calculus of Variations; 1.1 Introduction; 1.2 Euler's Equation for the Simplest Problem; 1.3 Some Properties of Extremals of the Simplest Functional; 1.4 Ritz's Method; 1.5 Natural Boundary Conditions; 1.6 Some Extensions to More General Functionals; 1.7 Functionals Depending on Functions in Many Variables; 1.8 A Functional with Integrand Depending on Partial Derivatives of Higher Order; 1.9 The First Variation; 1.10 Isoperimetric Problems; 1.11 General Form of the First Variation; 1.12 Movable Ends of Extremals
1.13 Weierstrass-Erdmann Conditions and Related Problems1.14 Sufficient Conditions for Minimum; 1.15 Exercises; 2. Elements of Optimal Control Theory; 2.1 A Variational Problem as a Problem of Optimal Control; 2.2 General Problem of Optimal Control; 2.3 Simplest Problem of Optimal Control; 2.4 Fundamental Solution of a Linear Ordinary Differential Equation; 2.5 The Simplest Problem Continued; 2.6 Pontryagin's Maximum Principle for the Simplest Problem; 2.7 Some Mathematical Preliminaries; 2.8 General Terminal Control Problem; 2.9 Pontryagin's Maximum Principle for the Terminal Optimal Problem 2.10 Generalization of the Terminal Control Problem2.11 Small Variations of Control Function for Terminal Control Problem; 2.12 A Discrete Version of Small Variations of Control Function for Generalized Terminal Control Problem; 2.13 Optimal Time Control Problems; 2.14 Final Remarks on Control Problems; 2.15 Exercises; 3. Functional Analysis; 3.1 A Normed Space as a Metric Space; 3.2 Dimension of a Linear Space and Separability; 3.3 Cauchy Sequences and Banach Spaces; 3.4 The Completion Theorem; 3.5 Contraction Mapping Principle; 3.6 Lp Spaces and the Lebesgue Integral; 3.7 Sobolev Spaces 3.8 Compactness3.9 Inner Product Spaces Hilbert Spaces; 3.10 Some Energy Spaces in Mechanics; 3.11 Operators and Functional; 3.12 Some Approximation Theory; 3.13 Orthogonal Decomposition of a Hilbert Space and the Riesz Representation Theorem; 3.14 Basis Gram-Schmidt Procedure Fourier Series in Hilbert Space; 3.15 Weak Convergence; 3.16 Adjoint and Self-adjoint Operators; 3.17 Compact Operators; 3.18 Closed Operators; 3.19 Introduction to Spectral Concepts; 3.20 The Fredholm Theory in Hilbert Spaces; 3.21 Exercises; 4. Some Applications in Mechanics 4.1 Some Problems of Mechanics from the Viewpoint of the Calculus of Variations the Virtual Work Principle; 4.2 Equilibrium Problem for a Clamped Membrane and its Generalized Solution; 4.3 Equilibrium of a Free Membrane; 4.4 Some Other Problems of Equilibrium of Linear Mechanics; 4.5 The Ritz and Bubnov-Galerkin Methods; 4.6 The Hamilton-Ostrogradskij Principle and the Generalized Setup of Dynamical Problems of Classical Mechanics; 4.7 Generalized Setup of Dynamic Problems for a Membrane; 4.8 Other Dynamic Problems of Linear Mechanics; 4.9 The Fourier Method 4.10 An Eigenfrequency Boundary Value Problem Arising in Linear Mechanics |
| Record Nr. | UNINA-9910454312903321 |
Lebedev L. P
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The calculus of variations and functional analysis [[electronic resource] ] : with optimal control and applications in mechanics / / Leonid P. Lebedev, Michael J. Cloud
| The calculus of variations and functional analysis [[electronic resource] ] : with optimal control and applications in mechanics / / Leonid P. Lebedev, Michael J. Cloud |
| Autore | Lebedev L. P |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (435 p.) |
| Disciplina | 515.7 |
| Altri autori (Persone) | CloudMichael J |
| Collana | Series on stability, vibration, and control of systems. Series A |
| Soggetto topico |
Functional analysis
Mechanics |
| ISBN |
1-281-93546-8
9786611935467 981-279-499-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Preface; Contents; 1. Basic Calculus of Variations; 1.1 Introduction; 1.2 Euler's Equation for the Simplest Problem; 1.3 Some Properties of Extremals of the Simplest Functional; 1.4 Ritz's Method; 1.5 Natural Boundary Conditions; 1.6 Some Extensions to More General Functionals; 1.7 Functionals Depending on Functions in Many Variables; 1.8 A Functional with Integrand Depending on Partial Derivatives of Higher Order; 1.9 The First Variation; 1.10 Isoperimetric Problems; 1.11 General Form of the First Variation; 1.12 Movable Ends of Extremals
1.13 Weierstrass-Erdmann Conditions and Related Problems1.14 Sufficient Conditions for Minimum; 1.15 Exercises; 2. Elements of Optimal Control Theory; 2.1 A Variational Problem as a Problem of Optimal Control; 2.2 General Problem of Optimal Control; 2.3 Simplest Problem of Optimal Control; 2.4 Fundamental Solution of a Linear Ordinary Differential Equation; 2.5 The Simplest Problem Continued; 2.6 Pontryagin's Maximum Principle for the Simplest Problem; 2.7 Some Mathematical Preliminaries; 2.8 General Terminal Control Problem; 2.9 Pontryagin's Maximum Principle for the Terminal Optimal Problem 2.10 Generalization of the Terminal Control Problem2.11 Small Variations of Control Function for Terminal Control Problem; 2.12 A Discrete Version of Small Variations of Control Function for Generalized Terminal Control Problem; 2.13 Optimal Time Control Problems; 2.14 Final Remarks on Control Problems; 2.15 Exercises; 3. Functional Analysis; 3.1 A Normed Space as a Metric Space; 3.2 Dimension of a Linear Space and Separability; 3.3 Cauchy Sequences and Banach Spaces; 3.4 The Completion Theorem; 3.5 Contraction Mapping Principle; 3.6 Lp Spaces and the Lebesgue Integral; 3.7 Sobolev Spaces 3.8 Compactness3.9 Inner Product Spaces Hilbert Spaces; 3.10 Some Energy Spaces in Mechanics; 3.11 Operators and Functional; 3.12 Some Approximation Theory; 3.13 Orthogonal Decomposition of a Hilbert Space and the Riesz Representation Theorem; 3.14 Basis Gram-Schmidt Procedure Fourier Series in Hilbert Space; 3.15 Weak Convergence; 3.16 Adjoint and Self-adjoint Operators; 3.17 Compact Operators; 3.18 Closed Operators; 3.19 Introduction to Spectral Concepts; 3.20 The Fredholm Theory in Hilbert Spaces; 3.21 Exercises; 4. Some Applications in Mechanics 4.1 Some Problems of Mechanics from the Viewpoint of the Calculus of Variations the Virtual Work Principle; 4.2 Equilibrium Problem for a Clamped Membrane and its Generalized Solution; 4.3 Equilibrium of a Free Membrane; 4.4 Some Other Problems of Equilibrium of Linear Mechanics; 4.5 The Ritz and Bubnov-Galerkin Methods; 4.6 The Hamilton-Ostrogradskij Principle and the Generalized Setup of Dynamical Problems of Classical Mechanics; 4.7 Generalized Setup of Dynamic Problems for a Membrane; 4.8 Other Dynamic Problems of Linear Mechanics; 4.9 The Fourier Method 4.10 An Eigenfrequency Boundary Value Problem Arising in Linear Mechanics |
| Record Nr. | UNINA-9910782117403321 |
|
Lebedev L. P
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The calculus of variations and functional analysis [[electronic resource] ] : with optimal control and applications in mechanics / / Leonid P. Lebedev, Michael J. Cloud
| The calculus of variations and functional analysis [[electronic resource] ] : with optimal control and applications in mechanics / / Leonid P. Lebedev, Michael J. Cloud |
| Autore | Lebedev L. P |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (435 p.) |
| Disciplina | 515.7 |
| Altri autori (Persone) | CloudMichael J |
| Collana | Series on stability, vibration, and control of systems. Series A |
| Soggetto topico |
Functional analysis
Mechanics |
| ISBN |
1-281-93546-8
9786611935467 981-279-499-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Preface; Contents; 1. Basic Calculus of Variations; 1.1 Introduction; 1.2 Euler's Equation for the Simplest Problem; 1.3 Some Properties of Extremals of the Simplest Functional; 1.4 Ritz's Method; 1.5 Natural Boundary Conditions; 1.6 Some Extensions to More General Functionals; 1.7 Functionals Depending on Functions in Many Variables; 1.8 A Functional with Integrand Depending on Partial Derivatives of Higher Order; 1.9 The First Variation; 1.10 Isoperimetric Problems; 1.11 General Form of the First Variation; 1.12 Movable Ends of Extremals
1.13 Weierstrass-Erdmann Conditions and Related Problems1.14 Sufficient Conditions for Minimum; 1.15 Exercises; 2. Elements of Optimal Control Theory; 2.1 A Variational Problem as a Problem of Optimal Control; 2.2 General Problem of Optimal Control; 2.3 Simplest Problem of Optimal Control; 2.4 Fundamental Solution of a Linear Ordinary Differential Equation; 2.5 The Simplest Problem Continued; 2.6 Pontryagin's Maximum Principle for the Simplest Problem; 2.7 Some Mathematical Preliminaries; 2.8 General Terminal Control Problem; 2.9 Pontryagin's Maximum Principle for the Terminal Optimal Problem 2.10 Generalization of the Terminal Control Problem2.11 Small Variations of Control Function for Terminal Control Problem; 2.12 A Discrete Version of Small Variations of Control Function for Generalized Terminal Control Problem; 2.13 Optimal Time Control Problems; 2.14 Final Remarks on Control Problems; 2.15 Exercises; 3. Functional Analysis; 3.1 A Normed Space as a Metric Space; 3.2 Dimension of a Linear Space and Separability; 3.3 Cauchy Sequences and Banach Spaces; 3.4 The Completion Theorem; 3.5 Contraction Mapping Principle; 3.6 Lp Spaces and the Lebesgue Integral; 3.7 Sobolev Spaces 3.8 Compactness3.9 Inner Product Spaces Hilbert Spaces; 3.10 Some Energy Spaces in Mechanics; 3.11 Operators and Functional; 3.12 Some Approximation Theory; 3.13 Orthogonal Decomposition of a Hilbert Space and the Riesz Representation Theorem; 3.14 Basis Gram-Schmidt Procedure Fourier Series in Hilbert Space; 3.15 Weak Convergence; 3.16 Adjoint and Self-adjoint Operators; 3.17 Compact Operators; 3.18 Closed Operators; 3.19 Introduction to Spectral Concepts; 3.20 The Fredholm Theory in Hilbert Spaces; 3.21 Exercises; 4. Some Applications in Mechanics 4.1 Some Problems of Mechanics from the Viewpoint of the Calculus of Variations the Virtual Work Principle; 4.2 Equilibrium Problem for a Clamped Membrane and its Generalized Solution; 4.3 Equilibrium of a Free Membrane; 4.4 Some Other Problems of Equilibrium of Linear Mechanics; 4.5 The Ritz and Bubnov-Galerkin Methods; 4.6 The Hamilton-Ostrogradskij Principle and the Generalized Setup of Dynamical Problems of Classical Mechanics; 4.7 Generalized Setup of Dynamic Problems for a Membrane; 4.8 Other Dynamic Problems of Linear Mechanics; 4.9 The Fourier Method 4.10 An Eigenfrequency Boundary Value Problem Arising in Linear Mechanics |
| Record Nr. | UNINA-9910809295403321 |
|
Lebedev L. P
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Functional analysis : applications in mechanics and inverse problems
| Functional analysis : applications in mechanics and inverse problems |
| Autore | Lebedev L. P |
| Edizione | [2nd Edition.] |
| Pubbl/distr/stampa | Dordrecht : , : Springer Netherlands, , 2002 |
| Descrizione fisica | 1 online resource (X, 254 p.) |
| Disciplina | 515/.7 |
| Collana | Solid mechanics and its applications Functional analysis |
| Soggetto topico | Functional analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-61907-4
9786610619078 0-306-48397-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | to Metric Spaces -- Energy Spaces and Generalized Solutions -- Approximation in a Normed Linear Space -- Elements of the Theory of Linear Operators -- Compactness and Its Consequences -- Spectral Theory of Linear Operators -- Applications to Inverse Problems. |
| Record Nr. | UNINA-9910449961103321 |
|
Lebedev L. P
|
||
| Dordrecht : , : Springer Netherlands, , 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Functional analysis : applications in mechanics and inverse problems
| Functional analysis : applications in mechanics and inverse problems |
| Autore | Lebedev L. P |
| Edizione | [2nd Edition.] |
| Pubbl/distr/stampa | Dordrecht : , : Springer Netherlands, , 2002 |
| Descrizione fisica | 1 online resource (X, 254 p.) |
| Disciplina | 515/.7 |
| Collana | Solid mechanics and its applications Functional analysis |
| Soggetto topico | Functional analysis |
| ISBN |
1-280-61907-4
9786610619078 0-306-48397-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | to Metric Spaces -- Energy Spaces and Generalized Solutions -- Approximation in a Normed Linear Space -- Elements of the Theory of Linear Operators -- Compactness and Its Consequences -- Spectral Theory of Linear Operators -- Applications to Inverse Problems. |
| Record Nr. | UNINA-9910783382703321 |
|
Lebedev L. P
|
||
| Dordrecht : , : Springer Netherlands, , 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Functional analysis : applications in mechanics and inverse problems
| Functional analysis : applications in mechanics and inverse problems |
| Autore | Lebedev L. P |
| Edizione | [2nd Edition.] |
| Pubbl/distr/stampa | Dordrecht : , : Springer Netherlands, , 2002 |
| Descrizione fisica | 1 online resource (X, 254 p.) |
| Disciplina | 515/.7 |
| Collana | Solid mechanics and its applications Functional analysis |
| Soggetto topico | Functional analysis |
| ISBN |
1-280-61907-4
9786610619078 0-306-48397-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | to Metric Spaces -- Energy Spaces and Generalized Solutions -- Approximation in a Normed Linear Space -- Elements of the Theory of Linear Operators -- Compactness and Its Consequences -- Spectral Theory of Linear Operators -- Applications to Inverse Problems. |
| Record Nr. | UNINA-9910826743003321 |
|
Lebedev L. P
|
||
| Dordrecht : , : Springer Netherlands, , 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to mathematical elasticity [[electronic resource] /] / Leonid P. Lebedev, Michael J. Cloud
| Introduction to mathematical elasticity [[electronic resource] /] / Leonid P. Lebedev, Michael J. Cloud |
| Autore | Lebedev L. P |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (317 p.) |
| Disciplina |
531.382
531.3820151 531/.3820151 |
| Altri autori (Persone) | CloudMichael J |
| Soggetto topico | Elasticity |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-75812-8
9786612758126 981-4273-73-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Foreword; Preface; Some Notation; 1. Models and Ideas of Classical Mechanics; 1.1 Orientation; 1.2 Some Words on the Fundamentals of Our Subject; 1.3 Metric Spaces and Spaces of Particles; 1.4 Vectors and Vector Spaces; 1.5 Normed Spaces and Inner Product Spaces; 1.6 Forces; 1.7 Equilibrium and Motion of a Rigid Body; 1.8 D'Alembert's Principle; 1.9 The Motion of a System of Particles; 1.10 The Rigid Body; 1.11 Motion of a System of Particles; Comparison of Trajectories; Notion of Operator; 1.12 Matrix Operators and Matrix Equations; 1.13 Complete Spaces; 1.14 Completion Theorem
1.15 Lebesgue Integration and the Lp Spaces1.16 Orthogonal Decomposition of Hilbert Space; 1.17 Work and Energy; 1.18 Virtual Work Principle; 1.19 Lagrange's Equations of the Second Kind; 1.20 Problem of Minimum of a Functional; 1.21 Hamilton's Principle; 1.22 Energy Conservation Revisited; 2. Simple Elastic Models; 2.1 Introduction; 2.2 Two Main Principles of Equilibrium and Motion for Bodies in Continuum Mechanics; 2.3 Equilibrium of a Spring; 2.4 Equilibrium of a String; 2.5 Equilibrium Boundary Value Problems for a String 2.6 Generalized Formulation of the Equilibrium Problem for a String2.7 Virtual Work Principle for a String; 2.8 Riesz Representation Theorem; 2.9 Generalized Setup of the Dirichlet Problem for a String; 2.10 First Theorems of Imbedding; 2.11 Generalized Setup of the Dirichlet Problem for a String, Continued; 2.12 Neumann Problem for the String; 2.13 The Generalized Solution of Linear Mechanical Problems and the Principle of Minimum Total Energy; 2.14 Nonlinear Model of a Membrane; 2.15 Linear Membrane Theory: Poisson's Equation 2.16 Generalized Setup of the Dirichlet Problem for a Linear Membrane2.17 Other Membrane Equilibrium Problems; 2.18 Banach's Contraction Mapping Principle; 3. Theory of Elasticity: Statics and Dynamics; 3.1 Introduction; 3.2 An Elastic Bar Under Stretching; 3.3 Bending of a beam; 3.4 Generalized Solutions to the Equilibrium Problem for a Beam; 3.5 Generalized Setup: Rough Qualitative Discussion; 3.6 Pressure and Stresses; 3.7 Vectors and Tensors; 3.8 The Cauchy Stress Tensor, Continued; 3.9 Basic Tensor Calculus in Curvilinear Coordinates; 3.10 Euler and Lagrange Descriptions of Continua 3.11 Strain Tensors3.12 The Virtual Work Principle; 3.13 Hooke's Law in Three Dimensions; 3.14 The Equilibrium Equations of Linear Elasticity in Displacements; 3.15 Virtual Work Principle in Linear Elasticity; 3.16 Generalized Setup of Elasticity Problems; 3.17 Existence Theorem for an Elastic Body; 3.18 Equilibrium of a Free Elastic Body; 3.19 Variational Methods for Equilibrium Problems; 3.20 A Brief but Important Remark; 3.21 Countable Sets and Separable Spaces; 3.22 Fourier Series; 3.23 Problem of Vibration for Elastic Structures; 3.24 Self-Adjointness of A and Its Consequences 3.25 Compactness of A |
| Record Nr. | UNINA-9910455858903321 |
|
Lebedev L. P
|
||
| Hackensack, N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to mathematical elasticity [[electronic resource] /] / Leonid P. Lebedev, Michael J. Cloud
| Introduction to mathematical elasticity [[electronic resource] /] / Leonid P. Lebedev, Michael J. Cloud |
| Autore | Lebedev L. P |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (317 p.) |
| Disciplina |
531.382
531.3820151 531/.3820151 |
| Altri autori (Persone) | CloudMichael J |
| Soggetto topico | Elasticity |
| ISBN |
1-282-75812-8
9786612758126 981-4273-73-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Foreword; Preface; Some Notation; 1. Models and Ideas of Classical Mechanics; 1.1 Orientation; 1.2 Some Words on the Fundamentals of Our Subject; 1.3 Metric Spaces and Spaces of Particles; 1.4 Vectors and Vector Spaces; 1.5 Normed Spaces and Inner Product Spaces; 1.6 Forces; 1.7 Equilibrium and Motion of a Rigid Body; 1.8 D'Alembert's Principle; 1.9 The Motion of a System of Particles; 1.10 The Rigid Body; 1.11 Motion of a System of Particles; Comparison of Trajectories; Notion of Operator; 1.12 Matrix Operators and Matrix Equations; 1.13 Complete Spaces; 1.14 Completion Theorem
1.15 Lebesgue Integration and the Lp Spaces1.16 Orthogonal Decomposition of Hilbert Space; 1.17 Work and Energy; 1.18 Virtual Work Principle; 1.19 Lagrange's Equations of the Second Kind; 1.20 Problem of Minimum of a Functional; 1.21 Hamilton's Principle; 1.22 Energy Conservation Revisited; 2. Simple Elastic Models; 2.1 Introduction; 2.2 Two Main Principles of Equilibrium and Motion for Bodies in Continuum Mechanics; 2.3 Equilibrium of a Spring; 2.4 Equilibrium of a String; 2.5 Equilibrium Boundary Value Problems for a String 2.6 Generalized Formulation of the Equilibrium Problem for a String2.7 Virtual Work Principle for a String; 2.8 Riesz Representation Theorem; 2.9 Generalized Setup of the Dirichlet Problem for a String; 2.10 First Theorems of Imbedding; 2.11 Generalized Setup of the Dirichlet Problem for a String, Continued; 2.12 Neumann Problem for the String; 2.13 The Generalized Solution of Linear Mechanical Problems and the Principle of Minimum Total Energy; 2.14 Nonlinear Model of a Membrane; 2.15 Linear Membrane Theory: Poisson's Equation 2.16 Generalized Setup of the Dirichlet Problem for a Linear Membrane2.17 Other Membrane Equilibrium Problems; 2.18 Banach's Contraction Mapping Principle; 3. Theory of Elasticity: Statics and Dynamics; 3.1 Introduction; 3.2 An Elastic Bar Under Stretching; 3.3 Bending of a beam; 3.4 Generalized Solutions to the Equilibrium Problem for a Beam; 3.5 Generalized Setup: Rough Qualitative Discussion; 3.6 Pressure and Stresses; 3.7 Vectors and Tensors; 3.8 The Cauchy Stress Tensor, Continued; 3.9 Basic Tensor Calculus in Curvilinear Coordinates; 3.10 Euler and Lagrange Descriptions of Continua 3.11 Strain Tensors3.12 The Virtual Work Principle; 3.13 Hooke's Law in Three Dimensions; 3.14 The Equilibrium Equations of Linear Elasticity in Displacements; 3.15 Virtual Work Principle in Linear Elasticity; 3.16 Generalized Setup of Elasticity Problems; 3.17 Existence Theorem for an Elastic Body; 3.18 Equilibrium of a Free Elastic Body; 3.19 Variational Methods for Equilibrium Problems; 3.20 A Brief but Important Remark; 3.21 Countable Sets and Separable Spaces; 3.22 Fourier Series; 3.23 Problem of Vibration for Elastic Structures; 3.24 Self-Adjointness of A and Its Consequences 3.25 Compactness of A |
| Record Nr. | UNINA-9910780722603321 |
|
Lebedev L. P
|
||
| Hackensack, N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to mathematical elasticity [[electronic resource] /] / Leonid P. Lebedev, Michael J. Cloud
| Introduction to mathematical elasticity [[electronic resource] /] / Leonid P. Lebedev, Michael J. Cloud |
| Autore | Lebedev L. P |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (317 p.) |
| Disciplina |
531.382
531.3820151 531/.3820151 |
| Altri autori (Persone) | CloudMichael J |
| Soggetto topico | Elasticity |
| ISBN |
1-282-75812-8
9786612758126 981-4273-73-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Foreword; Preface; Some Notation; 1. Models and Ideas of Classical Mechanics; 1.1 Orientation; 1.2 Some Words on the Fundamentals of Our Subject; 1.3 Metric Spaces and Spaces of Particles; 1.4 Vectors and Vector Spaces; 1.5 Normed Spaces and Inner Product Spaces; 1.6 Forces; 1.7 Equilibrium and Motion of a Rigid Body; 1.8 D'Alembert's Principle; 1.9 The Motion of a System of Particles; 1.10 The Rigid Body; 1.11 Motion of a System of Particles; Comparison of Trajectories; Notion of Operator; 1.12 Matrix Operators and Matrix Equations; 1.13 Complete Spaces; 1.14 Completion Theorem
1.15 Lebesgue Integration and the Lp Spaces1.16 Orthogonal Decomposition of Hilbert Space; 1.17 Work and Energy; 1.18 Virtual Work Principle; 1.19 Lagrange's Equations of the Second Kind; 1.20 Problem of Minimum of a Functional; 1.21 Hamilton's Principle; 1.22 Energy Conservation Revisited; 2. Simple Elastic Models; 2.1 Introduction; 2.2 Two Main Principles of Equilibrium and Motion for Bodies in Continuum Mechanics; 2.3 Equilibrium of a Spring; 2.4 Equilibrium of a String; 2.5 Equilibrium Boundary Value Problems for a String 2.6 Generalized Formulation of the Equilibrium Problem for a String2.7 Virtual Work Principle for a String; 2.8 Riesz Representation Theorem; 2.9 Generalized Setup of the Dirichlet Problem for a String; 2.10 First Theorems of Imbedding; 2.11 Generalized Setup of the Dirichlet Problem for a String, Continued; 2.12 Neumann Problem for the String; 2.13 The Generalized Solution of Linear Mechanical Problems and the Principle of Minimum Total Energy; 2.14 Nonlinear Model of a Membrane; 2.15 Linear Membrane Theory: Poisson's Equation 2.16 Generalized Setup of the Dirichlet Problem for a Linear Membrane2.17 Other Membrane Equilibrium Problems; 2.18 Banach's Contraction Mapping Principle; 3. Theory of Elasticity: Statics and Dynamics; 3.1 Introduction; 3.2 An Elastic Bar Under Stretching; 3.3 Bending of a beam; 3.4 Generalized Solutions to the Equilibrium Problem for a Beam; 3.5 Generalized Setup: Rough Qualitative Discussion; 3.6 Pressure and Stresses; 3.7 Vectors and Tensors; 3.8 The Cauchy Stress Tensor, Continued; 3.9 Basic Tensor Calculus in Curvilinear Coordinates; 3.10 Euler and Lagrange Descriptions of Continua 3.11 Strain Tensors3.12 The Virtual Work Principle; 3.13 Hooke's Law in Three Dimensions; 3.14 The Equilibrium Equations of Linear Elasticity in Displacements; 3.15 Virtual Work Principle in Linear Elasticity; 3.16 Generalized Setup of Elasticity Problems; 3.17 Existence Theorem for an Elastic Body; 3.18 Equilibrium of a Free Elastic Body; 3.19 Variational Methods for Equilibrium Problems; 3.20 A Brief but Important Remark; 3.21 Countable Sets and Separable Spaces; 3.22 Fourier Series; 3.23 Problem of Vibration for Elastic Structures; 3.24 Self-Adjointness of A and Its Consequences 3.25 Compactness of A |
| Record Nr. | UNINA-9910826606903321 |
|
Lebedev L. P
|
||
| Hackensack, N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Tensor analysis [[electronic resource] /] / Leonid P. Lebedev, Michael J. Cloud
| Tensor analysis [[electronic resource] /] / Leonid P. Lebedev, Michael J. Cloud |
| Autore | Lebedev L. P |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific Pub., c2003 |
| Descrizione fisica | 1 online resource (203 p.) |
| Disciplina | 515/.63 |
| Altri autori (Persone) | CloudMichael J |
| Soggetto topico | Calculus of tensors |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-87685-2
9786611876852 981-256-446-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Foreword; Preface; Contents; Chapter 1 Preliminaries; Chapter 2 Transformations and Vectors; Chapter 3 Tensors; Chapter 4 Tensor Fields; Chapter 5 Elements of Differential Geometry; Appendix A Formulary; Appendix B Hints and Answers; Bibliography; Index |
| Record Nr. | UNINA-9910449888303321 |
|
Lebedev L. P
|
||
| River Edge, NJ, : World Scientific Pub., c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
