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This book provides a comprehensive survey of analytic and approximate solutions of problems of applied mechanics, with particular emphasis on nonconservative phenomena. Include
Variational Methods in Nonconservative Phenomena
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Contents
Preface
Chapter 1. A Brief Account of the Variational Principles of Classical Holonomic Dynamics
1.1 Introduction
1.2 Constraints and the Forces of Constraint
1.3 Actual and Virtual Displacements
1.4 D' Alembert's Principle
1.5 The Lagrangian Equations with Multipliers
1.6 Generalized Coordinates. Lagrangian Equations
1.7 A Brief Analysis of the Lagrangian Equations
1.8 Hamilton's Principle
1.9 Variational Principles Describing the Paths of Conservative Dynamical Systems
1.10 Some Elementary Examples Involving Integral Variational Principles
1.11 References
Chapter 2. Variational Principles and Lagrangians
2.1 Introduction
2.2 Lagrangians for Systems with One Degree of Freedom
2.3 Quadratic Lagrangians for Systems with One Degree of Freedom
2.4 Some Other Lagrangians
2.5 The Inverse Problem of the Calculus of Variations
2.6 Partial Differential Equations
2.7 Lagrangians with Vanishing Parameters
2.8 Other Variational Principles
2.9 References
Chapter 3. Conservation Laws
3.1 Introduction
3.2 Simultaneous and Nonsimultaneous Variations. Infinitesimal Transformations
3.3 The Condition of Invariance of Hamilton's Action Integral. Absolute and Gauge Invariance
3.4 The Proof of Noether's Theorem. Conservation Laws
3.5 The Inertial Motion of a Dynamical System. Killing's Equations
3.6 The Generalized Killing Equations
3.7 Some Classical Conservation Laws of Dynamical Systems Completely Described by a Lagrangian Function
3.8 Examples of Conservation Laws of Dynamical Systems
3.9 Some Conservation Laws for the Kepler Problem
3.10 Inclusion of Generalized Nonconservative Forces in the Search for Conservation Laws. D'Alembert's Principle
3.11 Inclusion of Nonsimultaneous Variations into the Central Lagrangian Equation
3.12 The Conditions for Existence of a Conserved Quantity. Conservation Laws of Nonconservative Dynamical Systems
3.13 The Generalized Killing Equations for Nonconservative Dynamical Systems
3.14 Conservation Laws of Nonconservative Systems Obtained by Means of Variational Principles with Noncommutative Variational Rules
3.15 Conservation Laws of Conservative and Nonconservative Dynamical Systems Obtained by Means of the Differential Variational Principles of Gauss and Jourdain
3.16 Jourdainian and Gaussian Nonsimultaneous Variations
3.17 The Invariance Condition of the Gauss Constraint
3.18 An Equivalent Transformation of Jourdain's Principle
3.19 The Conservation Laws of Schul'gin and Painlevé
3.20 Energy-Like Conservation Laws of Linear Nonconservative Dynamical Systems
3.21 Energy-Like Conservation Laws of Linear Dissipative Dynamical Systems
3.22 A Special Class of Conservation Laws
3.23 References
Chapter 4. A Study of the Motion of Conservative and Nonconservative Dynamical Systems by Means of Field Theory
4.1 Introduction
4.2 Hamilton's Canonical Equations of Motion
4.3 Integration of Hamilton's Canonical Equations by Means of the Hamilton–Jacobi Method
4.4 Separation of Variables in the Hamilton-Jacobi Equation
4.5 Application of the Hamilton–Jacobi Method to Linear Nonconservative Oscillatory Systems
4.6 A Field Method for Nonconservative Dynamical Systems
4.7 The Complete Solutions of the Basic Field Equation and Their Properties
4.8 The Single Solutions of the Basic Field Equation
4.9 Illustrative Examples
4.10 Applications of the Complete Solutions of the Basic Field Equation to Two-Point Boundary-value Problems
4.11 The Potential Method of Arzhanik'h for Nonconservative Dynamical Systems
4.12 Applications of the Field Method to Nonlinear Vibration Problems
4.13 A Linear Oscillator with Slowly Varying Frequency
4.14 References
Chapter 5. Variational Principles with Vanishing Parameters and Their Applications
5.1 Introduction
5.2 A Short Review of Some Variational Formulations Frequently Used in Nonconservative Field Theory
5.3 The Variational Principle with Vanishing Parameter
5.4 Application of the Direct Method of Partial Integration to the Solution of Linear and Nonlinear Boundary-Value Problems
5.5 An Example: A Semi-Infinite Body with a Constant Heat Flux Input
5.6 A Semi-Infinite Body with an Arbitrary Heat Flux Input
5.7 The Temperature Distribution in a Body Whose End is Kept at Constant Temperature, Temperature-Dependent Thermophysical Coefficients
5.8 The Moment–Lagrangian Method
5.9 The Temperature Distribution in a Finite Rod with a Nonzero Initial Temperature Distribution
5.10 The Temperature Distribution in a Noninsulated Solid
5.11 Applications to Laminar Boundary Layer Theory
5.12 Applications to Two-Dimensional Boundary Layer Flow of Incompressible, Non-Newtonian Power-Law Fluids
5.13 A Variational Solution of the Rayleigh Problem for a Non-Newtonian Power-Law Conducting Fluid
5.14 References
Chapter 6. Variational Principles with Uncommutative Rules and Their Applications to Nonconservative Phenomena
6.1 Introduction
6.2 The Variational Principle with Uncommutative Rules
6.3 The Connection (Relation) between the Variational Principle with Uncommutative Rules and the Central Lagrangian Equation
6.4 The Bogoliubov–Krylov–Mitropolsky Method in Nonlinear Vibration Analysis as a Variational Problem
6.5 Applications to Heat Conduction in Solids
6.6 References
Chapter 7. Applications of Gauss's Principle of Least Constraint to Nonconservative Phenomena
7.1 Introduction
7.2 Methods of Approximation Based on the Gauss Principle of Least Constraint
7.3 Applications to Ordinary Differential Equations
7.4 Applications to Transient, Two-Dimensional, Nonlinear Heat Conduction through Prism-Like Infinite Bodies with a Given Cross Section
7.5 Melting or Freezing of a Semi-Infinite Solid
7.6 A Semi-Infinite Solid with an Arbitrary Heat Flux Input: Gauss's Approach
7.7 A Nonconservative Convective Problem
7.8 References
Author Index
Index
Mathematics in Science and Engineering
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This book provides a comprehensive survey of analytic and approximate solutions of problems of applied mechanics, with particular emphasis on nonconservative phenomena. Include
<span>Libro usado en buenas condiciones, por su antiguedad podria contener señales normales de uso</span>
<span>In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-L