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Advances in Computational Dynamics of Particles, Materials and Structures : a Unified Approach.
Advanced Computational Dynamics of Particles, Materials, and Structures: A Unified Approach breaks new ground with its in-depth, detailed coverage of modern computational mechanics in particle and continuum dynamics. Kumar Tamma provides a unique blend of classical and innovative theoretical and com...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
John Wiley & Sons,
2012.
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| Edición: | 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Advances in Computational Dynamics of Particles, Materials and Structures; Contents; Preface; Acknowledgments; About the Authors; Chapter 1 Introduction; 1.1 Overview; 1.1.1 The Mechanics Underlying Computational Dynamics; 1.1.2 The Numerics Underlying Computational Dynamics in Space and Time; 1.2 Applications; Chapter 2 Mathematical Preliminaries; 2.1 Sets and Functions; 2.1.1 Sets; 2.1.2 Functions; 2.2 Vector Spaces; 2.2.1 Real Vector Spaces; 2.2.2 Linear Dependence and Independence of Vectors; 2.2.3 Euclidean n-Space; 2.2.4 Inner Product Space; 2.2.5 Metric Spaces; 2.2.6 Normed Space.
- 2.3 Matrix Algebra; 2.3.1 Determinant of a Coefficient Matrix; 2.3.2 Matrix Multiplication; 2.4 Vector Differential Calculus; 2.4.1 Scalar-Valued Functions of Multivariables; 2.4.2 Vector-Valued Functions of Multivariables; 2.5 Vector Integral Calculus; 2.5.1 Green's Theorem in the Plane; 2.5.2 Gauss's Theorem; 2.6 Mean Value Theorem; 2.6.1 Scalar Function of a Real Variable; 2.6.2 Scalar Function of Multivariables; 2.6.3 Vector Function of Multivariables; 2.7 Function Spaces; 2.7.1 Inner Product Space; 2.7.2 Normed Space; 2.7.3 Metric Space; 2.7.4 Lebesgue Space; 2.7.5 Banach Space.
- 2.7.6 Sobolev Space; 2.7.7 Hilbert Space; 2.8 Tensor Analysis; 2.8.1 Tensor Algebra; 2.8.2 Tensor Differential Calculus; 2.8.3 Tensor Integral Calculus; Exercises; Part 1 N-Body Dynamical Systems; Chapter 3 Classical Mechanics; 3.1 Newtonian Mechanics; 3.1.1 Newton's Laws of Motion; 3.1.2 Newton's Equations of Motion; 3.2 Lagrangian Mechanics; 3.2.1 Constraints; 3.2.2 Lagrangian Form of D'Alembert's Principle; 3.2.3 Configuration Space; 3.2.4 Generalized Coordinates; 3.2.5 Tangent Bundle; 3.2.6 Lagrange's Equations of Motion; 3.2.7 Kinetic Energy in Generalized Coordinates.
- 3.2.8 Lagrange Multiplier Method; 3.2.9 Autonomous Lagrangian Systems; 3.3 Hamiltonian Mechanics; 3.3.1 Phase Space; 3.3.2 Canonical Coordinates; 3.3.3 Cotangent Bundle; 3.3.4 Legendre Transformation; 3.3.5 Hamilton's Equations of Motion; 3.3.6 Autonomous Hamiltonian Systems; 3.3.7 Symplectic Manifold; Exercises; Chapter 4 Principle of Virtual Work; 4.1 Virtual Work in N-Body Dynamical Systems; 4.2 Vector Formalism: Newtonian Mechanics in N-Body Dynamical Systems; 4.3 Scalar Formalisms: Lagrangian and Hamiltonian Mechanics in N-Body Dynamical Systems; Exercises.
- Chapter 5 Hamilton's Principle and Hamilton's Law of Varying Action; 5.1 Introduction; 5.2 Variation of the Principal Function; 5.3 Calculus of Variations; 5.4 Hamilton's Principle; 5.5 Hamilton's Law of Varying Action; 5.5.1 Newtonian Mechanics; 5.5.2 Lagrangian Mechanics; 5.5.3 Hamiltonian Mechanics; Exercises; Chapter 6 Principle of Balance of Mechanical Energy; 6.1 Introduction; 6.2 Principle of Balance of Mechanical Energy; 6.3 Total Energy Representations and Framework in the Differential Calculus Setting; 6.3.1 Principle of Balance of Mechanical Energy: Conservative System.