Fundamentals of Fluid-Solid Interactions-Analytical and

Contents
Preface vii
Chapter 1. Introduction 1
1.1. Historical background 1
1.2. Motivation 3
1.3. Outline 4
Chapter 2. Aspects of Mathematics and Mechanics 5
2.1. Preliminary concepts and notations 5
2.1.1 Logic; set, group, and field; Boolean algebra 5
2.1.2 Mapping and linear space; grad, div, and curl 9
2.1.3 Tensors and curvilinear coordinates; complex variables 15
2.1.4 Eigenvalues and eigenvectors; singular value decomposition 25
2.2. Kinematical descriptions and conservation laws 31
2.2.1 Mass point and rigid body; continuum 32
2.2.2 Vector calculus; transport theorems and conservation laws;
variational principles 37
2.3. Some mathematical tools 52
2.3.1 Fourier series and transform; Laplace transform 52
2.3.2 Contour integral; conformal mapping 58
2.3.3 Sturm–Liouville problems; Frobenius’ methods and special
functions 71
Chapter 3. Dynamical Systems 85
3.1. Single- and multi-degree of freedom systems 86
3.1.1 Basic concepts; limit sets 86
3.1.2 Bifurcations; Lagrangian dynamics 100
3.1.3 Van der Pol; perturbation method; Duffing 112
3.2. Lyapunov–Schmidt method 126
3.2.1 Floquet theory 129
3.2.2 Critical time step 133
3.2.3 Mathieu–Hill system 136
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