Dynamically Coupled Rigid Body-Fluid Flow Systems

Preface
Contents
1 Kirchhoff's Insufficiently-Celebrated Equations of Motion
	1.1 Introduction
	1.2 Kirchhoff's Equations
	1.3 The Legacy of Kirchhoff's Equations
	1.4 The Geometric Mechanics of Kirchhoff's Equations
		1.4.1 The Euler–Lagrange and Hamilton's Equations in the Spatially-Fixed Frame
	1.5 Extending Kirchhoff's Model
		1.5.1 The Sum Poisson Bracket
2 The Addition of Vortices
	2.1 The Importance of Vorticity
	2.2 Singular Vortex Models
		2.2.1 The N-Point-Vortex Model
		2.2.2 The N Vortex Ring Model
3 Dynamically Coupled Rigid Body+Point Vortices in R2
	3.1 N-Point-Vortices and Stationary Rigid Boundaries: C. C. Lin's Problem
	3.2 N-Point-Vortices Dynamically Coupled with a Single Rigid Contour of Arbitrary Shape
		3.2.1 The Euler–Lagrange Equations in a Spatially-FixedFrame
		3.2.2 The Vortical Momenta and Reciprocity Relations
	3.3 N-Point-Vortices Dynamically Coupled with a Single Rigid Circular Contour
		3.3.1 The Half-Space Model
4 Dynamically Coupled Rigid Body+Vortex Rings in R3
	4.1 N Vortex Rings and a Single Stationary Rigid Boundary
	4.2 N Vortex Rings Dynamically Coupled with a Single Rigid Body of Arbitrary Shape
		4.2.1 The Euler–Lagrange Equations in a Spatially-FixedFrame
		4.2.2 The Vortical Momenta and Reciprocity Relations
	4.3 N Vortex Rings Dynamically Coupled with a Rigid Sphere
		4.3.1 The Axisymmetric Model of a Sphere and N CircularRings
5 Viscous Effects and Their Modeling
	5.1 System Momentum Balance Laws in the Viscous Setting
	5.2 Some Experimental and Numerical Work of Vortex Rings Colliding with Rigid Bodies
6 Miscellaneous Extensions
	6.1 Dynamically Coupled Rigid Body+free Surface
		6.1.1 A Free Surface Dynamically Coupled with a Completely Submerged Single Rigid Body of Arbitrary Shape
			6.1.1.1 Phase Space and Hamiltonian Formalism
	6.2 Dynamically Coupled N Rigid Bodies in the Absenceof Vorticity
		6.2.1 The Euler–Lagrange Equations in a Spatially-FixedFrame
	6.3 A Single Buoyant Rigid Body Above an Impermeable FlatBoundary
A Brief Introduction to Geometric Mechanics
B Leading Order Behavior of Velocity and Vector Potential Fields of a Curved Vortex Filament
C Hamiltonian Function and Vector Field in the Half-space Model for Np=2 Sh2006
References
Index