Intro -- 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.