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Motion of Vortex Filaments
https://doi.org/10.1142/9789812565747_0009Cited by:0 (Source: Crossref)
Abstract:
The following sections are included:
A Vortex Filament
Filament Equation
Basic Properties
Left-invariance and right-invariance
Landau–Lifshitz equation
Lie–Poisson bracket and Hamilton's equation
Metric and loop algebra
Geometrical Formulation and Geodesic Equation
Vortex Filaments as a Bi-Invariant System
Circular vortex filaments
General vortex filaments
Integral invariants
Killing Fields on Vortex Filaments
A rectilinear vortex
A circular vortex
A helical vortex
Sectional Curvature and Geodesic Stability
Killing fields
General tangent field X
Central Extension of the Algebra of Filament Motion
