منابع مشابه
Straightening soliton curves
A canonical straightening process is described for soliton curves associated with the localized induction hierarchy. Following computer animated examples, the present topic is placed in the context of a larger theme: the soliton class is a natural setting for representation of diverse topological and geometrical behavior of curves and their motions. The constructions we describe here pertain to...
متن کاملGeodesics Between 3D Closed Curves Using Path-Straightening
In order to analyze shapes of continuous curves in R, we parameterize them by arc-length and represent them as curves on a unit two-sphere. We identify the subset denoting the closed curves, and study its differential geometry. To compute geodesics between any two such curves, we connect them with an arbitrary path, and then iteratively straighten this path using the gradient of an energy assoc...
متن کاملOn the Curve Straightening Flow of Inextensible, Open, Planar Curves
We consider the curve straightening flow of inextensible, open, planar curves generated by the Kirchhoff bending energy. It can be considered as a model for the motion of elastic, inextensible rods in a high friction regime. We derive governing equations, namely a semilinear fourth order parabolic equation for the indicatrix and a second order elliptic equation for the Lagrange multiplier. We p...
متن کاملMotion of Curves on Two Dimensional Surfaces and Soliton Equations
A connection is established between the soliton equations and curves moving in a three dimensional space V3. The sign of the selfinteracting terms of the soliton equations are related to the signature of V3. It is shown that there corresponds a moving curve to each soliton equations.
متن کاملNew connections between moving curves and soliton equations
Lamb has identified a certain class of moving space curves with soliton equations. We show that there are two other classes of curve evolution that may be so identified. Hence three distinct classes of curve evolution are associated with a given integrable equation. The nonlinear Schrödinger equation is used to illustrate this explicitly. PACS: 02.30.Jr, 02.40.Hw, 03.40.Kf, 75.10.Hk
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2001
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00166-x