منابع مشابه
Parametrization of Cosserat Equations
As a matter of fact, the solution space of many systems of ordinary differential (OD) or partial differential (PD) equations in engineering or mathematical physics ”can/cannot” be parametrized by a certain number of arbitrary functions behaving like ”potentials”. In view of the explicit examples to be met later on, it must be noticed that the parametrizing operator, though often of the first or...
متن کاملOn the General Analytical Solution of the Kinematic Cosserat Equations
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies...
متن کاملOn the parametrization of solutions of the Yang–Baxter equations
We study all five-, six-, and one eight-vertex type two-state solutions of the YangBaxter equations in the form A12B13C23 = C23B13A12, and analyze the interplay of the ‘gauge’ and ‘inversion’ symmetries of these solution. Starting with algebraic solutions, whose parameters have no specific interpretation, and then using these symmetries we can construct a parametrization where we can identify g...
متن کاملParametrization invariance and shape equations of elastic axisymmetric vesicles.
The issue of different parameterizations of the axisymmetric vesicle shape addressed by Hu Jian-Guo and Ou-Yang Zhong-Can [ Phys.Rev. E 47 (1993) 461 ] is reassesed, especially as it transpires through the corresponding Euler Lagrange equations of the associated elastic energy functional. It is argued that for regular, smooth contours of vesicles with spherical topology, different parameterizat...
متن کاملStable Integration of the Dynamic Cosserat Equations with Application to Hair Modeling
In this paper we propose a new method for stable numerical integration of the dynamic Cosserat equations for rods, which constitute a mechanical framework for the physically based modeling of slender structures like DNA strands, drill strings, marine cables or human hair. Our integration method is well-established in the field of structural dynamics and has the major advantage of unconditional ...
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ژورنال
عنوان ژورنال: Acta Mechanica
سال: 2010
ISSN: 0001-5970,1619-6937
DOI: 10.1007/s00707-010-0292-y