Rotation indicatrix

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rotation diagram

One of the twelve Darboux surfaces associated with the infinitesimal deformation of a surface. It is the set of points in space described by a position vector $ \mathbf y $ which are parallel to the rotation vector (instantaneous angular velocity) defined by the equation $ d \mathbf z = [ \mathbf y d \mathbf x ] $, where $ \mathbf z $ is the velocity vector of the infinitesimal deformation of the surface described by the position vector $ \mathbf x $. The displacement indicatrix (displacement diagram) is defined in a similar manner by the displacement vector $ \mathbf s = \mathbf z - [ \mathbf y \mathbf x ] $.


[1] N.V. Efimov, "Qualitative questions of the theory of deformations of surfaces" Uspekhi Mat. Nauk , 3 : 2 (1948) pp. 47–158 (In Russian)
[2] S.E. Cohn-Vossen, "Some problems of differential geometry in the large" , Moscow (1959) (In Russian)
[a1] G. Darboux, "Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal" , 1–4 , Chelsea, reprint (1972) Zbl 0257.53001
[a2] M. Spivak, "A comprehensive introduction to differential geometry" , 1979 , Publish or Perish pp. 1–5
[a3] N.V. Efimov, "Qualitative problems of the theory of deformation of surfaces" , Amer. Math. Soc. (1951) (Translated from Russian)
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Rotation indicatrix. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article