Rotation indicatrix

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 ] $.

References

[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)