# 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 $\mathbf s = \mathbf z - [ \mathbf y \mathbf x ]$.

#### 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)