View source for Rotation indicatrix

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''rotation diagram''

One of the twelve [[Darboux surfaces|Darboux surfaces]] associated with the [[Infinitesimal deformation|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====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  N.V. Efimov,   "Qualitative questions of the theory of deformations of surfaces"  ''Uspekhi Mat. Nauk'' , '''3''' :  2  (1948)  pp. 47–158  (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  S.E. Cohn-Vossen,   "Some problems of differential geometry in the large" , Moscow  (1959)  (In Russian)</TD></TR>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  G. Darboux,   "Leçons sur la théorie générale des surfaces et ses applications géométriques du calcul infinitésimal" , '''1–4''' , Chelsea, reprint  (1972)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  M. Spivak,   "A comprehensive introduction to differential geometry" , '''1979''' , Publish or Perish  pp. 1–5</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  N.V. Efimov,   "Qualitative problems of the theory of deformation of surfaces" , Amer. Math. Soc.  (1951)  (Translated from Russian)</TD></TR>
</table>