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 ] $.

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