Differential Geometry/Vector of Darboux

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We consider the rotation of the body formed by the three vectors t, p, and b. We define the rotation vector d as follows:

  1. d is in the direction of the axis of rotation.
  2. d points in the direction such that the rotation is clockwise in that direction.
  3. |d| has the value of the angular velocity of the rigid body, or the velocity when at a distance of 1 away from the axis of rotation.