The Moving Triplet

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This animation shows how the so-called moving triplet twists and turns as it moves along a curve. (See notes below.)


Here we examine the behavior of the moving triplet associated with a curve in space. As we travel along a curve, the triplet consists of
  1. the unit tangent vector (shown here in red), which points in the direction of travel,
  2. the unit normal vector (shown here in purple), which points in the direction of the center of curvature and is always at right angles to the unit tangent vector, and
  3. the unit binormal vector (shown here in green), which is perpendicular to both the unit tangent vector and the unit normal vector and forms the third element of a right-handed coordinate system with the other two vectors.
The curve in this animation is known as the trefoil knot. It has parametric equations
x = [2 + cos(3t ⁄ 2)] cos t;

y = [2 + cos(3t ⁄ 2)] sin t;

z = sin(3t ⁄ 2).
(11/25/07)