Examples from Section 13.3

The following examples use the trefoil knot for the space curve. Our scaling and choice of coordinates gives: x = sin(t) + 2 sin(2t)
y = sin(3t)
z = cos(t) - 2 cos(2t) The first animation below shows three vectors: The red vector is position, the velocity vector is yellow and the acceleration is green. The lengths correspond to the magnitude of each: Trefoil Knot, Figure 1

The next animation shows the vectors scaled back for better viewing. Again, red is position, yellow is velocity, acceleration is green. Trefoil Knot, Figure 1

The next animation shows the Frenet frame (a.k.a. TNB frame) for the trefoil knot- The unit tangent is red, the unit normal is yellow, and the binormal vector is green. Trefoil Knot, Figure 1