3D Curvature Example: Exponential Spiral

The "spiral" r(t)=< e-t cos(t), e-t sin(t), e-t >,
0 ≤ t ≤ 2π .
  • Yellow: Osculating Circle

Move the mouse pointer over the picture to begin the animation. It repeats in an endless loop. You can use the following controls:

  • Click+Drag: rotate the image
  • Shift+Click+Drag Up/Down: zoom in/out
  • Home: reset the image
  • Double Click: stop/restart the animation

Question: why does the motion slow down so much as the particle approaches the bottom? Will it ever reach the bottom?

Created using Mathematica and LiveGraphics3D.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.