Warren Weckesser -- Research

Whirling of the N-Chain

The N-Chain

Here are some animated GIF files for the whirling modes of the N-chain:

Whirling Mode 1 of the 5-Chain (118K)
Whirling Mode 2 of the 5-Chain (125K)
Whirling Mode 3 of the 5-Chain (129K)
Whirling Mode 4 of the 5-Chain (129K)
Whirling Mode 5 of the 5-Chain (112K)
Whirling Mode 4 of the 6-Chain (188K)
Whirling Mode 4 of the 7-Chain (179K)
Whirling Mode 6 of the 15-Chain (262K)
Whirling Mode 5 of the 23-Chain (436K)
Whirling Mode 9 of the 23-Chain (453K)

And here, for example, is the bifurcation diagram for the whirling modes that bifurcate from the straight down position of the 7-chain. The vertical axis is the sine of the angle of the top-most link.