I believe there is quite a large classical literature on the herpolhode. For example

http://www.archive.org/stream/cu31924005727965#page/n477/mode/2up

and following pages. I actually came across the term first, I think, in Greenhill's book on the application of elliptic functions - seems to come up via the intersection of two quadrics.

Given that anything on rigid body motion must be a way of describing paths in the Euclidean group, I suppose a more accurate question would be: how does this as a way of talking about kinematics tally with more familiar charts (on SO(3), in particular)? Since the approach seems to have gone right out of fashion, it is presumably less convenient. One has to bear in mind that the old mathematical physics was quite largely devoted to closed-form solutions, so that redescriptions might work well for particular problems.

I believe there is quite a large classical literature on the herpolhode. For example

http://www.archive.org/stream/cu31924005727965#page/n477/mode/2up

and following pages. I actually came across the term first, I think, in Greenhill's book on the application of elliptic functions - seems to come up via the intersection of two quadrics.

Given that anything on rigid body motion must be a way of describing paths in the Euclidean group, I suppose a more accurate question would be: how does this as a way of talking about kinematics tally with more familiar charts (on SO(3), in particular)? Since the approach seems to have gone right out of fashion, it is presumably less convenient. One has to bear in mind that the old mathematical physics was quite largely devoted to closed-form solutions, so that redescriptions might work well for particular problems.

Edit: There is a treatment on pp. 152-155 of E. T. Whittaker's Treatise on Analytical Dynamics; the polar coordinates of the herpolhode come out in terms of standard Weierstrass elliptic functions (P, sigma and zeta).