Fig. 10.

In these plots we show the effect of increasing component tube curvature on the relative stability metric. We simulated three fully overlapping tubes with zero transmission length and an overlapped length of 50 mm and equal curvature and stiffness. The curvatures, from left to right, are 21 m⁻¹, 27.5 m⁻¹, 31 m⁻¹, and 36 m⁻¹. As the curvature increases, the regions of instability grow from the bifurcated equilibria until they disconnect the stable equilibria. In the last figure it can be seen that very small contours surround the special case equilibria at (2π/3, 4π/3) and (4π/3, 2π/3), where the precurvatures are offset by 120°, which are remarkably still stable despite the entire area surrounding them being unstable.