Corrigendum

This article refers to:

Motions of a rimless spoked wheel: a simple three-dimensional system with impacts

Coleman, M.J., Chatterjee, A., Ruina, A. Motions of a rimless spoked wheel: a simple three-dimensional system with impacts. Dyn Stab Syst. 2012;12(3):139–159. http://dx.doi.org/10.1080/02681119708806242.

In the above-mentioned article, we have found several typographical errors in two equations and one incorrect plot within one figure. The equations used by the authors in any numerical or analytical calculations were the correct ones. The results have been double-checked independently and are correct everywhere (except for the incorrect plot which was not the result of the incorrect equations.) Thus the conclusions of the paper remain unchanged. The details of the errors are as follows.

Figure 4. State of the rimless wheel plotted versus τ for 350 collisions after it is perturbed from its limit cycle with a disturbance in the bank angle Δψ₀ = 0.001. For this simulation, 2J = 0.75 (or ), n = 16, α = 2/n, and φ*₀ = π/10. Note that θ and are plotted over only about 17 collisions since their variation with τ is at too high a frequency to be usefully displayed over 350 collisions. The discontinuities in the graphs of angular rates are due to the collisions while the discontinuities in the graph of θ(τ) are due to resetting θ from to at collisions.

1.	In Equation(3), there are several typographical errors. The equation is reprinted below with the following corrections (highlighted by boxes): (a) In the first term inside the brackets in the second of the three equations, a minus sign has been added and the has been changed to . (b) In the third of the three equations, a has been added to the first term inside the brackets. (3)
2.	In Equation (6), a factor of 2 is missing in the (2,1) element of the T matrix. The equation is reprinted below with the correction highlighted by a box. (6)
3.	The plot of versus τ in Figure 4 is incorrect (again, not due to the incorrect equations). The correct figure is reprinted here with the correct plot highlighted with a box.

The authors thank Melih Eriten for finding the missing factor of 2 in the matrix T and noticing that the plot in Figure 4 was incorrect.