Correction

This article refers to:

Unsteady-state brush theory

Article title: Unsteady-state brush theory

Authors: Luigi Romano, Fredrik Bruzelius, Bengt Jacobson

Journal: Vehicle System Dynamics

Bibliometrics: Volume 59, Number 11, pages 1643–1671

DOI: 10.1080/00423114.2020.1774625

When the above article was first published online, the equations (6), (7b), and (13) were written incorrectly.

The coordinate change in Eq. (6) yields Eqs. (7) only when the contact patch is fixed over time or travelled distance (see [1, 2]). Therefore, Eq. (6) should be modified as $\mathit{\xi }=\left[\begin{array}{c}\xi \\ \eta \\ \zeta \end{array}\right]=\left[\begin{array}{c}{x}_L(y)-x\\ y\\ z\end{array}\right].$

Consequently, Eq. (7b) should be modified as follows: $v_{sy}(\mathit{\xi },t)=V_{sy}(t)+{\omega }_z(t)[x_L(\eta )-\xi ]+\frac{\mathrm{\partial }{u}_y(\mathit{\xi },t)}{\mathrm{\partial }t}+V_r(t)\frac{\mathrm{\partial }{u}_y(\mathit{\xi },t)}{\mathrm{\partial }\xi }+{\dot{d}}_y(t).$

Similarly, in the adhesion region, Eq. (13) should be recast as $\frac{\mathrm{\partial }{u}_y(\mathit{\xi },t)}{\mathrm{\partial }t}+V_r(t)\frac{\mathrm{\partial }{u}_y(\mathit{\xi },t)}{\mathrm{\partial }\xi }=-V_{sy}(t)-{\omega }_z(t)[x_L(\eta )-\xi ]-{\dot{d}}_y(t).$

The authors sincerely apologise for the inconvenience.