Correction: Popov, V.L. An Approximate Solution for the Contact Problem of Profiles Slightly Deviating from Axial Symmetry. Symmetry 2022, 14, 390

Text Correction

There were misprints in Equations (40), (65), (66), and (67) in the original publication [1].

The correct Equation (40) of the original publication is:

$$p(r,\phi )=\frac{E^{*}}{\pi }{\displaystyle \underset{r}{\overset{a(\phi )}{\int }}\frac{\tilde{a}(\phi )}{\sqrt{\tilde{a}{(\phi )}^2-r^2}}}\frac{1}{{\tilde{a}}_0}\frac{\mathrm{d}{g}_0({\tilde{a}}_0)}{\mathrm{d}\tilde{a}(\phi )}\mathrm{d}\tilde{a}(\phi )=\frac{2}{\pi }{E}^{*}{\left(2d\cdot \overline{\psi }\right)}^{1/2}\sqrt{1-{\left(\frac{r}{a(\phi )}\right)}^2}$$

(40)

The correct form of Equations (65) of the original publication is:

$$\gamma (a)=a{\displaystyle \underset{0}{\overset{a}{\int }}\frac{n{r}^{n-1}}{\sqrt{a^2-r^2}}\mathrm{d}r}={\kappa }_n{a}^n,{\kappa }_n={\displaystyle \underset{0}{\overset{1}{\int }}\frac{{\xi }^{n-1}\mathrm{d}\xi }{\sqrt{1-{\xi }^2}}}=\frac{\sqrt{\pi }}{2}\frac{n\Gamma \left(\frac{n}{2}\right)}{\Gamma \left(\frac{n}{2}+\frac{1}{2}\right)}$$

(65)

The correct form of Equations (66) of the original publication is:

$$\delta g_{\phi }(a)={\kappa }_n{a}^n\left(\psi (\phi )-\overline{\psi }\right),\delta G_{\phi }(a)={\kappa }_n\frac{a^{n+1}}{n+1}\left(\psi (\phi )-\overline{\psi }\right)$$

(66)

The correct form of Equation (67) of the original publication is:

$$a(\phi )=a_0\left(1+\frac{n+2}{n(n+1)}\left(1-\frac{\psi (\phi )}{\overline{\psi }}\right)\right)$$

(67)

The author apologizes for any inconvenience caused and state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.