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

Valentin L. Popov

doi:10.3390/sym14102108

¹

Department of System Dynamics and Friction Physics, Technische Universität Berlin, 10623 Berlin, Germany

²

National Research Tomsk State University, 634050 Tomsk, Russia

Symmetry2022, 14(10), 2108;https://doi.org/10.3390/sym14102108

This article belongs to the Special Issue Axisymmetry in Mechanical Engineering

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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, φ) = \frac{E^{*}}{π} \int_{r}^{a (φ)} \frac{\tilde{a} (φ)}{\sqrt{\tilde{a} {(φ)}^{2} - r^{2}}} \frac{1}{{\tilde{a}}_{0}} \frac{d g_{0} ({\tilde{a}}_{0})}{d \tilde{a} (φ)} d \tilde{a} (φ) = \frac{2}{π} E^{*} {(2 d \cdot \bar{ψ})}^{1 / 2} \sqrt{1 - {(\frac{r}{a (φ)})}^{2}}

(40)

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

γ (a) = a \int_{0}^{a} \frac{n r^{n - 1}}{\sqrt{a^{2} - r^{2}}} d r = κ_{n} a^{n}, κ_{n} = \int_{0}^{1} \frac{ξ^{n - 1} d ξ}{\sqrt{1 - ξ^{2}}} = \frac{\sqrt{π}}{2} \frac{n Γ (\frac{n}{2})}{Γ (\frac{n}{2} + \frac{1}{2})}

(65)

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

δ g_{φ} (a) = κ_{n} a^{n} (ψ (φ) - \bar{ψ}), δ G_{φ} (a) = κ_{n} \frac{a^{n + 1}}{n + 1} (ψ (φ) - \bar{ψ})

(66)

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

a (φ) = a_{0} (1 + \frac{n + 2}{n (n + 1)} (1 - \frac{ψ (φ)}{\bar{ψ}}))

(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.

Reference

Popov, V.L. An Approximate Solution for the Contact Problem of Profiles Slightly Deviating from Axial Symmetry. Symmetry 2022, 14, 390. [Google Scholar] [CrossRef]

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

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