From 7ec42764de400df4db629780f3c758f553ac5a93 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Fri, 9 Jun 2023 23:33:22 +0200
Subject: Improve knowledge base
---
source/know/concept/cylindrical-polar-coordinates/index.md | 12 ++++++------
1 file changed, 6 insertions(+), 6 deletions(-)
(limited to 'source/know/concept/cylindrical-polar-coordinates')
diff --git a/source/know/concept/cylindrical-polar-coordinates/index.md b/source/know/concept/cylindrical-polar-coordinates/index.md
index 3c54ef8..fe7d7c1 100644
--- a/source/know/concept/cylindrical-polar-coordinates/index.md
+++ b/source/know/concept/cylindrical-polar-coordinates/index.md
@@ -257,14 +257,14 @@ $$\begin{aligned}
\boxed{
\begin{aligned}
\nabla^2 \vb{V}
- &= \quad \vu{e}_r \bigg( \pdvn{2}{V_r}{r} + \frac{1}{r} \pdv{V_r}{r} + \frac{1}{r^2} \pdvn{2}{V_r}{\varphi}
- + \pdvn{2}{V_r}{z} - \frac{2}{r^2} \pdv{V_\varphi}{\varphi} - \frac{V_r}{r^2} \bigg)
+ &= \quad \vu{e}_r \bigg( \pdvn{2}{V_r}{r} + \frac{1}{r^2} \pdvn{2}{V_r}{\varphi} + \pdvn{2}{V_r}{z}
+ + \frac{1}{r} \pdv{V_r}{r} - \frac{2}{r^2} \pdv{V_\varphi}{\varphi} - \frac{V_r}{r^2} \bigg)
\\
- &\quad\: + \vu{e}_\varphi \bigg( \pdvn{2}{V_\varphi}{r} + \frac{1}{r} \pdv{V_\varphi}{r} + \frac{1}{r^2} \pdvn{2}{V_\varphi}{\varphi}
- + \pdvn{2}{V_\varphi}{z} + \frac{2}{r^2} \pdv{V_r}{\varphi} - \frac{V_\varphi}{r^2} \bigg)
+ &\quad\: + \vu{e}_\varphi \bigg( \pdvn{2}{V_\varphi}{r} + \frac{1}{r^2} \pdvn{2}{V_\varphi}{\varphi} + \pdvn{2}{V_\varphi}{z}
+ + \frac{2}{r^2} \pdv{V_r}{\varphi} + \frac{1}{r} \pdv{V_\varphi}{r} - \frac{V_\varphi}{r^2} \bigg)
\\
- &\quad\: + \vu{e}_z \bigg( \pdvn{2}{V_z}{r} + \frac{1}{r} \pdv{V_z}{r}
- + \frac{1}{r^2} \pdvn{2}{V_z}{\varphi} + \pdvn{2}{V_z}{z} \bigg)
+ &\quad\: + \vu{e}_z \bigg( \pdvn{2}{V_z}{r} + \frac{1}{r^2} \pdvn{2}{V_z}{\varphi}
+ + \pdvn{2}{V_z}{z} + \frac{1}{r} \pdv{V_z}{r} \bigg)
\end{aligned}
}
\end{aligned}$$
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