From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 20 Oct 2022 18:25:31 +0200
Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

---
 .../know/concept/navier-cauchy-equation/index.md   | 26 +++++++++++-----------
 1 file changed, 13 insertions(+), 13 deletions(-)

(limited to 'source/know/concept/navier-cauchy-equation')

diff --git a/source/know/concept/navier-cauchy-equation/index.md b/source/know/concept/navier-cauchy-equation/index.md
index 13a1ebb..5071c5f 100644
--- a/source/know/concept/navier-cauchy-equation/index.md
+++ b/source/know/concept/navier-cauchy-equation/index.md
@@ -12,9 +12,9 @@ The **Navier-Cauchy equation** describes **elastodynamics**:
 the movements inside an elastic solid
 in response to external forces and/or internal stresses.
 
-For a particle of the solid, whose position is given by the displacement field $\va{u}$,
+For a particle of the solid, whose position is given by the displacement field $$\va{u}$$,
 Newton's second law is as follows,
-where $\dd{m}$ and $\dd{V}$ are the particle's mass and volume, respectively:
+where $$\dd{m}$$ and $$\dd{V}$$ are the particle's mass and volume, respectively:
 
 $$\begin{aligned}
     \va{f^*} \dd{V}
@@ -22,10 +22,10 @@ $$\begin{aligned}
     = \rho \pdvn{2}{\va{u}}{t} \dd{V}
 \end{aligned}$$
 
-Where $\rho$ is the mass density,
-and $\va{f^*}$ is the effective force density,
-defined from the [Cauchy stress tensor](/know/concept/cauchy-stress-tensor/) $\hat{\sigma}$
-like so, with $\va{f}$ being an external body force, e.g. from gravity:
+Where $$\rho$$ is the mass density,
+and $$\va{f^*}$$ is the effective force density,
+defined from the [Cauchy stress tensor](/know/concept/cauchy-stress-tensor/) $$\hat{\sigma}$$
+like so, with $$\va{f}$$ being an external body force, e.g. from gravity:
 
 $$\begin{aligned}
     \va{f^*}
@@ -34,17 +34,17 @@ $$\begin{aligned}
 
 We can therefore write Newton's second law as follows,
 while switching to index notation,
-where $\nabla_j = \ipdv{}{x_j}$ is the partial derivative
-with respect to the $j$th coordinate:
+where $$\nabla_j = \ipdv{}{x_j}$$ is the partial derivative
+with respect to the $$j$$th coordinate:
 
 $$\begin{aligned}
     f_i + \sum_{j} \nabla_j \sigma_{ij}
     = \rho \pdvn{2}{u_i}{t}
 \end{aligned}$$
 
-The components $\sigma_{ij}$ of the Cauchy stress tensor
+The components $$\sigma_{ij}$$ of the Cauchy stress tensor
 are given by [Hooke's law](/know/concept/hookes-law/),
-where $\mu$ and $\lambda$ are the Lamé coefficients,
+where $$\mu$$ and $$\lambda$$ are the Lamé coefficients,
 which describe the material:
 
 $$\begin{aligned}
@@ -52,10 +52,10 @@ $$\begin{aligned}
     = 2 \mu u_{ij} + \lambda \delta_{ij} \sum_{k} u_{kk}
 \end{aligned}$$
 
-In turn, the components $u_{ij}$ of the
+In turn, the components $$u_{ij}$$ of the
 [Cauchy strain tensor](/know/concept/cauchy-strain-tensor/)
 are defined as follows,
-where $u_i$ are once again the components of the displacement vector $\va{u}$:
+where $$u_i$$ are once again the components of the displacement vector $$\va{u}$$:
 
 $$\begin{aligned}
     u_{ij}
@@ -72,7 +72,7 @@ $$\begin{aligned}
     &= f_i + 2 \mu \sum_{j} \nabla_j u_{ij} + \lambda \nabla_i \sum_{j} u_{jj}
 \end{aligned}$$
 
-And then into this we insert the definition of the strain components $u_{ij}$, yielding:
+And then into this we insert the definition of the strain components $$u_{ij}$$, yielding:
 
 $$\begin{aligned}
     \rho \pdvn{2}{u_i}{t}
-- 
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