User:FloraC/Fokker analysis of rank-3 scales: Difference between revisions

Fix an overlooked case
m Something happened that broke my otherwise nicely typeset math
 
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<math>\displaystyle
<math>\displaystyle
C_\text{r} + C_\text{d} = L - s \\
\begin{align}
C_\text{r} - C_\text{d} = l - S
C_\text{r} + C_\text{d} &= L - s \\
C_\text{r} - C_\text{d} &= l - S
\end{align}
</math>
</math>


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<math>\displaystyle
<math>\displaystyle
C_1 = C_\text{r} + C_\text{d} \\
\begin{align}
C_2 = C_\text{r} \\
C_1 &= C_\text{r} + C_\text{d} \\
C_3 = C_\text{r} - C_\text{d} \\
C_2 &= C_\text{r} \\
C_4 = C_\text{d}
C_3 &= C_\text{r} - C_\text{d} \\
C_4 &= C_\text{d}
\end{align}
</math>
</math>


except that ''C''<sub>d</sub> can be larger than ''C''<sub>r</sub> − ''C''<sub>d</sub>.  
except that ''C''<sub>d</sub> can be larger than ''C''<sub>r</sub> − ''C''<sub>d</sub>.


== Modal, Domal and Residual Rotation ==
== Modal, Domal and Residual Rotation ==
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If we denote the stabilities ''σ''<sub>d</sub>, ''σ''<sub>r</sub>, and ''σ''<sub>t</sub>, respectively, they can be derived by
If we denote the stabilities ''σ''<sub>d</sub>, ''σ''<sub>r</sub>, and ''σ''<sub>t</sub>, respectively, they can be derived by


<math>\displaystyle  
<math>\displaystyle
\sigma_\text{d} = 1 - (n - n_\text{p})C_d \\
\begin{align}
\sigma_\text{r} = 1 - (n - n_\text{p})C_r \\
\sigma_\text{d} &= 1 - (n - n_\text{p})C_d \\
\sigma_\text{t} = 1 - (n - n_\text{p})(C_r + C_d)
\sigma_\text{r} &= 1 - (n - n_\text{p})C_r \\
\sigma_\text{t} &= 1 - (n - n_\text{p})(C_r + C_d)
\end{align}
</math>
</math>