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> | ||