Changed stability classification terminology

Tarang74 · Jun 23, 2023 · 02daade · 02daade
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diff --git a/MXB225 Lecture Notes.pdf b/MXB225 Lecture Notes.pdf
diff --git a/MXB225 Lecture Notes.tex b/MXB225 Lecture Notes.tex
@@ -926,8 +926,8 @@ \subsubsection{Complex Conjugate Eigenvalues}
 \end{equation*}
 The stability of this system is determined by the real part of \(\lambda\).
 \begin{itemize}
-    \item When \(\alpha < 0\), the origin is a \textbf{stable spiral}.
-    \item When \(\alpha > 0\), the origin is an \textbf{unstable spiral}.
+    \item When \(\alpha < 0\), the origin is a \textbf{stable spiral point}.
+    \item When \(\alpha > 0\), the origin is an \textbf{unstable spiral point}.
     \item When \(\alpha = 0\), the origin is a \textbf{centre}.
 \end{itemize}
 To draw a phase portait, choose an arbitary initial state \(\symbf{x}_0\) (i.e., \(\symbf{x}_0 = \abracket{1,\: 0}\)),
@@ -957,12 +957,12 @@ \subsubsection{Complex Conjugate Eigenvalues}
         \midrule
         \multicolumn{3}{c}{Complex conjugate eigenvalues \(\lambda = \sigma \pm \omega i\) with eigenvectors \(\symbf{v} = \symbf{a} \pm \symbf{b} i\) (\(\tau^2 - 4\Delta < 0\))}                                                                                   \\
         \midrule
-        \(\sigma < 0\) (\(\tau \ne 0\))                         & Stable spiral            & \multirow{3}{*}{\(\begin{aligned}
+        \(\sigma < 0\) (\(\tau \ne 0\))                         & Stable spiral point      & \multirow{3}{*}{\(\begin{aligned}
                                                                                                                        %    \symbf{x}\left( t \right)   & = c_1 \symbf{x}_1\left( t \right) + c_2 \symbf{x}_2\left( t \right)                                             \\
                                                                                                                        x_1\left( t \right) & = e^{\sigma t} \left( \symbf{a} \cos{\left( \omega t \right)} - \symbf{b} \sin{\left( \omega t \right)} \right) \\
                                                                                                                        x_2\left( t \right) & = e^{\sigma t} \left( \symbf{a} \sin{\left( \omega t \right)} + \symbf{b} \cos{\left( \omega t \right)} \right)
                                                                                                                    \end{aligned}\)} \\
-        \(\sigma > 0\) (\(\tau \ne 0\))                         & Unstable spiral          &                                                                                                                                                                         \\
+        \(\sigma > 0\) (\(\tau \ne 0\))                         & Unstable spiral point    &                                                                                                                                                                         \\
         \(\sigma = 0\) (\(\tau = 0\))                           & Centre                   &                                                                                                                                                                         \\
         \bottomrule
     \end{tabular}