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Display information for equation id:math.2038.47 on revision:2038
* Page found: Stabilität und Langzeitverhalten (eq math.2038.47)
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Hash: 22a95a8d342847f2225a4e7ec1c15708
TeX (original user input):
\begin{align}
& \bar{\varpi }{{*}^{(1)}}:{{\varpi }_{1}}=\varpi ,{{\varpi }_{2}}=0,{{\varpi }_{3}}=0 \\
& 0=\det (A-\lambda 1)=\left| \begin{matrix}
-\lambda & 0 & 0 \\
0 & -\lambda & {{k}_{2}}{{\omega }_{{}}} \\
0 & -{{k}_{3}}\omega & -\lambda \\
\end{matrix} \right|=-\lambda \left( {{\lambda }^{2}}+{{k}_{2}}{{k}_{3}}{{\omega }^{2}} \right) \\
& \Rightarrow {{\lambda }_{1}}^{(1)}=0,{{\lambda }_{2/3}}^{(1)}=\pm i\omega \sqrt{{{k}_{2}}{{k}_{3}}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\bar {\varpi }}{{*}^{(1)}}:{{\varpi }_{1}}=\varpi ,{{\varpi }_{2}}=0,{{\varpi }_{3}}=0\\&0=\det(A-\lambda 1)=\left|{\begin{matrix}-\lambda &0&0\\0&-\lambda &{{k}_{2}}{{\omega }_{}}\\0&-{{k}_{3}}\omega &-\lambda \\\end{matrix}}\right|=-\lambda \left({{\lambda }^{2}}+{{k}_{2}}{{k}_{3}}{{\omega }^{2}}\right)\\&\Rightarrow {{\lambda }_{1}}^{(1)}=0,{{\lambda }_{2/3}}^{(1)}=\pm i\omega {\sqrt {{{k}_{2}}{{k}_{3}}}}\\\end{aligned}}
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