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Sources/Lexikon/Modalanalyse - Versionsgeschichte
2026-05-10T15:06:23Z
Versionsgeschichte dieser Seite in numpedia
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https://numpedia.rzbt.haw-hamburg.de/index.php?title=Sources/Lexikon/Modalanalyse&diff=4702&oldid=prev
Mechaniker am 23. Mai 2024 um 10:13 Uhr
2024-05-23T10:13:00Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 23. Mai 2024, 10:13 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l102">Zeile 102:</td>
<td colspan="2" class="diff-lineno">Zeile 102:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Aussage von 2. ist: Die Eigenvektoren zu zwei verschiedenen Eigenwerten sind im Sinne des Skalarprodukts</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Aussage von 2. ist: Die Eigenvektoren zu zwei verschiedenen Eigenwerten sind im Sinne des Skalarprodukts</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{\hat{Q}}^T_l \cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_k = <del style="font-weight: bold; text-decoration: none;">\underline{</del>0<del style="font-weight: bold; text-decoration: none;">}</del></math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{\hat{Q}}^T_l \cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_k = 0</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>orthogonal. Das heißt auch, dass die Eigenvektoren nur dann zueinander selbst orthogonal sind, wenn die Massenmatrix proportional zur Einheitsmatrix ist.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>orthogonal. Das heißt auch, dass die Eigenvektoren nur dann zueinander selbst orthogonal sind, wenn die Massenmatrix proportional zur Einheitsmatrix ist.</div></td></tr>
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Mechaniker am 23. Mai 2024 um 10:12 Uhr
2024-05-23T10:12:28Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 23. Mai 2024, 10:12 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l93">Zeile 93:</td>
<td colspan="2" class="diff-lineno">Zeile 93:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>die Aussage</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>die Aussage</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\left(\Lambda_k - \Lambda_l\right)\;\;\;\underline{\hat{Q}}^T_l \cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_k = <del style="font-weight: bold; text-decoration: none;">\underline{</del>0<del style="font-weight: bold; text-decoration: none;">}</del></math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\left(\Lambda_k - \Lambda_l\right)\;\;\;\underline{\hat{Q}}^T_l \cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_k = 0</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dann ist also</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dann ist also</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># <math>\ldots \text{ für } k=l: \left(\Lambda_k - \Lambda_l\right) = 0 \text{ und }</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># <math>\ldots \text{ für } k=l: \left(\Lambda_k - \Lambda_l\right) = 0 \text{ und }</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># <math>\ldots \text{ für } k\neq l: \underline{\hat{Q}}^T_l \cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_k = <del style="font-weight: bold; text-decoration: none;">\underline{</del>0<del style="font-weight: bold; text-decoration: none;">} </del>\;\;\;\text{ und damit übrigens auch } \underline{\hat{Q}}^T_l \cdot\underline{\underline{K}} \cdot \underline{\hat{Q}}_k = <del style="font-weight: bold; text-decoration: none;">\underline{</del>0<del style="font-weight: bold; text-decoration: none;">}</del></math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># <math>\ldots \text{ für } k\neq l: \underline{\hat{Q}}^T_l \cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_k = 0 \;\;\;\text{ und damit übrigens auch } \underline{\hat{Q}}^T_l \cdot\underline{\underline{K}} \cdot \underline{\hat{Q}}_k = 0</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Aussage von 2. ist: Die Eigenvektoren zu zwei verschiedenen Eigenwerten sind im Sinne des Skalarprodukts</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Aussage von 2. ist: Die Eigenvektoren zu zwei verschiedenen Eigenwerten sind im Sinne des Skalarprodukts</div></td></tr>
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Mechaniker am 23. Mai 2024 um 10:11 Uhr
2024-05-23T10:11:15Z
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<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 23. Mai 2024, 10:11 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l89">Zeile 89:</td>
<td colspan="2" class="diff-lineno">Zeile 89:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die beiden Zeilen oben subtrahieren wir nun von einander und finden wegen</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die beiden Zeilen oben subtrahieren wir nun von einander und finden wegen</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{\underline{K}}^T = \underline{\underline{K}}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{\underline{K}}^T = \underline{\underline{K<ins style="font-weight: bold; text-decoration: none;">}}</math> und <math>\underline{\underline{M}}^T = \underline{\underline{M</ins>}}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>die Aussage</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>die Aussage</div></td></tr>
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Mechaniker am 23. Mai 2024 um 10:09 Uhr
2024-05-23T10:09:42Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 23. Mai 2024, 10:09 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l81">Zeile 81:</td>
<td colspan="2" class="diff-lineno">Zeile 81:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>abkürzen. Einsetzten der Eigenlösungen in die homogene Bewegungsgleichung - jeweils einmal für die Lösung ''n=k'' und ''n=l'' - liefert zwei Gleichungssysteme, die wir mit den Eigenvektoren der jeweils anderen Lösung (rot) durchmultiplizieren. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>abkürzen. Einsetzten der Eigenlösungen in die homogene Bewegungsgleichung - jeweils einmal für die Lösung ''n=k'' und ''n=l'' - liefert zwei Gleichungssysteme, die wir mit den Eigenvektoren der jeweils anderen Lösung (rot) durchmultiplizieren. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{array}{rrr}\Lambda_k\;\;\; {\color{red}{\underline{\hat{Q}^T_l<del style="font-weight: bold; text-decoration: none;">}</del>}}\cdot \underline{\underline{M}} \cdot \underline{\hat{Q}}_k &+ {\color{red}{\underline{\hat{Q}}^T_l}}\cdot \underline{\underline{K}} \cdot \underline{\hat{Q}}_k &= <del style="font-weight: bold; text-decoration: none;">\underline{</del>0<del style="font-weight: bold; text-decoration: none;">}</del>\\\Lambda_l\;\;\; {\color{red}{\underline{\hat{Q}}^T_k}}\cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_l &+ {\color{red}{\underline{\hat{Q}}^T_k}}\cdot\underline{\underline{K}} \cdot \underline{\hat{Q}}_l &= <del style="font-weight: bold; text-decoration: none;">\underline{</del>0<del style="font-weight: bold; text-decoration: none;">}</del>\end{array}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{array}{rrr}\Lambda_k\;\;\; {\color{red}{\underline{\hat{Q<ins style="font-weight: bold; text-decoration: none;">}</ins>}^T_l}}\cdot \underline{\underline{M}} \cdot \underline{\hat{Q}}_k &+ {\color{red}{\underline{\hat{Q}}^T_l}}\cdot \underline{\underline{K}} \cdot \underline{\hat{Q}}_k &= 0\\\Lambda_l\;\;\; {\color{red}{\underline{\hat{Q}}^T_k}}\cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_l &+ {\color{red}{\underline{\hat{Q}}^T_k}}\cdot\underline{\underline{K}} \cdot \underline{\hat{Q}}_l &= 0\end{array}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Jetzt transponieren wir die zweite Zeile und führen die Transposition jeweils auf die Matrix-Ebene zurück, z.B. so:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Jetzt transponieren wir die zweite Zeile und führen die Transposition jeweils auf die Matrix-Ebene zurück, z.B. so:</div></td></tr>
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Mechaniker am 23. Mai 2024 um 10:07 Uhr
2024-05-23T10:07:50Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 23. Mai 2024, 10:07 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l81">Zeile 81:</td>
<td colspan="2" class="diff-lineno">Zeile 81:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>abkürzen. Einsetzten der Eigenlösungen in die homogene Bewegungsgleichung - jeweils einmal für die Lösung ''n=k'' und ''n=l'' - liefert zwei Gleichungssysteme, die wir mit den Eigenvektoren der jeweils anderen Lösung (rot) durchmultiplizieren. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>abkürzen. Einsetzten der Eigenlösungen in die homogene Bewegungsgleichung - jeweils einmal für die Lösung ''n=k'' und ''n=l'' - liefert zwei Gleichungssysteme, die wir mit den Eigenvektoren der jeweils anderen Lösung (rot) durchmultiplizieren. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{array}{rrr}\Lambda_k\;\;\; {\color{red}{\underline{\hat{Q}^T_l}}}\cdot \underline{\underline{M}} \cdot \underline{\hat{Q}}_k &+ {\color{red}{\underline{\hat{Q}^T_l<del style="font-weight: bold; text-decoration: none;">}</del>}}\cdot \underline{\underline{K}} \cdot \underline{\hat{Q}}_k &= \underline{0}\\\Lambda_l\;\;\; {\color{red}{\underline{\hat{Q}^T_k<del style="font-weight: bold; text-decoration: none;">}</del>}}\cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_l &+ {\color{red}{\underline{\hat{Q}^T_k<del style="font-weight: bold; text-decoration: none;">}</del>}}\cdot\underline{\underline{K}} \cdot \underline{\hat{Q}}_l &= \underline{0}\end{array}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{array}{rrr}\Lambda_k\;\;\; {\color{red}{\underline{\hat{Q}^T_l}}}\cdot \underline{\underline{M}} \cdot \underline{\hat{Q}}_k &+ {\color{red}{\underline{\hat{Q<ins style="font-weight: bold; text-decoration: none;">}</ins>}^T_l}}\cdot \underline{\underline{K}} \cdot \underline{\hat{Q}}_k &= \underline{0}\\\Lambda_l\;\;\; {\color{red}{\underline{\hat{Q<ins style="font-weight: bold; text-decoration: none;">}</ins>}^T_k}}\cdot\underline{\underline{M}} \cdot \underline{\hat{Q}}_l &+ {\color{red}{\underline{\hat{Q<ins style="font-weight: bold; text-decoration: none;">}</ins>}^T_k}}\cdot\underline{\underline{K}} \cdot \underline{\hat{Q}}_l &= \underline{0}\end{array}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Jetzt transponieren wir die zweite Zeile und führen die Transposition jeweils auf die Matrix-Ebene zurück, z.B. so:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Jetzt transponieren wir die zweite Zeile und führen die Transposition jeweils auf die Matrix-Ebene zurück, z.B. so:</div></td></tr>
</table>
Mechaniker
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Mechaniker am 28. Oktober 2023 um 08:17 Uhr
2023-10-28T08:17:33Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 28. Oktober 2023, 08:17 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td>
<td colspan="2" class="diff-lineno">Zeile 1:</td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Eigenvektor]][[Category:Eigenwert]][[Category:Eigenwertproblem]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Eigenfrequenzen und deren Eigenschwingungsformen reichen meist vollständig aus, um das charakteristische Verhalten von schwingungsfähigen, linearen Systemen zu erfassen. Eine [https://de.wikipedia.org/wiki/Stimmgabel Stimmgabel] z.B. schwingt hauptsächlich mit 440 Hz - dem Kammerton "a" - und dient damit als Referenz beim Stimmen von Musikinstrumenten. Musikinstrumente, Getriebe und die Oberfläche von Flugzeug-Triebwerken haben ähnliche Schwingungs-Charakteristika, die maßgeblich Ihre strukturellen Belastungen und Schall-Emission steuern.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Eigenfrequenzen und deren Eigenschwingungsformen reichen meist vollständig aus, um das charakteristische Verhalten von schwingungsfähigen, linearen Systemen zu erfassen. Eine [https://de.wikipedia.org/wiki/Stimmgabel Stimmgabel] z.B. schwingt hauptsächlich mit 440 Hz - dem Kammerton "a" - und dient damit als Referenz beim Stimmen von Musikinstrumenten. Musikinstrumente, Getriebe und die Oberfläche von Flugzeug-Triebwerken haben ähnliche Schwingungs-Charakteristika, die maßgeblich Ihre strukturellen Belastungen und Schall-Emission steuern.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>
Mechaniker
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Mechaniker am 16. Mai 2022 um 14:48 Uhr
2022-05-16T14:48:17Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Mai 2022, 14:48 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l180">Zeile 180:</td>
<td colspan="2" class="diff-lineno">Zeile 180:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>überführen wir dann unsere Bewegungsgleichungen in die Form, die wir in Matlab angesteuert haben.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>überführen wir dann unsere Bewegungsgleichungen in die Form, die wir in Matlab angesteuert haben.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Im Allgemeinen sind die Eigenwerte <i>λ<sub>i</sub></i>komplexwertig - und damit auch das <math>\underline{\hat{U}}</math>. Wir nehmen dann nur den Realteil der Lösung, also</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Im Allgemeinen sind die Eigenwerte <i>λ<sub>i</sub></i> komplexwertig - und damit auch das <math>\underline{\hat{U}}</math>. Wir nehmen dann nur den Realteil der Lösung, also</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \Re \left( \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}\right)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \Re \left( \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}\right)</math>.</div></td></tr>
</table>
Mechaniker
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Mechaniker am 16. Mai 2022 um 14:47 Uhr
2022-05-16T14:47:53Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Mai 2022, 14:47 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l180">Zeile 180:</td>
<td colspan="2" class="diff-lineno">Zeile 180:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>überführen wir dann unsere Bewegungsgleichungen in die Form, die wir in Matlab angesteuert haben.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>überführen wir dann unsere Bewegungsgleichungen in die Form, die wir in Matlab angesteuert haben.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Im Allgemeinen sind die Eigenwerte <<del style="font-weight: bold; text-decoration: none;">it</del>>λ<sub>i</sub></<del style="font-weight: bold; text-decoration: none;">it</del>>komplexwertig - und damit auch das <math>\underline{\hat{U}}</math>. Wir nehmen dann nur den Realteil der Lösung, also</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Im Allgemeinen sind die Eigenwerte <<ins style="font-weight: bold; text-decoration: none;">i</ins>>λ<sub>i</sub></<ins style="font-weight: bold; text-decoration: none;">i</ins>>komplexwertig - und damit auch das <math>\underline{\hat{U}}</math>. Wir nehmen dann nur den Realteil der Lösung, also</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \Re \left( \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}\right)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \Re \left( \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}\right)</math>.</div></td></tr>
</table>
Mechaniker
https://numpedia.rzbt.haw-hamburg.de/index.php?title=Sources/Lexikon/Modalanalyse&diff=4279&oldid=prev
Mechaniker am 16. Mai 2022 um 14:46 Uhr
2022-05-16T14:46:18Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Mai 2022, 14:46 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l178">Zeile 178:</td>
<td colspan="2" class="diff-lineno">Zeile 178:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Mit dem Ansatz</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Mit dem Ansatz</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>überführen wir dann unsere Bewegungsgleichungen in die Form, die wir in Matlab <del style="font-weight: bold; text-decoration: none;">angesteuern </del>haben.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>überführen wir dann unsere Bewegungsgleichungen in die Form, die wir in Matlab <ins style="font-weight: bold; text-decoration: none;">angesteuert </ins>haben.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Im Allgemeinen sind die Eigenwerte λ komplexwertig - und damit auch das <math>\underline{\hat{U}}</math>. Wir nehmen dann nur den Realteil der Lösung, also</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Im Allgemeinen sind die Eigenwerte <ins style="font-weight: bold; text-decoration: none;"><it></ins>λ<ins style="font-weight: bold; text-decoration: none;"><sub>i</sub></it></ins>komplexwertig - und damit auch das <math>\underline{\hat{U}}</math>. Wir nehmen dann nur den Realteil der Lösung, also</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \Re \left( \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}\right)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \Re \left( \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}\right)</math>.</div></td></tr>
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Mechaniker
https://numpedia.rzbt.haw-hamburg.de/index.php?title=Sources/Lexikon/Modalanalyse&diff=4278&oldid=prev
Mechaniker am 16. Mai 2022 um 14:44 Uhr
2022-05-16T14:44:59Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Mai 2022, 14:44 Uhr</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\underline{U}(t) = \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>überführen wir dann unsere Bewegungsgleichungen in die Form, die wir in Matlab angesteuern haben.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>überführen wir dann unsere Bewegungsgleichungen in die Form, die wir in Matlab angesteuern haben.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Im Allgemeinen sind die Eigenwerte λ komplexwertig - und damit auch das <math>\underline{\hat{U}}</math>. Wir nehmen dann nur den Realteil der Lösung, also</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">::<math>\underline{U}(t) = \Re \left( \underline{\hat{U}}\cdot e^{\displaystyle \lambda t}\right)</math>.</ins></div></td></tr>
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Mechaniker