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Display information for equation id:math.1354.112 on revision:1354
* Page found: Dynamische Systeme und deterministisches Chaos (eq math.1354.112)
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Hash: 42eb076aa123b024f8b89a8caf60e87e
TeX (original user input):
\begin{align}
& {{{\dot{\omega }}}_{1}}=-\frac{\left( {{J}_{3}}-{{J}_{2}} \right)}{{{J}_{1}}}{{\omega }_{2}}{{\omega }_{3}}=-{{k}_{1}}{{\omega }_{2}}{{\omega }_{3}} \\
& {{{\dot{\omega }}}_{2}}=\frac{\left( {{J}_{3}}-{{J}_{1}} \right)}{{{J}_{2}}}{{\omega }_{3}}{{\omega }_{1}}={{k}_{2}}{{\omega }_{3}}{{\omega }_{1}} \\
& {{{\dot{\omega }}}_{3}}=-\frac{\left( {{J}_{2}}-{{J}_{1}} \right)}{{{J}_{3}}}{{\omega }_{1}}{{\omega }_{2}}=-{{k}_{3}}{{\omega }_{1}}{{\omega }_{2}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\dot {\omega }}_{1}}=-{\frac {\left({{J}_{3}}-{{J}_{2}}\right)}{{J}_{1}}}{{\omega }_{2}}{{\omega }_{3}}=-{{k}_{1}}{{\omega }_{2}}{{\omega }_{3}}\\&{{\dot {\omega }}_{2}}={\frac {\left({{J}_{3}}-{{J}_{1}}\right)}{{J}_{2}}}{{\omega }_{3}}{{\omega }_{1}}={{k}_{2}}{{\omega }_{3}}{{\omega }_{1}}\\&{{\dot {\omega }}_{3}}=-{\frac {\left({{J}_{2}}-{{J}_{1}}\right)}{{J}_{3}}}{{\omega }_{1}}{{\omega }_{2}}=-{{k}_{3}}{{\omega }_{1}}{{\omega }_{2}}\\\end{aligned}}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ω</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo>−</mo><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mfrac></mrow><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo>=</mo><mo>−</mo><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ω</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo>−</mo><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ω</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>−</mo><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub></mrow></mfrac></mrow><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><mo>−</mo><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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