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Display information for equation id:math.1255.131 on revision:1255
* Page found: Das d'Alembertsche Prinzip (eq math.1255.131)
(force rerendering)Occurrences on the following pages:
Hash: 7eca4aaef8f306b7b399b1d6a57f35ee
TeX (original user input):
\begin{align}
& T({{q}_{{}}},{{{\dot{q}}}_{{}}},t)=\frac{1}{2}({{m}_{{{1}_{{}}}}}+{{m}_{2}}){{{\dot{q}}}^{2}} \\
& V(q,\dot{q},t)={{m}_{1}}gq+{{m}_{2}}(l-q)g \\
& \frac{\partial L}{\partial q}={{m}_{1}}g-{{m}_{2}}g \\
& \frac{\partial L}{\partial \dot{q}}=({{m}_{1}}+{{m}_{2}})\dot{q} \\
& ({{m}_{1}}+{{m}_{2}})\ddot{q}+{{m}_{1}}g-{{m}_{2}}g=0 \\
& \\
\end{align}
TeX (checked):
{\begin{aligned}&T({{q}_{}},{{\dot {q}}_{}},t)={\frac {1}{2}}({{m}_{{1}_{}}}+{{m}_{2}}){{\dot {q}}^{2}}\\&V(q,{\dot {q}},t)={{m}_{1}}gq+{{m}_{2}}(l-q)g\\&{\frac {\partial L}{\partial q}}={{m}_{1}}g-{{m}_{2}}g\\&{\frac {\partial L}{\partial {\dot {q}}}}=({{m}_{1}}+{{m}_{2}}){\dot {q}}\\&({{m}_{1}}+{{m}_{2}}){\ddot {q}}+{{m}_{1}}g-{{m}_{2}}g=0\\&\\\end{aligned}}
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MathML (3.565 KB / 508 B) :
<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><mi>T</mi><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo stretchy="false">(</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><msub><mn>1</mn><mrow data-mjx-texclass="ORD"></mrow></msub></mrow></msub><mo>+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi>V</mi><mo stretchy="false">(</mo><mi>q</mi><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>g</mi><mi>q</mi><mo>+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>l</mi><mo>−</mo><mi>q</mi><mo stretchy="false">)</mo><mi>g</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>L</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow><mo>=</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>g</mi><mo>−</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mi>g</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>L</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo>=</mo><mo stretchy="false">(</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">(</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¨</mo></mover></mrow></mrow><mo>+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>g</mi><mo>−</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mi>g</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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