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Display information for equation id:math.1256.183 on revision:1256

* Page found: Das d'Alembertsche Prinzip (eq math.1256.183)

Occurrences on the following pages:

Normalschwingungen Eq: math.1515.46

Hash: 030a10262a3044609fd3c046ff04a485

TeX (original user input):

\begin{align}
  & T=\frac{1}{2}m({{{\dot{q}}}_{1}}^{2}+{{{\dot{q}}}_{2}}^{2}) \\
 & V=mg{{z}_{1}}+mg{{z}_{2}}+\frac{1}{2}k{{({{q}_{1}}-{{q}_{2}})}^{2}}=mgl(1-\cos \frac{{{q}_{1}}}{l})+\frac{1}{2}k{{({{q}_{1}}-{{q}_{2}})}^{2}}+mgl(1-\cos \frac{{{q}_{2}}}{l}) \\
 & V\approx \frac{1}{2}mgl{{\phi }_{1}}^{2}+\frac{1}{2}mgl{{\phi }_{2}}^{2}+\frac{1}{2}k{{({{q}_{1}}-{{q}_{2}})}^{2}}=\frac{1}{2}\frac{g}{l}m{{q}_{1}}^{2}+\frac{1}{2}\frac{g}{l}m{{q}_{2}}^{2}+\frac{1}{2}k{{({{q}_{1}}-{{q}_{2}})}^{2}} \\
\end{align}

TeX (checked):

{\begin{aligned}&T={\frac {1}{2}}m({{\dot {q}}_{1}}^{2}+{{\dot {q}}_{2}}^{2})\\&V=mg{{z}_{1}}+mg{{z}_{2}}+{\frac {1}{2}}k{{({{q}_{1}}-{{q}_{2}})}^{2}}=mgl(1-\cos {\frac {{q}_{1}}{l}})+{\frac {1}{2}}k{{({{q}_{1}}-{{q}_{2}})}^{2}}+mgl(1-\cos {\frac {{q}_{2}}{l}})\\&V\approx {\frac {1}{2}}mgl{{\phi }_{1}}^{2}+{\frac {1}{2}}mgl{{\phi }_{2}}^{2}+{\frac {1}{2}}k{{({{q}_{1}}-{{q}_{2}})}^{2}}={\frac {1}{2}}{\frac {g}{l}}m{{q}_{1}}^{2}+{\frac {1}{2}}{\frac {g}{l}}m{{q}_{2}}^{2}+{\frac {1}{2}}k{{({{q}_{1}}-{{q}_{2}})}^{2}}\\\end{aligned}}

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\begin{aligned} T = \frac{1}{2} m ({\dot{q}}_{1}^{2} + {\dot{q}}_{2}^{2}) \\ V = m g z_{1} + m g z_{2} + \frac{1}{2} k {(q_{1} - q_{2})}^{2} = m g l (1 - \cos \frac{q_{1}}{l}) + \frac{1}{2} k {(q_{1} - q_{2})}^{2} + m g l (1 - \cos \frac{q_{2}}{l}) \\ V \approx \frac{1}{2} m g l {ϕ_{1}}^{2} + \frac{1}{2} m g l {ϕ_{2}}^{2} + \frac{1}{2} k {(q_{1} - q_{2})}^{2} = \frac{1}{2} \frac{g}{l} m {q_{1}}^{2} + \frac{1}{2} \frac{g}{l} m {q_{2}}^{2} + \frac{1}{2} k {(q_{1} - q_{2})}^{2} \end{aligned}

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data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></mfrac></mrow><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><mi>k</mi><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>&#x2212;</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>m</mi><mi>g</mi><mi>l</mi><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><mi>cos</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow><mrow 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stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>&#x2212;</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><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><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>g</mi></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></mfrac></mrow><mi>m</mi><msup><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><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><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>g</mi></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></mfrac></mrow><mi>m</mi><msup><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><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><mi>k</mi><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>&#x2212;</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Identifiers

$T$

$m$

${\dot{q}}_{1}$

${\dot{q}}_{2}$

$V$

$m$

$g$

$z_{1}$

$m$

$g$

$z_{2}$

$k$

$q_{1}$

$q_{2}$

$m$

$g$

$l$

$q_{1}$

$l$

$k$

$q_{1}$

$q_{2}$

$m$

$g$

$l$

$q_{2}$

$l$

$V$

$m$

$g$

$l$

$ϕ_{1}$

$m$

$g$

$l$

$ϕ_{2}$

$k$

$q_{1}$

$q_{2}$

$g$

$l$

$m$

$q_{1}$

$g$

$l$

$m$

$q_{2}$

$k$

$q_{1}$

$q_{2}$

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