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Display information for equation id:math.1255.187 on revision:1255

* Page found: Das d'Alembertsche Prinzip (eq math.1255.187)

Occurrences on the following pages:

Normalschwingungen Eq: math.1515.50

Hash: 3975007c427de7166a1cbd5ffb38c991

TeX (original user input):

\begin{align}
  & T=\frac{1}{2}m({{{\dot{q}}}_{1}}^{2}+{{{\dot{q}}}_{2}}^{2}) \\
 & 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}} \\
 & L=T-V=\frac{1}{2}m({{{\dot{q}}}_{1}}^{2}+{{{\dot{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\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}}\\&L=T-V={\frac {1}{2}}m({{\dot {q}}_{1}}^{2}+{{\dot {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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MathML (5.707 KB / 508 B) :

\begin{aligned} T = \frac{1}{2} m ({\dot{q}}_{1}^{2} + {\dot{q}}_{2}^{2}) \\ 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} \\ L = T - V = \frac{1}{2} m ({\dot{q}}_{1}^{2} + {\dot{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"><mn>2</mn></mrow></mfrac></mrow><mi>m</mi><mo stretchy="false">(</mo><msup><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"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><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"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">)</mo><mo>&#x2212;</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 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Identifiers

$T$

$m$

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

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

$V$

$m$

$g$

$l$

$ϕ_{1}$

$m$

$g$

$l$

$ϕ_{2}$

$k$

$q_{1}$

$q_{2}$

$g$

$l$

$m$

$q_{1}$

$g$

$l$

$m$

$q_{2}$

$k$

$q_{1}$

$q_{2}$

$L$

$T$

$V$

$m$

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

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

$g$

$l$

$m$

$q_{1}$

$g$

$l$

$m$

$q_{2}$

$k$

$q_{1}$

$q_{2}$

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