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Display information for equation id:math.1515.48 on revision:1515

* Page found: Normalschwingungen (eq math.1515.48)

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TeX (original user input): 

\begin{align}
  & {{\left( \frac{{{\partial }^{2}}V}{\partial {{q}_{1}}^{2}} \right)}_{0}}={{\left( \frac{{{\partial }^{2}}V}{\partial {{q}_{2}}^{2}} \right)}_{0}}=m\frac{g}{l}+k \\
 & \left( \frac{{{\partial }^{2}}V}{\partial {{q}_{1}}\partial {{q}_{2}}} \right)=mg\frac{\partial }{\partial {{q}_{1}}}(\sin \frac{{{q}_{2}}}{l})-k\frac{\partial }{\partial {{q}_{1}}}({{q}_{1}}-{{q}_{2}})=-k \\
\end{align}

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MathML (30.857 KB / 3.208 KB) :

( ∂ 2 ⁡ V ∂ ⁡ q 1 2 ) 0 = ( ∂ 2 ⁡ V ∂ ⁡ q 2 2 ) 0 = m ⁢ g l + k ( ∂ 2 ⁡ V ∂ ⁡ q 1 ⁢ ∂ ⁡ q 2 ) = m ⁢ g ⁢ ∂ ∂ ⁡ q 1 ⁢ ( sin ⁡ q 2 l ) - k ⁢ ∂ ∂ ⁡ q 1 ⁢ ( q 1 - q 2 ) = - k missing-subexpression subscript superscript 2 𝑉 superscript subscript 𝑞 1 2 0 subscript superscript 2 𝑉 superscript subscript 𝑞 2 2 0 𝑚 𝑔 𝑙 𝑘 missing-subexpression superscript 2 𝑉 subscript 𝑞 1 subscript 𝑞 2 𝑚 𝑔 subscript 𝑞 1 subscript 𝑞 2 𝑙 𝑘 subscript 𝑞 1 subscript 𝑞 1 subscript 𝑞 2 𝑘 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle{{\left(\frac{{{% \partial}^{2}}V}{\partial{{q}_{1}}^{2}}\right)}_{0}}={{\left(\frac{{{\partial}% ^{2}}V}{\partial{{q}_{2}}^{2}}\right)}_{0}}=m\frac{g}{l}+k\\ &\displaystyle\left(\frac{{{\partial}^{2}}V}{\partial{{q}_{1}}\partial{{q}_{2}% }}\right)=mg\frac{\partial}{\partial{{q}_{1}}}(\sin\frac{{{q}_{2}}}{l})-k\frac% {\partial}{\partial{{q}_{1}}}({{q}_{1}}-{{q}_{2}})=-k\\ \end{aligned}}}

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MathML (3.509 KB / 487 B) :

(∂2V∂q12)0=(∂2V∂q22)0=mgl+k(∂2V∂q1∂q2)=mg∂∂q1(sin⁡q2l)−k∂∂q1(q1−q2)=−k

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