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Display information for equation id:math.1515.3 on revision:1515

* Page found: Normalschwingungen (eq math.1515.3)

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\begin{align}
  & V(0,....,0)=0 \\
 & \sum\limits_{j}{{{\left( \frac{\partial V}{\partial {{q}_{j}}} \right)}_{0}}{{q}_{j}}}=0\quad \left( \frac{\partial V}{\partial {{q}_{j}}} \right)=-{{Q}_{j}}=0 \\
 & \frac{1}{2}\sum\limits_{j,k}{{{\left( \frac{{{\partial }^{2}}V}{\partial {{q}_{j}}\partial {{q}_{k}}} \right)}_{0}}{{q}_{j}}{{q}_{k}}}=\frac{1}{2}\sum\limits_{j,k}{{{V}_{jk}}{{q}_{j}}{{q}_{k}}} \\
\end{align}

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V ( 0 , … . , 0 ) = 0 ∑ j ( ∂ ⁡ V ∂ ⁡ q j ) 0 ⁢ q j = 0   ( ∂ ⁡ V ∂ ⁡ q j ) = - Q j = 0 1 2 ⁢ ∑ j , k ( ∂ 2 ⁡ V ∂ ⁡ q j ⁢ ∂ ⁡ q k ) 0 ⁢ q j ⁢ q k = 1 2 ⁢ ∑ j , k V j ⁢ k ⁢ q j ⁢ q k missing-subexpression fragments V fragments ( 0 , … . , 0 ) 0 missing-subexpression formulae-sequence subscript 𝑗 subscript 𝑉 subscript 𝑞 𝑗 0 subscript 𝑞 𝑗 0 𝑉 subscript 𝑞 𝑗 subscript 𝑄 𝑗 0 missing-subexpression 1 2 subscript 𝑗 𝑘 subscript superscript 2 𝑉 subscript 𝑞 𝑗 subscript 𝑞 𝑘 0 subscript 𝑞 𝑗 subscript 𝑞 𝑘 1 2 subscript 𝑗 𝑘 subscript 𝑉 𝑗 𝑘 subscript 𝑞 𝑗 subscript 𝑞 𝑘 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle V(0,....,0)=0\\ &\displaystyle\sum\limits_{j}{{{\left(\frac{\partial V}{\partial{{q}_{j}}}% \right)}_{0}}{{q}_{j}}}=0\quad\left(\frac{\partial V}{\partial{{q}_{j}}}\right% )=-{{Q}_{j}}=0\\ &\displaystyle\frac{1}{2}\sum\limits_{j,k}{{{\left(\frac{{{\partial}^{2}}V}{% \partial{{q}_{j}}\partial{{q}_{k}}}\right)}_{0}}{{q}_{j}}{{q}_{k}}}=\frac{1}{2% }\sum\limits_{j,k}{{{V}_{jk}}{{q}_{j}}{{q}_{k}}}\\ \end{aligned}}}

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V(0,....,0)=0∑j(∂V∂qj)0qj=0(∂V∂qj)=−Qj=012∑j,k(∂2V∂qj∂qk)0qjqk=12∑j,kVjkqjqk

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