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Display information for equation id:math.1497.18 on revision:1497

* Page found: Generalisierte Koordinaten (eq math.1497.18)

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TeX (original user input): 

-\frac{\partial V}{\partial {{q}_{j}}}=-\sum\limits_{i}^{{}}{{{\nabla }_{\vec{r}i}}V({{{\bar{r}}}_{1}},{{{\bar{r}}}_{2}},...,{{{\bar{r}}}_{N}})\frac{\partial {{{\bar{r}}}_{i}}}{\partial {{q}_{j}}}}=\sum\limits_{i}^{{}}{{{{\vec{X}}}_{i}}\frac{\partial {{{\bar{r}}}_{i}}}{\partial {{q}_{j}}}}={{Q}_{j}}

TeX (checked): 

-{\frac {\partial V}{\partial {{q}_{j}}}}=-\sum \limits _{i}^{}{{{\nabla }_{{\vec {r}}i}}V({{\bar {r}}_{1}},{{\bar {r}}_{2}},...,{{\bar {r}}_{N}}){\frac {\partial {{\bar {r}}_{i}}}{\partial {{q}_{j}}}}}=\sum \limits _{i}^{}{{{\vec {X}}_{i}}{\frac {\partial {{\bar {r}}_{i}}}{\partial {{q}_{j}}}}}={{Q}_{j}}

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MathML (20 KB / 2.589 KB) :

- ∂ ⁡ V ∂ ⁡ q j = - ∑ i ∇ r → ⁢ i ⁡ V ⁢ ( r ¯ 1 , r ¯ 2 , … , r ¯ N ) ⁢ ∂ ⁡ r ¯ i ∂ ⁡ q j = ∑ i X → i ⁢ ∂ ⁡ r ¯ i ∂ ⁡ q j = Q j 𝑉 subscript 𝑞 𝑗 subscript 𝑖 subscript ∇ → 𝑟 𝑖 𝑉 subscript ¯ 𝑟 1 subscript ¯ 𝑟 2 … subscript ¯ 𝑟 𝑁 subscript ¯ 𝑟 𝑖 subscript 𝑞 𝑗 subscript 𝑖 subscript → 𝑋 𝑖 subscript ¯ 𝑟 𝑖 subscript 𝑞 𝑗 subscript 𝑄 𝑗 {\displaystyle{\displaystyle-\frac{\partial V}{\partial{{q}_{j}}}=-\sum\limits% _{i}{{{\nabla}_{\vec{r}i}}V({{{\bar{r}}}_{1}},{{{\bar{r}}}_{2}},...,{{{\bar{r}% }}_{N}})\frac{\partial{{{\bar{r}}}_{i}}}{\partial{{q}_{j}}}}=\sum\limits_{i}{{% {{\vec{X}}}_{i}}\frac{\partial{{{\bar{r}}}_{i}}}{\partial{{q}_{j}}}}={{Q}_{j}}}}

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MathML (2.93 KB / 423 B) :

−∂V∂qj=−∑i∇r→iV(r¯1,r¯2,...,r¯N)∂r¯i∂qj=∑iX→i∂r¯i∂qj=Qj

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Calculated based on the variables occurring on the entire Generalisierte Koordinaten page

Identifiers

  • V
  • qj
  • i
  • r→
  • i
  • V
  • r¯1
  • r¯2
  • r¯N
  • r¯i
  • qj
  • i
  • X→i
  • r¯i
  • qj
  • Qj

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