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Display information for equation id:math.1500.14 on revision:1500

* Page found: Generalisierte Koordinaten (eq math.1500.14)

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TeX (original user input): 

\frac{\partial }{\partial {{{\dot{q}}}_{j}}}{{\vec{v}}_{i}}=\frac{\partial }{\partial {{{\dot{q}}}_{j}}}{{\left[ \sum\limits_{j=1}^{f}{\left( \frac{\partial {{{\bar{r}}}_{i}}}{\partial {{q}_{j}}}{{{\dot{q}}}_{j}} \right)}+\frac{\partial }{\partial t}{{{\bar{r}}}_{i}} \right]}_{{}}}=\frac{\partial }{\partial {{q}_{j}}}{{\bar{r}}_{i}}({{q}_{1}},...,{{q}_{f}},t)

TeX (checked): 

{\frac {\partial }{\partial {{\dot {q}}_{j}}}}{{\vec {v}}_{i}}={\frac {\partial }{\partial {{\dot {q}}_{j}}}}{{\left[\sum \limits _{j=1}^{f}{\left({\frac {\partial {{\bar {r}}_{i}}}{\partial {{q}_{j}}}}{{\dot {q}}_{j}}\right)}+{\frac {\partial }{\partial t}}{{\bar {r}}_{i}}\right]}_{}}={\frac {\partial }{\partial {{q}_{j}}}}{{\bar {r}}_{i}}({{q}_{1}},...,{{q}_{f}},t)

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∂ ∂ ⁡ q ˙ j ⁢ v → i = ∂ ∂ ⁡ q ˙ j ⁢ [ ∑ j = 1 f ( ∂ ⁡ r ¯ i ∂ ⁡ q j ⁢ q ˙ j ) + ∂ ∂ ⁡ t ⁢ r ¯ i ] = ∂ ∂ ⁡ q j ⁢ r ¯ i ⁢ ( q 1 , … , q f , t ) subscript ˙ 𝑞 𝑗 subscript → 𝑣 𝑖 subscript ˙ 𝑞 𝑗 delimited-[] superscript subscript 𝑗 1 𝑓 subscript ¯ 𝑟 𝑖 subscript 𝑞 𝑗 subscript ˙ 𝑞 𝑗 𝑡 subscript ¯ 𝑟 𝑖 subscript 𝑞 𝑗 subscript ¯ 𝑟 𝑖 subscript 𝑞 1 … subscript 𝑞 𝑓 𝑡 {\displaystyle{\displaystyle\frac{\partial}{\partial{{{\dot{q}}}_{j}}}{{\vec{v% }}_{i}}=\frac{\partial}{\partial{{{\dot{q}}}_{j}}}{{\left[\sum\limits_{j=1}^{f% }{\left(\frac{\partial{{{\bar{r}}}_{i}}}{\partial{{q}_{j}}}{{{\dot{q}}}_{j}}% \right)}+\frac{\partial}{\partial t}{{{\bar{r}}}_{i}}\right]}}=\frac{\partial}% {\partial{{q}_{j}}}{{\bar{r}}_{i}}({{q}_{1}},...,{{q}_{f}},t)}}

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∂∂q˙jv→i=∂∂q˙j[∑j=1f(∂r¯i∂qjq˙j)+∂∂tr¯i]=∂∂qjr¯i(q1,...,qf,t)

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

Identifiers

  • q˙j
  • v→i
  • q˙j
  • j
  • f
  • r¯i
  • qj
  • q˙j
  • t
  • r¯i
  • qj
  • r¯i
  • q1
  • qf
  • t

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