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Display information for equation id:math.1926.14 on revision:1926

* Page found: Zeitliche Translationsinvarianz (eq math.1926.14)

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TeX (original user input): 

\frac{dL}{dt}=\sum\limits_{k}^{{}}{\left( \frac{\partial L}{\partial {{{\dot{q}}}_{k}}}{{{\ddot{q}}}_{k}}+\frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}{{{\dot{q}}}_{k}} \right)}=\frac{d}{dt}\sum\limits_{k}^{{}}{\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}{{{\dot{q}}}_{k}}=2\frac{dT}{dt}}

TeX (checked): 

{\frac {dL}{dt}}=\sum \limits _{k}^{}{\left({\frac {\partial L}{\partial {{\dot {q}}_{k}}}}{{\ddot {q}}_{k}}+{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}{{\dot {q}}_{k}}\right)}={\frac {d}{dt}}\sum \limits _{k}^{}{{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}{{\dot {q}}_{k}}=2{\frac {dT}{dt}}}

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MathML (21.787 KB / 2.672 KB) :

d ⁢ L d ⁢ t = ∑ k ( ∂ ⁡ L ∂ ⁡ q ˙ k ⁢ q ¨ k + d d ⁢ t ⁢ ∂ ⁡ L ∂ ⁡ q ˙ k ⁢ q ˙ k ) = d d ⁢ t ⁢ ∑ k ∂ ⁡ L ∂ ⁡ q ˙ k ⁢ q ˙ k = 2 ⁢ d ⁢ T d ⁢ t 𝑑 𝐿 𝑑 𝑡 subscript 𝑘 𝐿 subscript ˙ 𝑞 𝑘 subscript ¨ 𝑞 𝑘 𝑑 𝑑 𝑡 𝐿 subscript ˙ 𝑞 𝑘 subscript ˙ 𝑞 𝑘 𝑑 𝑑 𝑡 subscript 𝑘 𝐿 subscript ˙ 𝑞 𝑘 subscript ˙ 𝑞 𝑘 2 𝑑 𝑇 𝑑 𝑡 {\displaystyle{\displaystyle\frac{dL}{dt}=\sum\limits_{k}{\left(\frac{\partial L% }{\partial{{{\dot{q}}}_{k}}}{{{\ddot{q}}}_{k}}+\frac{d}{dt}\frac{\partial L}{% \partial{{{\dot{q}}}_{k}}}{{{\dot{q}}}_{k}}\right)}=\frac{d}{dt}\sum\limits_{k% }{\frac{\partial L}{\partial{{{\dot{q}}}_{k}}}{{{\dot{q}}}_{k}}=2\frac{dT}{dt}% }}}

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MathML (3.217 KB / 385 B) :

dLdt=∑k(∂L∂q˙kq¨k+ddt∂L∂q˙kq˙k)=ddt∑k∂L∂q˙kq˙k=2dTdt

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Identifiers

  • d
  • L
  • d
  • t
  • k
  • L
  • q˙k
  • q¨k
  • d
  • d
  • t
  • L
  • q˙k
  • q˙k
  • d
  • d
  • t
  • k
  • L
  • q˙k
  • q˙k
  • d
  • T
  • d
  • t

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