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Display information for equation id:math.1899.13 on revision:1899

* Page found: Eichtransformation der Lagrangefunktion (eq math.1899.13)

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TeX (original user input): 

\begin{align}
  & L\acute{\ }(q,\dot{q},t)=\frac{m}{2}{{{\dot{\bar{q}}}}^{2}}+e\left( \dot{\bar{q}}\bar{A}\acute{\ }(\bar{q},t)-\Phi \acute{\ }(\bar{q},t) \right) \\
 & L\acute{\ }(q,\dot{q},t)=\frac{m}{2}{{{\dot{\bar{q}}}}^{2}}+e\left( \dot{\bar{q}}\bar{A}(\bar{q},t)+\dot{\bar{q}}\cdot \nabla \chi -\Phi (\bar{q},t)+\dot{\chi } \right) \\
 & L\acute{\ }(q,\dot{q},t)=L+e\left( \dot{\chi }+\dot{\bar{q}}\cdot \nabla \chi  \right)\acute{\ }=L+\frac{d}{dt}\left( e\chi (\bar{q},t) \right) \\
\end{align}

TeX (checked): 

{\begin{aligned}&L{\acute {\ }}(q,{\dot {q}},t)={\frac {m}{2}}{{\dot {\bar {q}}}^{2}}+e\left({\dot {\bar {q}}}{\bar {A}}{\acute {\ }}({\bar {q}},t)-\Phi {\acute {\ }}({\bar {q}},t)\right)\\&L{\acute {\ }}(q,{\dot {q}},t)={\frac {m}{2}}{{\dot {\bar {q}}}^{2}}+e\left({\dot {\bar {q}}}{\bar {A}}({\bar {q}},t)+{\dot {\bar {q}}}\cdot \nabla \chi -\Phi ({\bar {q}},t)+{\dot {\chi }}\right)\\&L{\acute {\ }}(q,{\dot {q}},t)=L+e\left({\dot {\chi }}+{\dot {\bar {q}}}\cdot \nabla \chi \right){\acute {\ }}=L+{\frac {d}{dt}}\left(e\chi ({\bar {q}},t)\right)\\\end{aligned}}

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MathML (49.957 KB / 5.123 KB) :

L ⁢ ´ ⁢ ( q , q ˙ , t ) = m 2 ⁢ q ¯ ˙ 2 + e ⁢ ( q ¯ ˙ ⁢ A ¯ ⁢ ´ ⁢ ( q ¯ , t ) - Φ ⁢ ´ ⁢ ( q ¯ , t ) ) L ⁢ ´ ⁢ ( q , q ˙ , t ) = m 2 ⁢ q ¯ ˙ 2 + e ⁢ ( q ¯ ˙ ⁢ A ¯ ⁢ ( q ¯ , t ) + q ¯ ˙ ⋅ ∇ ⁡ χ - Φ ⁢ ( q ¯ , t ) + χ ˙ ) L ⁢ ´ ⁢ ( q , q ˙ , t ) = L + e ⁢ ( χ ˙ + q ¯ ˙ ⋅ ∇ ⁡ χ ) ⁢ ´ = L + d d ⁢ t ⁢ ( e ⁢ χ ⁢ ( q ¯ , t ) ) missing-subexpression 𝐿 ´ absent 𝑞 ˙ 𝑞 𝑡 𝑚 2 superscript ˙ ¯ 𝑞 2 𝑒 ˙ ¯ 𝑞 ¯ 𝐴 ´ absent ¯ 𝑞 𝑡 Φ ´ absent ¯ 𝑞 𝑡 missing-subexpression 𝐿 ´ absent 𝑞 ˙ 𝑞 𝑡 𝑚 2 superscript ˙ ¯ 𝑞 2 𝑒 ˙ ¯ 𝑞 ¯ 𝐴 ¯ 𝑞 𝑡 ⋅ ˙ ¯ 𝑞 ∇ 𝜒 Φ ¯ 𝑞 𝑡 ˙ 𝜒 missing-subexpression 𝐿 ´ absent 𝑞 ˙ 𝑞 𝑡 𝐿 𝑒 ˙ 𝜒 ⋅ ˙ ¯ 𝑞 ∇ 𝜒 ´ absent 𝐿 𝑑 𝑑 𝑡 𝑒 𝜒 ¯ 𝑞 𝑡 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle L\acute{\ }(q,\dot{% q},t)=\frac{m}{2}{{{\dot{\bar{q}}}}^{2}}+e\left(\dot{\bar{q}}\bar{A}\acute{\ }% (\bar{q},t)-\Phi\acute{\ }(\bar{q},t)\right)\\ &\displaystyle L\acute{\ }(q,\dot{q},t)=\frac{m}{2}{{{\dot{\bar{q}}}}^{2}}+e% \left(\dot{\bar{q}}\bar{A}(\bar{q},t)+\dot{\bar{q}}\cdot\nabla\chi-\Phi(\bar{q% },t)+\dot{\chi}\right)\\ &\displaystyle L\acute{\ }(q,\dot{q},t)=L+e\left(\dot{\chi}+\dot{\bar{q}}\cdot% \nabla\chi\right)\acute{\ }=L+\frac{d}{dt}\left(e\chi(\bar{q},t)\right)\\ \end{aligned}}}

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L´(q,q˙,t)=m2q¯˙2+e(q¯˙A¯´(q¯,t)−Φ´(q¯,t))L´(q,q˙,t)=m2q¯˙2+e(q¯˙A¯(q¯,t)+q¯˙⋅∇χ−Φ(q¯,t)+χ˙)L´(q,q˙,t)=L+e(χ˙+q¯˙⋅∇χ)´=L+ddt(eχ(q¯,t))

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