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Display information for equation id:math.2174.6 on revision:2174

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Transformationsverhalten der Ströme und Felder Eq: math.2174.6

Hash: fde297a154f1b44d3ad8baa6dbc8267e

TeX (original user input):

\begin{align}
& {{x}^{0}}\acute{\ }=\gamma \left( {{x}^{0}}-\beta {{x}^{1}} \right)\Leftrightarrow t\acute{\ }=\gamma \left( t-\frac{v}{{{c}^{2}}}{{x}^{1}} \right) \\
& {{x}^{1}}\acute{\ }=\gamma \left( {{x}^{1}}-\beta {{x}^{0}} \right)\Leftrightarrow {{x}^{1}}\acute{\ }=\gamma \left( {{x}^{1}}-vt \right) \\
& {{x}^{2}}\acute{\ }={{x}^{2}} \\
& {{x}^{3}}\acute{\ }={{x}^{3}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{{x}^{0}}{\acute {\ }}=\gamma \left({{x}^{0}}-\beta {{x}^{1}}\right)\Leftrightarrow t{\acute {\ }}=\gamma \left(t-{\frac {v}{{c}^{2}}}{{x}^{1}}\right)\\&{{x}^{1}}{\acute {\ }}=\gamma \left({{x}^{1}}-\beta {{x}^{0}}\right)\Leftrightarrow {{x}^{1}}{\acute {\ }}=\gamma \left({{x}^{1}}-vt\right)\\&{{x}^{2}}{\acute {\ }}={{x}^{2}}\\&{{x}^{3}}{\acute {\ }}={{x}^{3}}\\\end{aligned}}

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\begin{matrix} x^{0} \overset{´}{} = γ (x^{0} - β x^{1}) \Leftrightarrow t \overset{´}{} = γ (t - \frac{v}{c^{2}} x^{1}) \\ x^{1} \overset{´}{} = γ (x^{1} - β x^{0}) \Leftrightarrow x^{1} \overset{´}{} = γ (x^{1} - v t) \\ x^{2} \overset{´}{} = x^{2} \\ x^{3} \overset{´}{} = x^{3} \end{matrix}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mi>γ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo stretchy="false">−</mo><mi>β</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">⇔</mo><mi>t</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mi>γ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mi>γ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo stretchy="false">−</mo><mi>β</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">⇔</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mi>γ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo stretchy="false">−</mo><mi>v</mi><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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$\overset{´}{}$

$γ$

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$\overset{´}{}$

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$c$

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