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Display information for equation id:math.2176.13 on revision:2176

* Page found: Relativistisches Hamiltonprinzip (eq math.2176.13)

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Relativistisches Hamiltonprinzip Eq: math.2176.13

Hash: 796fc0dbe3290b05d5831009a129408f

TeX (original user input):

\begin{align}
& d{{\phi }^{\mu }}={{\partial }^{\nu }}{{\phi }^{\mu }}d{{x}_{\nu }}={{\partial }^{\nu }}{{\phi }^{\mu }}{{u}_{\nu }}ds \\
& \delta {{\phi }^{\mu }}={{\partial }^{\nu }}{{\phi }^{\mu }}\delta {{x}_{\nu }} \\
& \delta {{\phi }^{\mu }}d{{x}_{\mu }}={{\partial }^{\nu }}{{\phi }^{\mu }}\delta {{x}_{\nu }}d{{x}_{\mu }}=i<->k={{\partial }^{\mu }}{{\phi }^{\nu }}\delta {{x}_{\mu }}d{{x}_{\nu }}={{\partial }^{\mu }}{{\phi }^{\nu }}{{u}_{\nu }}\delta {{x}_{\mu }}ds \\
\end{align}

TeX (checked):

{\begin{aligned}&d{{\phi }^{\mu }}={{\partial }^{\nu }}{{\phi }^{\mu }}d{{x}_{\nu }}={{\partial }^{\nu }}{{\phi }^{\mu }}{{u}_{\nu }}ds\\&\delta {{\phi }^{\mu }}={{\partial }^{\nu }}{{\phi }^{\mu }}\delta {{x}_{\nu }}\\&\delta {{\phi }^{\mu }}d{{x}_{\mu }}={{\partial }^{\nu }}{{\phi }^{\mu }}\delta {{x}_{\nu }}d{{x}_{\mu }}=i<->k={{\partial }^{\mu }}{{\phi }^{\nu }}\delta {{x}_{\mu }}d{{x}_{\nu }}={{\partial }^{\mu }}{{\phi }^{\nu }}{{u}_{\nu }}\delta {{x}_{\mu }}ds\\\end{aligned}}

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\begin{matrix} d ϕ^{μ} = \partial^{ν} ϕ^{μ} d x_{ν} = \partial^{ν} ϕ^{μ} u_{ν} d s \\ δ ϕ^{μ} = \partial^{ν} ϕ^{μ} δ x_{ν} \\ δ ϕ^{μ} d x_{μ} = \partial^{ν} ϕ^{μ} δ x_{ν} d x_{μ} = i < - > k = \partial^{μ} ϕ^{ν} δ x_{μ} d x_{ν} = \partial^{μ} ϕ^{ν} u_{ν} δ x_{μ} d s \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"><mi>d</mi><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo stretchy="false">=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi>d</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo stretchy="false">=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mi>d</mi><mi>s</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>δ</mi><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo stretchy="false">=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi>δ</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>δ</mi><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi>d</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msub><mo stretchy="false">=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi>δ</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mi>d</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msub><mo stretchy="false">=</mo><mi>i</mi><mo>&lt;</mo><mo stretchy="false">−</mo><mo>&gt;</mo><mi>k</mi><mo stretchy="false">=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mi>δ</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msub><mi>d</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo stretchy="false">=</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msup><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mi>δ</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msub><mi>d</mi><mi>s</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

$d$

$ϕ$

$μ$

$ν$

$ϕ$

$μ$

$d$

$x_{ν}$

$ν$

$ϕ$

$μ$

$u_{ν}$

$d$

$s$

$δ$

$ϕ$

$μ$

$ν$

$ϕ$

$μ$

$δ$

$x_{ν}$

$δ$

$ϕ$

$μ$

$d$

$x_{μ}$

$ν$

$ϕ$

$μ$

$δ$

$x_{ν}$

$d$

$x_{μ}$

$i$

$k$

$μ$

$ϕ$

$ν$

$δ$

$x_{μ}$

$d$

$x_{ν}$

$μ$

$ϕ$

$ν$

$u_{ν}$

$δ$

$x_{μ}$

$d$

$s$

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