- testwiki

General

Display information for equation id:math.1321.33 on revision:1321

* Page found: Das Hamiltonsche Prinzip (eq math.1321.33)

Occurrences on the following pages:

Variationsprinzipien Eq: math.1889.35

Hash: 14c1c7b9c4320b15ec06f157c4486e38

TeX (original user input):

\delta f=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt\frac{dF(x)}{dx}\delta x(t)}\quad =0\ f\ddot{u}r\ beliebige\ \delta x(t)\ (Extremum)

TeX (checked):

\delta f=\int \limits _{{t}_{1}}^{{t}_{2}}{dt{\frac {dF(x)}{dx}}\delta x(t)}\quad =0\ f{\ddot {u}}r\ beliebige\ \delta x(t)\ (Extremum)

LaTeXML (experimental; uses MathML) rendering

MathML (11.5 KB / 1.879 KB) :

{\displaystyle{\displaystyle\delta f=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt% \frac{dF(x)}{dx}\delta x(t)}\quad=0\ f\ddot{u}r\ beliebige\ \delta x(t)\ (% Extremum)}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\delta f=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt%&#10;\frac{dF(x)}{dx}\delta x(t)}\quad=0\ f\ddot{u}r\ beliebige\ \delta x(t)\ (%&#10;Extremum)}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">δ</mi>
      <mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">f</mi>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
      <mstyle displaystyle="true" id="p1.1.m1.1.51" xref="p1.1.m1.1.51.cmml">
        <munderover id="p1.1.m1.1.51a" xref="p1.1.m1.1.51.cmml">
          <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">∫</mo>
          <msub id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">
            <mi id="p1.1.m1.1.5.1.1" xref="p1.1.m1.1.5.1.1.cmml">t</mi>
            <mn id="p1.1.m1.1.5.1.2.1" xref="p1.1.m1.1.5.1.2.1.cmml">1</mn>
          </msub>
          <msub id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">
            <mi id="p1.1.m1.1.6.1.1" xref="p1.1.m1.1.6.1.1.cmml">t</mi>
            <mn id="p1.1.m1.1.6.1.2.1" xref="p1.1.m1.1.6.1.2.1.cmml">2</mn>
          </msub>
        </munderover>
      </mstyle>
      <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">d</mi>
      <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">t</mi>
      <mstyle displaystyle="true" id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
        <mfrac id="p1.1.m1.1.9a" xref="p1.1.m1.1.9.cmml">
          <mrow id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">
            <mi id="p1.1.m1.1.9.2.1" xref="p1.1.m1.1.9.2.1.cmml">d</mi>
            <mo id="p1.1.m1.1.9.2.6" xref="p1.1.m1.1.9.2.6.cmml">⁢</mo>
            <mi id="p1.1.m1.1.9.2.2" xref="p1.1.m1.1.9.2.2.cmml">F</mi>
            <mo id="p1.1.m1.1.9.2.6a" xref="p1.1.m1.1.9.2.6.cmml">⁢</mo>
            <mrow id="p1.1.m1.1.9.2.7" xref="p1.1.m1.1.9.2.cmml">
              <mo stretchy="false" id="p1.1.m1.1.9.2.3" xref="p1.1.m1.1.9.2.cmml">(</mo>
              <mi id="p1.1.m1.1.9.2.4" xref="p1.1.m1.1.9.2.4.cmml">x</mi>
              <mo stretchy="false" id="p1.1.m1.1.9.2.5" xref="p1.1.m1.1.9.2.cmml">)</mo>
            </mrow>
          </mrow>
          <mrow id="p1.1.m1.1.9.3" xref="p1.1.m1.1.9.3.cmml">
            <mi id="p1.1.m1.1.9.3.1" xref="p1.1.m1.1.9.3.1.cmml">d</mi>
            <mo id="p1.1.m1.1.9.3.3" xref="p1.1.m1.1.9.3.3.cmml">⁢</mo>
            <mi id="p1.1.m1.1.9.3.2" xref="p1.1.m1.1.9.3.2.cmml">x</mi>
          </mrow>
        </mfrac>
      </mstyle>
      <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">δ</mi>
      <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">x</mi>
      <mrow id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
        <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">(</mo>
        <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">t</mi>
        <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">)</mo>
      </mrow>
      <mo mathvariant="italic" separator="true" id="p1.1.m1.1.50" xref="p1.1.m1.1.50.cmml"> </mo>
      <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">=</mo>
      <mpadded width="+5pt" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">
        <mn id="p1.1.m1.1.17a" xref="p1.1.m1.1.17.cmml">0</mn>
      </mpadded>
      <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">f</mi>
      <mover accent="true" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
        <mi id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">u</mi>
        <mo id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">¨</mo>
      </mover>
      <mpadded width="+5pt" id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
        <mi id="p1.1.m1.1.21a" xref="p1.1.m1.1.21.cmml">r</mi>
      </mpadded>
      <mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">b</mi>
      <mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">e</mi>
      <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">l</mi>
      <mi id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">i</mi>
      <mi id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">e</mi>
      <mi id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">b</mi>
      <mi id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">i</mi>
      <mi id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">g</mi>
      <mpadded width="+5pt" id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">
        <mi id="p1.1.m1.1.31a" xref="p1.1.m1.1.31.cmml">e</mi>
      </mpadded>
      <mi id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">δ</mi>
      <mi id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">x</mi>
      <mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
        <mo stretchy="false" id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">(</mo>
        <mi id="p1.1.m1.1.36" xref="p1.1.m1.1.36.cmml">t</mi>
        <mo rspace="7.5pt" stretchy="false" id="p1.1.m1.1.37" xref="p1.1.m1.1.37.cmml">)</mo>
      </mrow>
      <mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
        <mo stretchy="false" id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">(</mo>
        <mi id="p1.1.m1.1.40" xref="p1.1.m1.1.40.cmml">E</mi>
        <mi id="p1.1.m1.1.41" xref="p1.1.m1.1.41.cmml">x</mi>
        <mi id="p1.1.m1.1.42" xref="p1.1.m1.1.42.cmml">t</mi>
        <mi id="p1.1.m1.1.43" xref="p1.1.m1.1.43.cmml">r</mi>
        <mi id="p1.1.m1.1.44" xref="p1.1.m1.1.44.cmml">e</mi>
        <mi id="p1.1.m1.1.45" xref="p1.1.m1.1.45.cmml">m</mi>
        <mi id="p1.1.m1.1.46" xref="p1.1.m1.1.46.cmml">u</mi>
        <mi id="p1.1.m1.1.47" xref="p1.1.m1.1.47.cmml">m</mi>
        <mo stretchy="false" id="p1.1.m1.1.48" xref="p1.1.m1.1.48.cmml">)</mo>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
      <cerror id="p1.1.m1.1d">
        <csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">δ</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">f</csymbol>
        <eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
        <apply id="p1.1.m1.1.51.cmml" xref="p1.1.m1.1.51">
          <csymbol cd="ambiguous" id="p1.1.m1.1.51.1.cmml" xref="p1.1.m1.1.51">superscript</csymbol>
          <apply id="p1.1.m1.1.51.2.cmml" xref="p1.1.m1.1.51">
            <csymbol cd="ambiguous" id="p1.1.m1.1.51.2.1.cmml" xref="p1.1.m1.1.51">subscript</csymbol>
            <int id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
            <apply id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.5.1.3.cmml" xref="p1.1.m1.1.5.1">subscript</csymbol>
              <ci id="p1.1.m1.1.5.1.1.cmml" xref="p1.1.m1.1.5.1.1">𝑡</ci>
              <cn type="integer" id="p1.1.m1.1.5.1.2.1.cmml" xref="p1.1.m1.1.5.1.2.1">1</cn>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.6.1.3.cmml" xref="p1.1.m1.1.6.1">subscript</csymbol>
            <ci id="p1.1.m1.1.6.1.1.cmml" xref="p1.1.m1.1.6.1.1">𝑡</ci>
            <cn type="integer" id="p1.1.m1.1.6.1.2.1.cmml" xref="p1.1.m1.1.6.1.2.1">2</cn>
          </apply>
        </apply>
        <csymbol cd="unknown" id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">d</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">t</csymbol>
        <apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
          <divide id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9"/>
          <apply id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">
            <times id="p1.1.m1.1.9.2.6.cmml" xref="p1.1.m1.1.9.2.6"/>
            <ci id="p1.1.m1.1.9.2.1.cmml" xref="p1.1.m1.1.9.2.1">𝑑</ci>
            <ci id="p1.1.m1.1.9.2.2.cmml" xref="p1.1.m1.1.9.2.2">𝐹</ci>
            <ci id="p1.1.m1.1.9.2.4.cmml" xref="p1.1.m1.1.9.2.4">𝑥</ci>
          </apply>
          <apply id="p1.1.m1.1.9.3.cmml" xref="p1.1.m1.1.9.3">
            <times id="p1.1.m1.1.9.3.3.cmml" xref="p1.1.m1.1.9.3.3"/>
            <ci id="p1.1.m1.1.9.3.1.cmml" xref="p1.1.m1.1.9.3.1">𝑑</ci>
            <ci id="p1.1.m1.1.9.3.2.cmml" xref="p1.1.m1.1.9.3.2">𝑥</ci>
          </apply>
        </apply>
        <csymbol cd="unknown" id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">δ</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">x</csymbol>
        <cerror id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
          <csymbol cd="ambiguous" id="p1.1.m1.1.5a.cmml" xref="p1.1.m1.1.5">fragments</csymbol>
          <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">t</csymbol>
          <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">)</ci>
        </cerror>
        <ci id="p1.1.m1.1.50.cmml" xref="p1.1.m1.1.50">italic- </ci>
        <eq id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
        <cn type="integer" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">0</cn>
        <csymbol cd="unknown" id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">f</csymbol>
        <apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
          <ci id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">¨</ci>
          <ci id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">𝑢</ci>
        </apply>
        <csymbol cd="unknown" id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">r</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">b</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">e</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">l</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">i</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">e</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">b</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">i</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">g</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31">e</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">δ</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">x</csymbol>
        <cerror id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
          <csymbol cd="ambiguous" id="p1.1.m1.1.6a.cmml" xref="p1.1.m1.1.6">fragments</csymbol>
          <ci id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.36.cmml" xref="p1.1.m1.1.36">t</csymbol>
          <ci id="p1.1.m1.1.37.cmml" xref="p1.1.m1.1.37">)</ci>
        </cerror>
        <cerror id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
          <csymbol cd="ambiguous" id="p1.1.m1.1.15a.cmml" xref="p1.1.m1.1.15">fragments</csymbol>
          <ci id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.40.cmml" xref="p1.1.m1.1.40">E</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.41.cmml" xref="p1.1.m1.1.41">x</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.42.cmml" xref="p1.1.m1.1.42">t</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.43.cmml" xref="p1.1.m1.1.43">r</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.44.cmml" xref="p1.1.m1.1.44">e</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.45.cmml" xref="p1.1.m1.1.45">m</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.46.cmml" xref="p1.1.m1.1.46">u</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.47.cmml" xref="p1.1.m1.1.47">m</csymbol>
          <ci id="p1.1.m1.1.48.cmml" xref="p1.1.m1.1.48">)</ci>
        </cerror>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle\delta f=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt%
\frac{dF(x)}{dx}\delta x(t)}\quad=0\ f\ddot{u}r\ beliebige\ \delta x(t)\ (%
Extremum)}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimental; no images) rendering

MathML (1.494 KB / 408 B) :

δ f = \int_{t_{1}}^{t_{2}} d t \frac{d F (x)}{d x} δ x (t) = 0 f \ddot{u} r b e l i e b i g e δ x (t) (E x t r e m u m)

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>&#x03B4;</mi><mi>f</mi><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></munderover><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>x</mi></mrow></mrow></mfrac></mrow><mi>&#x03B4;</mi><mi>x</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mspace width="1em"></mspace><mo>=</mo><mn>0</mn><mspace width="0.5em"/><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>u</mi><mo>¨</mo></mover></mrow></mrow><mi>r</mi><mspace width="0.5em"/><mi>b</mi><mi>e</mi><mi>l</mi><mi>i</mi><mi>e</mi><mi>b</mi><mi>i</mi><mi>g</mi><mi>e</mi><mspace width="0.5em"/><mi>&#x03B4;</mi><mi>x</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mspace width="0.5em"/><mo stretchy="false">(</mo><mi>E</mi><mi>x</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>m</mi><mi>u</mi><mi>m</mi><mo stretchy="false">)</mo></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$δ$

$f$

$t_{1}$

$t_{2}$

$t$

$d$

$F$

$x$

$d$

$x$

$δ$

$x$

$t$

$f$

$\ddot{u}$

$r$

$b$

$e$

$l$

$i$

$e$

$b$

$i$

$g$

$e$

$δ$

$x$

$t$

$E$

$x$

$t$

$r$

$e$

$m$

$u$

$m$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search