– PhysikWiki

General

Display information for equation id:math.1254.158 on revision:1254

* Page found: Das d'Alembertsche Prinzip (eq math.1254.158)

Occurrences on the following pages:

Normalschwingungen Eq: math.1515.2

Hash: a3122c2be48ffbe0c775e47cdf5bbc49

TeX (original user input):

V({{q}_{1}},...,{{q}_{f}})=V(0,....,0)+\sum\limits_{j}{{{\left( \frac{\partial V}{\partial {{q}_{j}}} \right)}_{0}}{{q}_{j}}+\frac{1}{2}\sum\limits_{j,k}{{{\left( \frac{{{\partial }^{2}}V}{\partial {{q}_{j}}\partial {{q}_{k}}} \right)}_{0}}{{q}_{j}}{{q}_{k}}+...}}

TeX (checked):

V({{q}_{1}},...,{{q}_{f}})=V(0,....,0)+\sum \limits _{j}{{{\left({\frac {\partial V}{\partial {{q}_{j}}}}\right)}_{0}}{{q}_{j}}+{\frac {1}{2}}\sum \limits _{j,k}{{{\left({\frac {{{\partial }^{2}}V}{\partial {{q}_{j}}\partial {{q}_{k}}}}\right)}_{0}}{{q}_{j}}{{q}_{k}}+...}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (16.62 KB / 2.419 KB) :

{\displaystyle{\displaystyle V({{q}_{1}},...,{{q}_{f}})=V(0,....,0)+\sum% \limits_{j}{{{\left(\frac{\partial V}{\partial{{q}_{j}}}\right)}_{0}}{{q}_{j}}% +\frac{1}{2}\sum\limits_{j,k}{{{\left(\frac{{{\partial}^{2}}V}{\partial{{q}_{j% }}\partial{{q}_{k}}}\right)}_{0}}{{q}_{j}}{{q}_{k}}+...}}}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle V({{q}_{1}},...,{{q}_{f}})=V(0,....,0)+\sum%&#10;\limits_{j}{{{\left(\frac{\partial V}{\partial{{q}_{j}}}\right)}_{0}}{{q}_{j}}%&#10;+\frac{1}{2}\sum\limits_{j,k}{{{\left(\frac{{{\partial}^{2}}V}{\partial{{q}_{j%&#10;}}\partial{{q}_{k}}}\right)}_{0}}{{q}_{j}}{{q}_{k}}+...}}}}" 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">V</mi>
      <mrow id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
        <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">(</mo>
        <msub id="p1.1.m1.1.50" xref="p1.1.m1.1.50.cmml">
          <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">q</mi>
          <mn id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">1</mn>
        </msub>
        <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">,</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">…</mi>
        <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">,</mo>
        <msub id="p1.1.m1.1.51" xref="p1.1.m1.1.51.cmml">
          <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">q</mi>
          <mi id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">f</mi>
        </msub>
        <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">=</mo>
      <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">V</mi>
      <mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
        <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">(</mo>
        <mn id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">0</mn>
        <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">,</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">…</mi>
        <mo id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">.</mo>
        <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">,</mo>
        <mn id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">0</mn>
        <mo stretchy="false" id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">+</mo>
      <mstyle displaystyle="true" id="p1.1.m1.1.52" xref="p1.1.m1.1.52.cmml">
        <munder id="p1.1.m1.1.52a" xref="p1.1.m1.1.52.cmml">
          <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">∑</mo>
          <mi id="p1.1.m1.1.27.1" xref="p1.1.m1.1.27.1.cmml">j</mi>
        </munder>
      </mstyle>
      <msub id="p1.1.m1.1.53" xref="p1.1.m1.1.53.cmml">
        <mrow id="p1.1.m1.1.53.2" xref="p1.1.m1.1.53.2.cmml">
          <mo id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">(</mo>
          <mstyle displaystyle="true" id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">
            <mfrac id="p1.1.m1.1.29a" xref="p1.1.m1.1.29.cmml">
              <mrow id="p1.1.m1.1.29.2" xref="p1.1.m1.1.29.2.cmml">
                <mo id="p1.1.m1.1.29.2.1" xref="p1.1.m1.1.29.2.1.cmml">∂</mo>
                <mo id="p1.1.m1.1.29.2a" xref="p1.1.m1.1.29.2.cmml">⁡</mo>
                <mi id="p1.1.m1.1.29.2.2" xref="p1.1.m1.1.29.2.2.cmml">V</mi>
              </mrow>
              <mrow id="p1.1.m1.1.29.3" xref="p1.1.m1.1.29.3.cmml">
                <mo id="p1.1.m1.1.29.3.1" xref="p1.1.m1.1.29.3.1.cmml">∂</mo>
                <mo id="p1.1.m1.1.29.3a" xref="p1.1.m1.1.29.3.cmml">⁡</mo>
                <msub id="p1.1.m1.1.29.3.4" xref="p1.1.m1.1.29.3.4.cmml">
                  <mi id="p1.1.m1.1.29.3.2" xref="p1.1.m1.1.29.3.2.cmml">q</mi>
                  <mi id="p1.1.m1.1.29.3.3.1" xref="p1.1.m1.1.29.3.3.1.cmml">j</mi>
                </msub>
              </mrow>
            </mfrac>
          </mstyle>
          <mo id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">)</mo>
        </mrow>
        <mn id="p1.1.m1.1.31.1" xref="p1.1.m1.1.31.1.cmml">0</mn>
      </msub>
      <msub id="p1.1.m1.1.54" xref="p1.1.m1.1.54.cmml">
        <mi id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">q</mi>
        <mi id="p1.1.m1.1.33.1" xref="p1.1.m1.1.33.1.cmml">j</mi>
      </msub>
      <mo id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">+</mo>
      <mstyle displaystyle="true" id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">
        <mfrac id="p1.1.m1.1.35a" xref="p1.1.m1.1.35.cmml">
          <mn id="p1.1.m1.1.35.2" xref="p1.1.m1.1.35.2.cmml">1</mn>
          <mn id="p1.1.m1.1.35.3" xref="p1.1.m1.1.35.3.cmml">2</mn>
        </mfrac>
      </mstyle>
      <mstyle displaystyle="true" id="p1.1.m1.1.55" xref="p1.1.m1.1.55.cmml">
        <munder id="p1.1.m1.1.55a" xref="p1.1.m1.1.55.cmml">
          <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.36" xref="p1.1.m1.1.36.cmml">∑</mo>
          <mrow id="p1.1.m1.1.37.1" xref="p1.1.m1.1.37.1.4.cmml">
            <mi id="p1.1.m1.1.37.1.1" xref="p1.1.m1.1.37.1.1.cmml">j</mi>
            <mo id="p1.1.m1.1.37.1.2" xref="p1.1.m1.1.37.1.4.cmml">,</mo>
            <mi id="p1.1.m1.1.37.1.3" xref="p1.1.m1.1.37.1.3.cmml">k</mi>
          </mrow>
        </munder>
      </mstyle>
      <msub id="p1.1.m1.1.56" xref="p1.1.m1.1.56.cmml">
        <mrow id="p1.1.m1.1.56.2" xref="p1.1.m1.1.56.2.cmml">
          <mo id="p1.1.m1.1.38" xref="p1.1.m1.1.38.cmml">(</mo>
          <mstyle displaystyle="true" id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">
            <mfrac id="p1.1.m1.1.39a" xref="p1.1.m1.1.39.cmml">
              <mrow id="p1.1.m1.1.39.2" xref="p1.1.m1.1.39.2.cmml">
                <msup id="p1.1.m1.1.39.2.4" xref="p1.1.m1.1.39.2.4.cmml">
                  <mo id="p1.1.m1.1.39.2.1" xref="p1.1.m1.1.39.2.1.cmml">∂</mo>
                  <mn id="p1.1.m1.1.39.2.2.1" xref="p1.1.m1.1.39.2.2.1.cmml">2</mn>
                </msup>
                <mo id="p1.1.m1.1.39.2a" xref="p1.1.m1.1.39.2.cmml">⁡</mo>
                <mi id="p1.1.m1.1.39.2.3" xref="p1.1.m1.1.39.2.3.cmml">V</mi>
              </mrow>
              <mrow id="p1.1.m1.1.39.3" xref="p1.1.m1.1.39.3.cmml">
                <mrow id="p1.1.m1.1.39.3.8" xref="p1.1.m1.1.39.3.8.cmml">
                  <mo id="p1.1.m1.1.39.3.1" xref="p1.1.m1.1.39.3.1.cmml">∂</mo>
                  <mo id="p1.1.m1.1.39.3.8a" xref="p1.1.m1.1.39.3.8.cmml">⁡</mo>
                  <msub id="p1.1.m1.1.39.3.8.1" xref="p1.1.m1.1.39.3.8.1.cmml">
                    <mi id="p1.1.m1.1.39.3.2" xref="p1.1.m1.1.39.3.2.cmml">q</mi>
                    <mi id="p1.1.m1.1.39.3.3.1" xref="p1.1.m1.1.39.3.3.1.cmml">j</mi>
                  </msub>
                </mrow>
                <mo id="p1.1.m1.1.39.3.7" xref="p1.1.m1.1.39.3.7.cmml">⁢</mo>
                <mrow id="p1.1.m1.1.39.3.9" xref="p1.1.m1.1.39.3.9.cmml">
                  <mo id="p1.1.m1.1.39.3.4" xref="p1.1.m1.1.39.3.4.cmml">∂</mo>
                  <mo id="p1.1.m1.1.39.3.9a" xref="p1.1.m1.1.39.3.9.cmml">⁡</mo>
                  <msub id="p1.1.m1.1.39.3.9.1" xref="p1.1.m1.1.39.3.9.1.cmml">
                    <mi id="p1.1.m1.1.39.3.5" xref="p1.1.m1.1.39.3.5.cmml">q</mi>
                    <mi id="p1.1.m1.1.39.3.6.1" xref="p1.1.m1.1.39.3.6.1.cmml">k</mi>
                  </msub>
                </mrow>
              </mrow>
            </mfrac>
          </mstyle>
          <mo id="p1.1.m1.1.40" xref="p1.1.m1.1.40.cmml">)</mo>
        </mrow>
        <mn id="p1.1.m1.1.41.1" xref="p1.1.m1.1.41.1.cmml">0</mn>
      </msub>
      <msub id="p1.1.m1.1.57" xref="p1.1.m1.1.57.cmml">
        <mi id="p1.1.m1.1.42" xref="p1.1.m1.1.42.cmml">q</mi>
        <mi id="p1.1.m1.1.43.1" xref="p1.1.m1.1.43.1.cmml">j</mi>
      </msub>
      <msub id="p1.1.m1.1.58" xref="p1.1.m1.1.58.cmml">
        <mi id="p1.1.m1.1.44" xref="p1.1.m1.1.44.cmml">q</mi>
        <mi id="p1.1.m1.1.45.1" xref="p1.1.m1.1.45.1.cmml">k</mi>
      </msub>
      <mo id="p1.1.m1.1.46" xref="p1.1.m1.1.46.cmml">+</mo>
      <mi mathvariant="normal" id="p1.1.m1.1.49" xref="p1.1.m1.1.49.cmml">…</mi>
    </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">V</csymbol>
        <cerror id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
          <csymbol cd="ambiguous" id="p1.1.m1.1.4a.cmml" xref="p1.1.m1.1.4">fragments</csymbol>
          <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">(</ci>
          <apply id="p1.1.m1.1.50.cmml" xref="p1.1.m1.1.50">
            <csymbol cd="ambiguous" id="p1.1.m1.1.50.1.cmml" xref="p1.1.m1.1.50">subscript</csymbol>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑞</ci>
            <cn type="integer" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">1</cn>
          </apply>
          <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">,</ci>
          <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">…</ci>
          <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">,</ci>
          <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">subscript</csymbol>
            <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑞</ci>
            <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">𝑓</ci>
          </apply>
          <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">)</ci>
        </cerror>
        <eq id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
        <csymbol cd="unknown" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">V</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.m1.1.15.cmml" xref="p1.1.m1.1.15">(</ci>
          <cn type="integer" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">0</cn>
          <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">,</ci>
          <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">…</ci>
          <ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">.</ci>
          <ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">,</ci>
          <cn type="integer" id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">0</cn>
          <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">)</ci>
        </cerror>
        <plus id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25"/>
        <apply id="p1.1.m1.1.52.cmml" xref="p1.1.m1.1.52">
          <csymbol cd="ambiguous" id="p1.1.m1.1.52.1.cmml" xref="p1.1.m1.1.52">subscript</csymbol>
          <sum id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26"/>
          <ci id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27.1">𝑗</ci>
        </apply>
        <apply id="p1.1.m1.1.53.cmml" xref="p1.1.m1.1.53">
          <csymbol cd="ambiguous" id="p1.1.m1.1.53.1.cmml" xref="p1.1.m1.1.53">subscript</csymbol>
          <cerror id="p1.1.m1.1.53.2.cmml" xref="p1.1.m1.1.53.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.53.2a.cmml" xref="p1.1.m1.1.53.2">fragments</csymbol>
            <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">(</ci>
            <apply id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">
              <divide id="p1.1.m1.1.29.1.cmml" xref="p1.1.m1.1.29"/>
              <apply id="p1.1.m1.1.29.2.cmml" xref="p1.1.m1.1.29.2">
                <partialdiff id="p1.1.m1.1.29.2.1.cmml" xref="p1.1.m1.1.29.2.1"/>
                <ci id="p1.1.m1.1.29.2.2.cmml" xref="p1.1.m1.1.29.2.2">𝑉</ci>
              </apply>
              <apply id="p1.1.m1.1.29.3.cmml" xref="p1.1.m1.1.29.3">
                <partialdiff id="p1.1.m1.1.29.3.1.cmml" xref="p1.1.m1.1.29.3.1"/>
                <apply id="p1.1.m1.1.29.3.4.cmml" xref="p1.1.m1.1.29.3.4">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.29.3.4.1.cmml" xref="p1.1.m1.1.29.3.4">subscript</csymbol>
                  <ci id="p1.1.m1.1.29.3.2.cmml" xref="p1.1.m1.1.29.3.2">𝑞</ci>
                  <ci id="p1.1.m1.1.29.3.3.1.cmml" xref="p1.1.m1.1.29.3.3.1">𝑗</ci>
                </apply>
              </apply>
            </apply>
            <ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">)</ci>
          </cerror>
          <cn type="integer" id="p1.1.m1.1.31.1.cmml" xref="p1.1.m1.1.31.1">0</cn>
        </apply>
        <apply id="p1.1.m1.1.54.cmml" xref="p1.1.m1.1.54">
          <csymbol cd="ambiguous" id="p1.1.m1.1.54.1.cmml" xref="p1.1.m1.1.54">subscript</csymbol>
          <ci id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">𝑞</ci>
          <ci id="p1.1.m1.1.33.1.cmml" xref="p1.1.m1.1.33.1">𝑗</ci>
        </apply>
        <plus id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34"/>
        <apply id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">
          <divide id="p1.1.m1.1.35.1.cmml" xref="p1.1.m1.1.35"/>
          <cn type="integer" id="p1.1.m1.1.35.2.cmml" xref="p1.1.m1.1.35.2">1</cn>
          <cn type="integer" id="p1.1.m1.1.35.3.cmml" xref="p1.1.m1.1.35.3">2</cn>
        </apply>
        <apply id="p1.1.m1.1.55.cmml" xref="p1.1.m1.1.55">
          <csymbol cd="ambiguous" id="p1.1.m1.1.55.1.cmml" xref="p1.1.m1.1.55">subscript</csymbol>
          <sum id="p1.1.m1.1.36.cmml" xref="p1.1.m1.1.36"/>
          <list id="p1.1.m1.1.37.1.4.cmml" xref="p1.1.m1.1.37.1">
            <ci id="p1.1.m1.1.37.1.1.cmml" xref="p1.1.m1.1.37.1.1">𝑗</ci>
            <ci id="p1.1.m1.1.37.1.3.cmml" xref="p1.1.m1.1.37.1.3">𝑘</ci>
          </list>
        </apply>
        <apply id="p1.1.m1.1.56.cmml" xref="p1.1.m1.1.56">
          <csymbol cd="ambiguous" id="p1.1.m1.1.56.1.cmml" xref="p1.1.m1.1.56">subscript</csymbol>
          <cerror id="p1.1.m1.1.56.2.cmml" xref="p1.1.m1.1.56.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.56.2a.cmml" xref="p1.1.m1.1.56.2">fragments</csymbol>
            <ci id="p1.1.m1.1.38.cmml" xref="p1.1.m1.1.38">(</ci>
            <apply id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">
              <divide id="p1.1.m1.1.39.1.cmml" xref="p1.1.m1.1.39"/>
              <apply id="p1.1.m1.1.39.2.cmml" xref="p1.1.m1.1.39.2">
                <apply id="p1.1.m1.1.39.2.4.cmml" xref="p1.1.m1.1.39.2.4">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.39.2.4.1.cmml" xref="p1.1.m1.1.39.2.4">superscript</csymbol>
                  <partialdiff id="p1.1.m1.1.39.2.1.cmml" xref="p1.1.m1.1.39.2.1"/>
                  <cn type="integer" id="p1.1.m1.1.39.2.2.1.cmml" xref="p1.1.m1.1.39.2.2.1">2</cn>
                </apply>
                <ci id="p1.1.m1.1.39.2.3.cmml" xref="p1.1.m1.1.39.2.3">𝑉</ci>
              </apply>
              <apply id="p1.1.m1.1.39.3.cmml" xref="p1.1.m1.1.39.3">
                <times id="p1.1.m1.1.39.3.7.cmml" xref="p1.1.m1.1.39.3.7"/>
                <apply id="p1.1.m1.1.39.3.8.cmml" xref="p1.1.m1.1.39.3.8">
                  <partialdiff id="p1.1.m1.1.39.3.1.cmml" xref="p1.1.m1.1.39.3.1"/>
                  <apply id="p1.1.m1.1.39.3.8.1.cmml" xref="p1.1.m1.1.39.3.8.1">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.39.3.8.1.1.cmml" xref="p1.1.m1.1.39.3.8.1">subscript</csymbol>
                    <ci id="p1.1.m1.1.39.3.2.cmml" xref="p1.1.m1.1.39.3.2">𝑞</ci>
                    <ci id="p1.1.m1.1.39.3.3.1.cmml" xref="p1.1.m1.1.39.3.3.1">𝑗</ci>
                  </apply>
                </apply>
                <apply id="p1.1.m1.1.39.3.9.cmml" xref="p1.1.m1.1.39.3.9">
                  <partialdiff id="p1.1.m1.1.39.3.4.cmml" xref="p1.1.m1.1.39.3.4"/>
                  <apply id="p1.1.m1.1.39.3.9.1.cmml" xref="p1.1.m1.1.39.3.9.1">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.39.3.9.1.1.cmml" xref="p1.1.m1.1.39.3.9.1">subscript</csymbol>
                    <ci id="p1.1.m1.1.39.3.5.cmml" xref="p1.1.m1.1.39.3.5">𝑞</ci>
                    <ci id="p1.1.m1.1.39.3.6.1.cmml" xref="p1.1.m1.1.39.3.6.1">𝑘</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
            <ci id="p1.1.m1.1.40.cmml" xref="p1.1.m1.1.40">)</ci>
          </cerror>
          <cn type="integer" id="p1.1.m1.1.41.1.cmml" xref="p1.1.m1.1.41.1">0</cn>
        </apply>
        <apply id="p1.1.m1.1.57.cmml" xref="p1.1.m1.1.57">
          <csymbol cd="ambiguous" id="p1.1.m1.1.57.1.cmml" xref="p1.1.m1.1.57">subscript</csymbol>
          <ci id="p1.1.m1.1.42.cmml" xref="p1.1.m1.1.42">𝑞</ci>
          <ci id="p1.1.m1.1.43.1.cmml" xref="p1.1.m1.1.43.1">𝑗</ci>
        </apply>
        <apply id="p1.1.m1.1.58.cmml" xref="p1.1.m1.1.58">
          <csymbol cd="ambiguous" id="p1.1.m1.1.58.1.cmml" xref="p1.1.m1.1.58">subscript</csymbol>
          <ci id="p1.1.m1.1.44.cmml" xref="p1.1.m1.1.44">𝑞</ci>
          <ci id="p1.1.m1.1.45.1.cmml" xref="p1.1.m1.1.45.1">𝑘</ci>
        </apply>
        <plus id="p1.1.m1.1.46.cmml" xref="p1.1.m1.1.46"/>
        <ci id="p1.1.m1.1.49.cmml" xref="p1.1.m1.1.49">…</ci>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle V({{q}_{1}},...,{{q}_{f}})=V(0,....,0)+\sum%
\limits_{j}{{{\left(\frac{\partial V}{\partial{{q}_{j}}}\right)}_{0}}{{q}_{j}}%
+\frac{1}{2}\sum\limits_{j,k}{{{\left(\frac{{{\partial}^{2}}V}{\partial{{q}_{j%
}}\partial{{q}_{k}}}\right)}_{0}}{{q}_{j}}{{q}_{k}}+...}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimentell; keine Bilder) rendering

MathML (2.401 KB / 425 B) :

V (q_{1}, . . ., q_{f}) = V (0, . . . ., 0) + \sum_{j} {(\frac{\partial V}{\partial q_{j}})}_{0} q_{j} + \frac{1}{2} \sum_{j, k} {(\frac{\partial^{2} V}{\partial q_{j} \partial q_{k}})}_{0} q_{j} q_{k} + . . .

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>V</mi><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mi>V</mi><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mn>0</mn><mo stretchy="false">)</mo><mo>+</mo><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>V</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mo>,</mo><mi>k</mi></mrow></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>V</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mi>&#x2202;</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo></mrow></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$V$

$q_{1}$

$q_{f}$

$V$

$j$

$V$

$q_{j}$

$q_{j}$

$j$

$k$

$V$

$q_{j}$

$q_{k}$

$q_{j}$

$q_{k}$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

Suche