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Display information for equation id:math.1284.115 on revision:1284
* Page found: Das d'Alembertsche Prinzip (eq math.1284.115)
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Hash: 2c186acb66c5c4b5f3026102ff2214ba
TeX (original user input):
-\frac{\partial V}{\partial {{q}_{j}}}=-\sum\limits_{i}^{{}}{{{\nabla }_{\vec{r}i}}V({{{\bar{r}}}_{1}},{{{\bar{r}}}_{2}},...,{{{\bar{r}}}_{N}})\frac{\partial {{{\bar{r}}}_{i}}}{\partial {{q}_{j}}}}=\sum\limits_{i}^{{}}{{{{\vec{X}}}_{i}}\frac{\partial {{{\bar{r}}}_{i}}}{\partial {{q}_{j}}}}={{Q}_{j}}
TeX (checked):
-{\frac {\partial V}{\partial {{q}_{j}}}}=-\sum \limits _{i}^{}{{{\nabla }_{{\vec {r}}i}}V({{\bar {r}}_{1}},{{\bar {r}}_{2}},...,{{\bar {r}}_{N}}){\frac {\partial {{\bar {r}}_{i}}}{\partial {{q}_{j}}}}}=\sum \limits _{i}^{}{{{\vec {X}}_{i}}{\frac {\partial {{\bar {r}}_{i}}}{\partial {{q}_{j}}}}}={{Q}_{j}}
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MathML (2.582 KB / 434 B) :
<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"><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>V</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mo stretchy="false">−</mo><munderover><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo class="mwe-math-vec" stretchy="false">→</mo></mover><mi>i</mi></mrow></mrow></msub><mi>V</mi><mo stretchy="false">(</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><mi>...</mi><mo>,</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow></mfrac></mrow></mrow><mo stretchy="false">=</mo><munderover><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><msub><mover><mi>X</mi><mo class="mwe-math-vec" stretchy="false">→</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow></mfrac></mrow></mrow><mo stretchy="false">=</mo><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mstyle></mrow></math>
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