- testwiki

General

Display information for equation id:math.1507.26 on revision:1507

* Page found: Lagrangegleichungen 2. Art (eq math.1507.26)

Occurrences on the following pages:

Lagrangegleichungen 2. Art Eq: math.1508.26

Hash: 671c5f754b6c36fd02da29e702ba5b23

TeX (original user input):

\begin{align}
  & \vec{L}=m\vec{v}\times \vec{r} \\
 & {{{\vec{L}}}_{o}}=m{{\omega }_{o}}^{{}}{{R}_{o}}^{2}\quad {{v}_{o}}={{\omega }_{o}}{{R}_{o}}\quad {{r}_{o}}={{R}_{o}} \\
 & andererseits: \\
 & {{\omega }_{o}}=\frac{con\tilde{s}}{{{({{R}_{o}})}^{2}}} \\
 & \Rightarrow \omega =\frac{con\tilde{s}}{{{({{R}_{o}}-ct)}^{2}}}\Rightarrow con\tilde{s}=\frac{{{{\vec{L}}}_{o}}}{m} \\
 & \omega =\frac{{{{\vec{L}}}_{o}}}{m{{({{R}_{o}}-ct)}^{2}}}=\dot{q} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\vec {L}}=m{\vec {v}}\times {\vec {r}}\\&{{\vec {L}}_{o}}=m{{\omega }_{o}}^{}{{R}_{o}}^{2}\quad {{v}_{o}}={{\omega }_{o}}{{R}_{o}}\quad {{r}_{o}}={{R}_{o}}\\&andererseits:\\&{{\omega }_{o}}={\frac {con{\tilde {s}}}{{({{R}_{o}})}^{2}}}\\&\Rightarrow \omega ={\frac {con{\tilde {s}}}{{({{R}_{o}}-ct)}^{2}}}\Rightarrow con{\tilde {s}}={\frac {{\vec {L}}_{o}}{m}}\\&\omega ={\frac {{\vec {L}}_{o}}{m{{({{R}_{o}}-ct)}^{2}}}}={\dot {q}}\\\end{aligned}}

LaTeXML (experimental; uses MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimental; no images) rendering

MathML (4.259 KB / 544 B) :

\begin{matrix} \vec{L} = m \vec{v} \times \vec{r} \\ {\vec{L}}_{o} = m {ω_{o}}^{} {R_{o}}^{2} v_{o} = ω_{o} R_{o} r_{o} = R_{o} \\ a n d e r e r s e i t s : \\ ω_{o} = \frac{c o n \tilde{s}}{{(R_{o})}^{2}} \\ \Rightarrow ω = \frac{c o n \tilde{s}}{{(R_{o} - c t)}^{2}} \Rightarrow c o n \tilde{s} = \frac{{\vec{L}}_{o}}{m} \\ ω = \frac{{\vec{L}}_{o}}{m {(R_{o} - c t)}^{2}} = \dot{q} \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"><mover><mi>L</mi><mo class="mwe-math-vec" stretchy="false">→</mo></mover><mo stretchy="false">=</mo><mi>m</mi><mover><mi>v</mi><mo class="mwe-math-vec" stretchy="false">→</mo></mover><mo stretchy="false">×</mo><mover><mi>r</mi><mo class="mwe-math-vec" stretchy="false">→</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mover><mi>L</mi><mo class="mwe-math-vec" stretchy="false">→</mo></mover><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo stretchy="false">=</mo><mi>m</mi><msup><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mrow data-mjx-texclass="ORD"></mrow></msup><msup><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mspace width="1em"></mspace><msub><mi>v</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo stretchy="false">=</mo><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mspace width="1em"></mspace><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo stretchy="false">=</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>a</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>r</mi><mi>e</mi><mi>r</mi><mi>s</mi><mi>e</mi><mi>i</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>c</mi><mi>o</mi><mi>n</mi><mover><mi>s</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>ω</mi><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>c</mi><mi>o</mi><mi>n</mi><mover><mi>s</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo stretchy="false">−</mo><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo stretchy="false">⇒</mo><mi>c</mi><mi>o</mi><mi>n</mi><mover><mi>s</mi><mo>~</mo></mover><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mover><mi>L</mi><mo class="mwe-math-vec" stretchy="false">→</mo></mover><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>ω</mi><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mover><mi>L</mi><mo class="mwe-math-vec" stretchy="false">→</mo></mover><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo stretchy="false">−</mo><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mover><mi>q</mi><mo>˙</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$\vec{L}$

$m$

$\vec{v}$

$\vec{r}$

${\vec{L}}_{o}$

$m$

$ω_{o}$

$R_{o}$

$v_{o}$

$ω_{o}$

$R_{o}$

$r_{o}$

$R_{o}$

$a$

$n$

$d$

$e$

$r$

$e$

$r$

$s$

$e$

$i$

$t$

$s$

$ω_{o}$

$c$

$o$

$n$

$\tilde{s}$

$R_{o}$

$ω$

$c$

$o$

$n$

$\tilde{s}$

$R_{o}$

$c$

$t$

$c$

$o$

$n$

$\tilde{s}$

${\vec{L}}_{o}$

$m$

$ω$

${\vec{L}}_{o}$

$m$

$R_{o}$

$c$

$t$

$\dot{q}$

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