Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.1983.35 on revision:1983

* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1983.35)

(force rerendering)

Occurrences on the following pages:

Hash: 8f6429f6a751ce1b0be964c4d3064043

TeX (original user input): 

\begin{align}
  & \Rightarrow {{q}_{0}}=\frac{1}{\omega }\sqrt{\frac{2\alpha }{m}}\sin \left( \omega (\beta ) \right) \\
 & 0={{p}_{0}}=\sqrt{2\alpha m}\cos \left( \omega (\beta ) \right) \\
 & \Rightarrow \beta =\frac{\pi }{2\omega }\Rightarrow {{q}_{0}}=\sqrt{\frac{2\alpha }{m{{\omega }^{2}}}} \\
 & \Rightarrow \alpha =\frac{m}{2}{{\omega }^{2}}{{q}_{0}}^{2}=E \\
\end{align}

TeX (checked): 

{\begin{aligned}&\Rightarrow {{q}_{0}}={\frac {1}{\omega }}{\sqrt {\frac {2\alpha }{m}}}\sin \left(\omega (\beta )\right)\\&0={{p}_{0}}={\sqrt {2\alpha m}}\cos \left(\omega (\beta )\right)\\&\Rightarrow \beta ={\frac {\pi }{2\omega }}\Rightarrow {{q}_{0}}={\sqrt {\frac {2\alpha }{m{{\omega }^{2}}}}}\\&\Rightarrow \alpha ={\frac {m}{2}}{{\omega }^{2}}{{q}_{0}}^{2}=E\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (27.298 KB / 3.227 KB) :

⇒ q 0 = 1 ω ⁢ 2 ⁢ α m ⁢ sin ⁡ ( ω ⁢ ( β ) ) 0 = p 0 = 2 ⁢ α ⁢ m ⁢ cos ⁡ ( ω ⁢ ( β ) ) ⇒ β = π 2 ⁢ ω ⇒ q 0 = 2 ⁢ α m ⁢ ω 2 ⇒ α = m 2 ⁢ ω 2 ⁢ q 0 2 = E missing-subexpression ⇒ absent subscript 𝑞 0 1 𝜔 2 𝛼 𝑚 𝜔 𝛽 missing-subexpression 0 subscript 𝑝 0 2 𝛼 𝑚 𝜔 𝛽 missing-subexpression ⇒ absent 𝛽 𝜋 2 𝜔 ⇒ subscript 𝑞 0 2 𝛼 𝑚 superscript 𝜔 2 missing-subexpression ⇒ absent 𝛼 𝑚 2 superscript 𝜔 2 superscript subscript 𝑞 0 2 𝐸 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\Rightarrow{{q}_{0}}% =\frac{1}{\omega}\sqrt{\frac{2\alpha}{m}}\sin\left(\omega(\beta)\right)\\ &\displaystyle 0={{p}_{0}}=\sqrt{2\alpha m}\cos\left(\omega(\beta)\right)\\ &\displaystyle\Rightarrow\beta=\frac{\pi}{2\omega}\Rightarrow{{q}_{0}}=\sqrt{% \frac{2\alpha}{m{{\omega}^{2}}}}\\ &\displaystyle\Rightarrow\alpha=\frac{m}{2}{{\omega}^{2}}{{q}_{0}}^{2}=E\\ \end{aligned}}}

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (2.802 KB / 494 B) :

⇒q0=1ω2αmsin⁡(ω(β))0=p0=2αmcos⁡(ω(β))⇒β=π2ω⇒q0=2αmω2⇒α=m2ω2q02=E

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Hamilton-Jacobische Differenzialgleichung page

Identifiers

  • q0
  • ω
  • α
  • m
  • ω
  • β
  • p0
  • α
  • m
  • ω
  • β
  • β
  • π
  • ω
  • q0
  • α
  • m
  • ω
  • α
  • m
  • ω
  • q0
  • E

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“