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Display information for equation id:math.1149.5 on revision:1149

* Page found: Rotierendes Pendel (eq math.1149.5)

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Rotierendes Pendel Eq: math.1149.5

Hash: 42a7e3419eb40c24567bb9e6f21b6daf

TeX (original user input):

\begin{align}
  & {{{\dot{x}}}^{2}}={{a}^{2}}{{\omega }^{2}}{{\sin }^{2}}\left( \omega t \right)+{{L}^{2}}{{{\dot{\varphi }}}^{2}}{{\cos }^{2}}\left( \varphi  \right)-aL\omega \dot{\varphi }\cos \left( \varphi  \right)\sin \left( \omega t \right)+ \\
 & \quad \quad {{a}^{2}}{{\omega }^{2}}{{\cos }^{2}}\left( \omega t \right)+{{L}^{2}}{{{\dot{\varphi }}}^{2}}{{\sin }^{2}}\left( \varphi  \right)+aL\omega \dot{\varphi }\sin \left( \varphi  \right)\cos \left( \omega t \right) \\
 & \quad ={{a}^{2}}{{\omega }^{2}}+{{L}^{2}}{{{\dot{\varphi }}}^{2}}+aL\omega \dot{\varphi }\left( \sin \left( \varphi  \right)\cos \left( \omega t \right)-\cos \left( \varphi  \right)\sin \left( \omega t \right) \right) \\
 & \quad ={{a}^{2}}{{\omega }^{2}}+{{L}^{2}}{{{\dot{\varphi }}}^{2}}+aL\omega \dot{\varphi }\sin \left( \varphi -\omega t \right)
\end{align}

TeX (checked):

{\begin{aligned}&{{\dot {x}}^{2}}={{a}^{2}}{{\omega }^{2}}{{\sin }^{2}}\left(\omega t\right)+{{L}^{2}}{{\dot {\varphi }}^{2}}{{\cos }^{2}}\left(\varphi \right)-aL\omega {\dot {\varphi }}\cos \left(\varphi \right)\sin \left(\omega t\right)+\\&\quad \quad {{a}^{2}}{{\omega }^{2}}{{\cos }^{2}}\left(\omega t\right)+{{L}^{2}}{{\dot {\varphi }}^{2}}{{\sin }^{2}}\left(\varphi \right)+aL\omega {\dot {\varphi }}\sin \left(\varphi \right)\cos \left(\omega t\right)\\&\quad ={{a}^{2}}{{\omega }^{2}}+{{L}^{2}}{{\dot {\varphi }}^{2}}+aL\omega {\dot {\varphi }}\left(\sin \left(\varphi \right)\cos \left(\omega t\right)-\cos \left(\varphi \right)\sin \left(\omega t\right)\right)\\&\quad ={{a}^{2}}{{\omega }^{2}}+{{L}^{2}}{{\dot {\varphi }}^{2}}+aL\omega {\dot {\varphi }}\sin \left(\varphi -\omega t\right)\end{aligned}}

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\begin{aligned} {\dot{x}}^{2} = a^{2} ω^{2} \sin^{2} (ω t) + L^{2} {\dot{φ}}^{2} \cos^{2} (φ) - a L ω \dot{φ} \cos (φ) \sin (ω t) + \\ a^{2} ω^{2} \cos^{2} (ω t) + L^{2} {\dot{φ}}^{2} \sin^{2} (φ) + a L ω \dot{φ} \sin (φ) \cos (ω t) \\ = a^{2} ω^{2} + L^{2} {\dot{φ}}^{2} + a L ω \dot{φ} (\sin (φ) \cos (ω t) - \cos (φ) \sin (ω t)) \\ = a^{2} ω^{2} + L^{2} {\dot{φ}}^{2} + a L ω \dot{φ} \sin (φ - ω t) \end{aligned}

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Identifiers

$\dot{x}$

$a$

$ω$

$ω$

$t$

$L$

$\dot{φ}$

$φ$

$a$

$L$

$ω$

$\dot{φ}$

$φ$

$ω$

$t$

$a$

$ω$

$ω$

$t$

$L$

$\dot{φ}$

$φ$

$a$

$L$

$ω$

$\dot{φ}$

$φ$

$ω$

$t$

$a$

$ω$

$L$

$\dot{φ}$

$a$

$L$

$ω$

$\dot{φ}$

$φ$

$ω$

$t$

$φ$

$ω$

$t$

$a$

$ω$

$L$

$\dot{φ}$

$a$

$L$

$ω$

$\dot{φ}$

$φ$

$ω$

$t$

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