Gelöste Aufgaben/Bike

Aufgabenstellung

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Lösung mit Maxima

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$\underset{\_}{\tilde{Q}}=\left[\begin{array}{c}{W}_0\\ {\mathrm{\Phi }}_0\\ W_1\\ {\mathrm{\Phi }}_1\\ W_2\\ {\mathrm{\Phi }}_2,\\ {\mathrm{\Psi }}_1,\\ {\mathrm{\Psi }}_2\end{array}\right]$

$\underset{\_}{Y}=\left[\begin{array}{c}\underset{\_}{Q}\\ \underset{\_}{\dot{Q}}\end{array}\right]$

$\begin{array}{ll}\underset{\_}{\dot{Y}}& =\underset{\_}{f}\left(\underset{\_}{Y}\right)\\ & =\left[\begin{array}{l}\underset{\_}{\dot{Q}}\\ -{\underset{\_}{\underset{\_}{M}}}^{-1}\cdot \underset{\_}{\underset{\_}{K}}\cdot \underset{\_}{Q}+{\underset{\_}{\underset{\_}{M}}}^{-1}\cdot \underset{\_}{P}\end{array}\right]\end{array}$

$\underset{\_}{\underset{\_}{M}}\cdot \underset{\_}{\ddot{Q}}+\underset{\_}{\underset{\_}{K}}\cdot \underset{\_}{Q}=\underset{\_}{P}(\underset{\_}{Q},\underset{\_}{\dot{Q}})$

$\begin{array}{lcc}\delta W& =& \delta W^a-\delta \mathrm{\Pi }\\ & \stackrel{!}{=}& 0\end{array}$

$\delta \mathrm{\Pi }=\delta {\mathrm{\Pi }}_G+\delta {\mathrm{\Pi }}_S$

$\delta {\mathrm{\Pi }}_S=K_S\cdot ({\mathrm{\Psi }}_2-{\mathrm{\Psi }}_1)\cdot (\delta {\mathrm{\Psi }}_2-\delta {\mathrm{\Psi }}_1)$

$\delta {\mathrm{\Pi }}_G=\delta {\mathrm{\Pi }}_{G1}+\delta {\mathrm{\Pi }}_{G2}$

$\delta {\mathrm{\Pi }}_{Gi}=\underset{0}{\overset{{\ell }_i}{\int }}{M}_i(x)\cdot \delta {w_i}^{″}(x)dx$

$M_i(x)=E\cdot I(x)\cdot {w_i}^{″}(x)$

$w_i(x)={\underset{\_}{Q}}^T\cdot \underset{\_}{\phi }$

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