Difference between revisions of "WikiWaves:Test"
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\left\{ | \left\{ | ||
\begin{array}{l} | \begin{array}{l} | ||
| − | \ddot r - \gamma\ddot r_{ss} | + | \ddot r - \gamma\ddot r_{ss} + r_{ssss}=(\tau r_s)_s,\ \ r_s.r_s=1,\\ |
r(0,t)=(0,0), \;\; r_{s}(0,t)=(1,0),\\ | r(0,t)=(0,0), \;\; r_{s}(0,t)=(1,0),\\ | ||
| − | (\gamma\ddot r_s \tau r_{s}-r_{sss})|_{(1,t)}=-\alpha\dot{r}(1,t),\ | + | (\gamma\ddot r_s+\tau r_{s}-r_{sss})|_{(1,t)}=-\alpha\dot{r}(1,t),\ |
r_{ss}(1,t)=-\beta\dot r_s(1,t),\\ | r_{ss}(1,t)=-\beta\dot r_s(1,t),\\ | ||
r(s,0)=r_0(s),\ \dot r(s,0)=r_1(s). | r(s,0)=r_0(s),\ \dot r(s,0)=r_1(s). | ||
Latest revision as of 21:26, 10 April 2007
Here is a link Main Page.
Here is some [math]\displaystyle{ \begin{equation} \left\{ \begin{array}{l} \ddot r - \gamma\ddot r_{ss} + r_{ssss}=(\tau r_s)_s,\ \ r_s.r_s=1,\\ r(0,t)=(0,0), \;\; r_{s}(0,t)=(1,0),\\ (\gamma\ddot r_s+\tau r_{s}-r_{sss})|_{(1,t)}=-\alpha\dot{r}(1,t),\ r_{ss}(1,t)=-\beta\dot r_s(1,t),\\ r(s,0)=r_0(s),\ \dot r(s,0)=r_1(s). \end{array}\right. \end{equation} }[/math]
and a picture: \begin{figure}[ht] \begin{center} \begin{pspicture}(0,-1.5)(10,1.5) \psplot[linecolor=lightgray,linewidth=10pt]{0}{10}{x .07 mul 2 exp x .07 mul .5 sub mul x .07 mul .8 sub mul 600 mul x .07 mul 5 add div} \psline[linecolor=lightgray,linewidth=10pt](-.3,0)(0,0) \psframe[linestyle=dashed,dash=5pt 8pt](-.3,-.22)(10,.22) \psline[linestyle=dashed]{|<->|}(4,0)(4,1) \rput(4.9,1){$y(x,t)$} \psline[arrowsize=6.5pt,arrowlength=1.5]{->}(0,0)(11,0) \psline[arrowsize=6.5pt,arrowlength=1.5]{<->}(0,-1.5)(0,1.5) \rput(-.3,1){$y$} \rput(10.5,-.2){$x$} \rput(9.9,.6){$x=1$} \end{pspicture} \caption{\small The linear beam} \label{f1}\end{center} \end{figure}
