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</o:shapelayout></xml><![endif]--></head><body lang=FR link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Hello,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>it may have to do with the (non-physical?) expression of the ODE. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Besides the fact that the last term is mathematically ill-defined (starting with "+/"), in the case K=0, the second derivative of X is positive for x<%pi/2: it may then reach the value %pi/2, which makes denominators be 0. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Physically, these denominators (%pi/2-X) look very strange as they may govern divergence of the force in the last term. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>However, it appears also in the first term, where divergence is prevented because of (1-sin X): it may than be necessary to rewrite the function (1-sinX)/(%pi/2-X), with the addition of the case X=%pi/2, where the function goes to 0 by continuity.<o:p></o:p></span></p><div><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>HTH<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Denis</span><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p></o:p></span></p></div><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>De :</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> arnaud dujeu [mailto:fangorn813@hotmail.com] <br><b>Envoyé :</b> mardi 19 juillet 2011 11:46<br><b>À :</b> users@lists.scilab.org<br><b>Objet :</b> [scilab-Users] Problem with division by zero<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>Hi, <o:p></o:p></span></p><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>I am using scilab to solve a differential equation and I have an error ("error 27") I don't understand.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>When K=1 pr K>1 it's okay but as soon as K<1 there is the error.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>This is my code : <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'><o:p> </o:p></span></p></div><div><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#B01813'>function</span><span style='font-size:10.5pt;font-family:"Monospaced","serif"'> <span style='color:#4A55DB'>[</span><b><span style='color:#834310'>Xprime</span></b><span style='color:#4A55DB'>]</span><span style='color:#5C5C5C'>=</span><u><span style='color:black'>VanDerPol</span></u><span style='color:#4A55DB'>(</span><b><span style='color:#834310'>t</span></b><span style='color:black'>, </span><b><span style='color:#834310'>X</span></b><span style='color:#4A55DB'>)</span><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'> <o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'> <b><span style='color:#834310'>Xprime</span></b><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>1</span><span style='color:#4A55DB'>)</span> <span style='color:#5C5C5C'>=</span> <b><span style='color:#834310'>X</span></b><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>2</span><span style='color:#4A55DB'>)</span><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'> <b><span style='color:#834310'>Xprime</span></b><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>2</span><span style='color:#4A55DB'>)</span> <span style='color:#5C5C5C'>=</span> <span style='color:black'>g</span><span style='color:#5C5C5C'>/</span><span style='color:black'>R</span><span style='color:#5C5C5C'>*</span><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>1</span><span style='color:#5C5C5C'>-</span><span style='color:#32B9B9'>sin</span><span style='color:#4A55DB'>(</span><b><span style='color:#834310'>X</span></b><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>1</span><span style='color:#4A55DB'>)))</span><span style='color:#5C5C5C'>/</span><span style='color:#4A55DB'>(</span><span style='color:orchid'>%pi</span><span style='color:#5C5C5C'>/</span><span style='color:rosybrown'>2</span><span style='color:#5C5C5C'>-</span><b><span style='color:#834310'>X</span></b><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>1</span><span style='color:#4A55DB'>))</span><span style='color:#5C5C5C'>-</span><span style='color:#4A55DB'>(</span><span style='color:black'>mu</span><span style='color:#5C5C5C'>*</span><span style='color:#4A55DB'>(</span><span style='color:black'>K</span><span style='color:#4A55DB'>)</span><span style='color:#5C5C5C'>*</span><span style='color:black'>R</span><span style='color:#5C5C5C'>^</span><span style='color:rosybrown'>2</span><span style='color:#5C5C5C'>*</span><span style='color:#4A55DB'>((</span><b><span style='color:#834310'>X</span></b><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>2</span><span style='color:#4A55DB'>))</span><span style='color:#5C5C5C'>^</span><span style='color:rosybrown'>2</span><span style='color:#4A55DB'>)</span><span style='color:#5C5C5C'>/</span><span style='color:rosybrown'>2</span><span style='color:#4A55DB'>)</span><span style='color:#5C5C5C'>+/</span><span style='color:#4A55DB'>(</span><span style='color:black'>R</span><span style='color:#5C5C5C'>^</span><span style='color:rosybrown'>2</span><span style='color:#5C5C5C'>*</span><span style='color:black'>mu</span><span style='color:#5C5C5C'>*</span><span style='color:#4A55DB'>(</span><span style='color:orchid'>%pi</span><span style='color:#5C5C5C'>/</span><span style='color:rosybrown'>2</span><span style='color:#5C5C5C'>-</span><b><span style='color:#834310'>X</span></b><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>1</span><span style='color:#4A55DB'>)))</span><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'> <o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#B01813'>endfunction</span><span style='font-size:10.5pt;font-family:"Monospaced","serif"'><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'><o:p> </o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'> <span style='color:black'>t</span><span style='color:#5C5C5C'>=</span><u><span style='color:#AE5CB0'>linspace</span></u><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>0</span><span style='color:black'>,</span><span style='color:rosybrown'>4</span><span style='color:black'>,</span><span style='color:rosybrown'>3000</span><span style='color:#4A55DB'>)</span><span style='color:black'>;</span> <span style='color:black'>X0</span><span style='color:#5C5C5C'>=</span><span style='color:#4A55DB'>[</span><span style='color:rosybrown'>85</span><span style='color:#5C5C5C'>*</span><span style='color:orchid'>%pi</span><span style='color:#5C5C5C'>/</span><span style='color:rosybrown'>180</span><span style='color:black'>;</span><span style='color:rosybrown'>0</span><span style='color:#4A55DB'>]</span><span style='color:black'>;</span><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'> <span style='color:#4A55DB'>[</span><span style='color:black'>u</span><span style='color:#4A55DB'>]</span><span style='color:#5C5C5C'>=</span><span style='color:#32B9B9'>ode</span><span style='color:#4A55DB'>(</span><span style='color:black'>X0,</span><span style='color:rosybrown'>0</span><span style='color:black'>,t,<u>VanDerPol</u></span><span style='color:#4A55DB'>)</span><span style='color:black'>;</span><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'><o:p> </o:p></span></pre><pre><u><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#AE5CB0'>plot</span></u><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>(</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:black'>t,u</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>(</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:rosybrown'>1</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:black'>,</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#FFAA00'>:</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>)</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#5C5C5C'>*</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:rosybrown'>180</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#5C5C5C'>/</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:orchid'>%pi</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:black'>,</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:rosybrown'>'r'</span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>)</span><span style='font-size:10.5pt;font-family:"Monospaced","serif"'><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'> <u><span style='color:#AE5CB0'>plot</span></u><span style='color:#4A55DB'>(</span><span style='color:black'>t,R</span><span style='color:#5C5C5C'>*</span><span style='color:black'>u</span><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>2</span><span style='color:black'>,</span><span style='color:#FFAA00'>:</span><span style='color:#4A55DB'>))</span><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'><o:p> </o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'><o:p> </o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>And there is the Scilab message when K<1 : </span><span style='font-size:10.5pt;font-family:"Monospaced","serif"'><o:p></o:p></span></pre><pre><span style='font-size:10.5pt;font-family:"Monospaced","serif"'><o:p> </o:p></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>-->exec('C:\Documents and Settings\ademollerat\My Documents\accelerometre\Ecoulement\VanDerPol-2.sci', -1)<o:p></o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>Attention: redéfinition de la fonction: VanDerPol . Utilisez funcprot(0) pour éviter ce message<o:p></o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'><o:p> </o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'> !--error 27 <o:p></o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>Division par zéro ...<o:p></o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'><o:p> </o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>at line 7 of function VanDerPol called by : <o:p></o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'> [u]=ode(X0,0,t,VanDerPol);<o:p></o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>at line 35 of exec file called by : <o:p></o:p></span></span></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>exec('C:\Documents and Settings\ademollerat\My Documents\accelerometre\Ecoulement\VanDerPol-2.sci', -1)</span></span><o:p></o:p></pre><pre><o:p> </o:p></pre><pre><o:p> </o:p></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>Maybe I have made a mistake or maybe it is a bug.</span></span><o:p></o:p></pre><pre><o:p> </o:p></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>Thank you for helping me.</span></span><o:p></o:p></pre><pre><o:p> </o:p></pre><pre><span class=apple-style-span><span style='font-size:10.5pt;font-family:"Monospaced","serif";color:#4A55DB'>Best regards</span></span><o:p></o:p></pre></div></div></div></body></html>