<!DOCTYPE html> <html xmlns="http://www.w3.org/1999/xhtml"><head> <!--[ GuppY v5.0.9 CeCILL Copyright (C) 2004-2014 by Laurent Duveau - http://www.freeguppy.org/ ]--> <meta http-equiv="content-type" content="text/html; charset=UTF-8"> <meta name="application-name" content="Casyopée - Angle et Modélisation"> <title>Casyopée - Angle et Modélisation</title> <meta name="description" content="Casyopée: a learning environment dedicated to functions"> <meta name="generator" content="GuppY CMS"> <meta name="author" content="lagrange"> <meta name="keywords" content="casyopée, functions, mathematics, geodynamic geometry, cas, symbolic computation,"> <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"> <meta name="apple-mobile-web-app-capable" content="yes"> <meta name="apple-mobile-web-app-status-bar-style" content="black"> <link rel="shortcut icon" href="https://casyopee.math.univ-paris-diderot.fr/guppy.ico"> <link rel="alternate" type="application/rss+xml" title="Casyopée : Actualité" hreflang="fr" href="https://casyopee.math.univ-paris-diderot.fr/data/fr-news.xml"> <link type="text/css" rel="stylesheet" href="skins/casyop/style.css"> <link type="text/css" rel="stylesheet" href="skins/casyop/jqstyle.css"> <style type="text/css" media="screen"> @import url(inc/auto.css); </style> <style type="text/css" media="print"> @import url(inc/print.css); </style> <link type="text/css" rel="stylesheet" href="inc/csshead/fotorama.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/menubox.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/slidesjs.css"> <script type="text/javascript"> //<![CDATA[ <!-- var charset = "UTF-8"; var site0 = "Casyopée"; var site3 = "https://casyopee.math.univ-paris-diderot.fr/"; var sValue = screen.width + "||" + screen.height + "||" + screen.availWidth + "||" + screen.availHeight; var today = new Date(), expires = new Date(); expires.setTime(today.getTime() + (365*24*60*60*1000)); document.cookie = "GuppYScreen" + "=" + encodeURIComponent(sValue) + ";expires=" + expires.toGMTString(); //--> //]]> </script> <script type="text/javascript" src="inc/hpage.js"></script> <script type="text/javascript" src="inc/jquery-min.js"></script> <script type="text/javascript" src="inc/jquery-migrate-min.js"></script> <script type="text/javascript" src="inc/jqscript.js"></script> <script type="text/javascript" src="inc/jshead/boxmenu_toggle.js"></script> <script type="text/javascript" src="inc/jshead/fotorama.js"></script> <script type="text/javascript" src="inc/jshead/jquery.imagecube.min.js"></script> <script type="text/javascript" src="inc/jshead/sidephoto.js"></script> <script type="text/javascript" src="inc/jshead/slides.min.jquery.js"></script> <script type="text/javascript" src="inc/jshead/slidesjs.js"></script> </head><body> <table style="margin: auto auto auto 0px; width: 100%; text-align: left;"> <tbody> <tr> <td style="width: 100%; vertical-align: top;"> <div id="AboveBoxes"> </div> <div class="titre"> <div style="text-align: center;"> </div> <h1 style="text-align: center;">Angle et Modélisation</h1> </div> <div class="tbl tblout" onmouseover="this.className = 'tbl tblover'" onmouseout="this.className = 'tbl tblout'"> <div style="padding: 6px;"> <h2><span style="line-height: 115%;">Bielle et vilebrequin&nbsp;</span></h2> <div style="border: 1pt solid windowtext; padding: 1pt 4pt; margin-right: 94.3pt; margin-left: 77pt;"> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;">Soit M un point mobile sur le cercle de centre O et de rayon 1. Soit N le point de l axe des x à distance a de M, <span style="">&nbsp;</span>a étant un paramètre positif. On s intéresse à la distance ON en fonction de la position de M. Pour les mécaniciens, le segment [OM] est partie du vilebrequin, et le segment [MN] représente la bielle. On s intéresse à la distance ON, c est-à-dire la, distance entre l axe du vilebrequin et le piston,<span style="">&nbsp; </span>en fonction de la position de M. On repère cette position par la valeur de l angle entre l axe des x et le rayon [OM].</p> </div> <table class="MsoTableGrid" style="border: medium none currentcolor; margin-left: 1.9pt; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody> <tr style=""> <td style="border: 1pt solid black; padding: 0cm 5.4pt; width: 306pt;" valign="top" width="408"> <p class="MsoNormal" style="text-align: center; page-break-after: avoid;" align="center"><img src="/help/imgFrHelp/image239.gif" v:shapes="_x0000_i1163" border="0" height="450" width="354"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1163" DrawAspect="Content" ObjectID="_1473694213"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193857">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193857'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193857'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">100</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193857'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : la bielle, construction et animation</span></p> </td> <td style="border-style: solid solid solid none; border-color: black black black currentcolor; border-width: 1pt 1pt 1pt medium; padding: 0cm 5.4pt; width: 226.2pt;" valign="top" width="302"> <p class="MsoNormal">Point p0 renommé en O</p> <p class="MsoNormal">Création du cercle C1 de centre O et de rayon 1.</p> <p class="MsoNormal">Création du point libre p1 sur le cercle C1 renommé en M.</p> <p class="MsoNormal">Paramètre a positif.</p> <p class="MsoNormal">Création du cercle C2 de centre M et de rayon a.</p> <p class="MsoNormal">Création du Point p2 à l intersection de C2 et (Ox) renommé en N.</p> <p class="MsoNormal">Création du Point Repéré p3 (3,0)</p> <p class="MsoNormal">Création de l'Angle p3OM&nbsp;: Theta1.</p> <p class="MsoNormal">Vous pouvez affecter une vitesse au point M pour voir le mécanisme s animer.</p> </td> </tr> </tbody> </table> <p class="MsoNormal">Le calcul géométrique à choisir pour la valeur de la fonction est ON. Celui à choisir pour la variable est<span style="">&nbsp; </span><span style="font-family: Symbol;"><span style="">q</span></span>1.</p> <p class="MsoNormal" style="text-align: center; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1164" type="#_x0000_t75" style='width:183pt;height:96pt'> <v:imagedata src="/help/imgFrHelp/image240.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image241.jpg" v:shapes="_x0000_i1164" border="0" height="128" width="244"><!--[endif]--><span style="">&nbsp;&nbsp;&nbsp;&nbsp; </span><!--[if gte vml 1]><v:shape id="_x0000_i1165" type="#_x0000_t75" style='width:252pt;height:98.25pt'> <v:imagedata src="/help/imgFrHelp/image242.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image243.jpg" v:shapes="_x0000_i1165" border="0" height="131" width="336"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193858">Figure </a><!--[if supportFields]><span style='mso-bookmark: _Toc364193858'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193858'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">101</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193858'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : la bielle, modélisation</span></p> <p class="MsoNormal">Après avoir fait calculer la fonction modèle et avoir validé l ensemble de définition et la formule donnée par <span style="">Casyopée</span>, on obtient un message d avertissement indiquant que Maxima<span style="">&nbsp; </span>ne peut certifier l existence de cette fonction.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1166" type="#_x0000_t75" style='width:300pt;height:111.75pt'> <v:imagedata src="/help/imgFrHelp/image244.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image245.jpg" v:shapes="_x0000_i1166" border="0" height="149" width="400"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193859">Figure </a><!--[if supportFields]><span style='mso-bookmark: _Toc364193859'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193859'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">102</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193859'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : Avertissement de Maxima</span></p> <p class="MsoNormal">N<span style="line-height: 115%;">otez qu un tel avertissement peut se produire alors que la définition est correcte mathématiquement, du fait des limites du calcul formel. C est pourquoi la possibilité vous est laissée d ignorer l avertissement&nbsp; après une nouvelle mise en garde&nbsp;: la fonction pourra être créée. Fin de cet exemple.</span></p> <p class="MsoNormal" style="text-align: center; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1167" type="#_x0000_t75" style='width:342.75pt;height:272.25pt'> <v:imagedata src="/help/imgFrHelp/image246.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image247.jpg" v:shapes="_x0000_i1167" border="0" height="363" width="457"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193860">Figure </a><!--[if supportFields]><span style='mso-bookmark: _Toc364193860'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193860'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">103</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193860'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : la bielle, fonction modèle</span></p> </div> <hr> <br> </div> <br> <br> <div id="UnderBoxes"> </div> </td> </tr> </tbody> </table> </body></html>