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<HTML><HEAD><TITLE>new</TITLE><META content="text/html; charset=gb2312" http-equiv=Content-Type><LINK href="text.css" rel=stylesheet type=text/css><META content="Microsoft FrontPage 4.0" name=GENERATOR></HEAD><body leftmargin="15"><center><b><br>1 約束 約束的運(yùn)動學(xué)分類</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td width="20"></td> <td width="540"><b><font color="#FF0000">靜力學(xué)中講的約束</font></b>——<font color="#0000FF">約束的力的性質(zhì)</font>（約束的力的方面），用<font color="#0000FF">約束力</font>表示，常指物體；</td> </tr> <tr> <td width="20"></td> <td width="540"><b><font color="#FF0000">此處講的約束</font></b>——<font color="#0000FF">約束的運(yùn)動的性質(zhì)</font>（約束的運(yùn)動的方面），用<font color="#0000FF">約束方程</font>表示,指運(yùn)動限制條件。</td> </tr> <tr> <td width="20"><b><font color="#0000FF">一、</font></b></td> <td width="540"><b><font color="#0000FF">約束和約束方程</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"><b>自由質(zhì)點(diǎn)系：</b>運(yùn)動不受任何限制。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="524"> <tr> <td width="198"><b>非自由質(zhì)點(diǎn)系</b>:運(yùn)動受到限制</td> <td width="74"> <b>——約束</b></td> <td width="246">限制條件用數(shù)學(xué)方程表示<b>即約束方程</b></td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">二、</font></b></td> <td width="540"><font color="#0000FF"><b>約束的運(yùn)動學(xué)分類 </b></font><font color="#800000">從三方面理解：概念、實(shí)例和約束方程。</font></td> </tr> <tr> <td width="20"></td> <td width="540">常有以下4種（獨(dú)立）分類方法：</td> </tr> <tr> <td width="20"></td> <td width="540">1. <font color="#0000FF">幾何約束</font>和<font color="#0000FF">運(yùn)動約束</font></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="25%"><b>單擺</b>：桿為剛性</td> <td width="25%" rowspan="5"><img border="0" src="pic2/3071_170.GIF" width="122" height="143"></td> <td width="25%"><b>圓輪純滾動：</b></td> <td width="25%" rowspan="5"><img border="0" src="pic2/3071_171.GIF" width="129" height="130"></td> </tr> <tr> <td width="25%"><font color="#FF00FF">質(zhì)點(diǎn)</font>：小球</td> <td width="25%"><font color="#FF00FF">質(zhì)點(diǎn)系</font>：圓輪</td> </tr> <tr> <td width="25%"><font color="#FF00FF">約束</font>：鉸鏈和桿</td> <td width="25%"><font color="#FF00FF">約束</font>：地面，無滑動</td> </tr> <tr> <td width="25%"><font color="#FF00FF">約束方程</font>：</td> <td width="25%"><font color="#FF00FF">約束方程</font>：</td> </tr> <tr> <td width="25%"><img border="0" src="pic2/3071_172.GIF" width="95" height="29"></td> <td width="25%"><img border="0" src="pic2/3071_173.GIF" width="122" height="25"></td> </tr> <tr> <td width="50%" colspan="2" valign="top"><b>幾何約束——</b><br> 只限制質(zhì)點(diǎn)或質(zhì)點(diǎn)系在空間的位置，約束方程為位置坐標(biāo)的代數(shù)方程（不含位置坐標(biāo)的導(dǎo)數(shù)）；</td> <td width="50%" colspan="2"><b>運(yùn)動約束——</b><br> 除位移方面的限制外，還有速度或角速度方面的限制，約束方程為位置坐標(biāo)的微分方程（或速度、角速度及位置坐標(biāo)的代數(shù)方程，顯含位置坐標(biāo)的導(dǎo)數(shù)）。</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">2. <font color="#0000FF">定常約束</font>和<font color="#0000FF">非定常約束</font></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="64%"><b>定常約束</b> —約束方程中不顯含時(shí)間t;(如前二例)</td> <td width="36%" rowspan="5"> <p align="center"><img border="0" src="pic2/3071_174.GIF" width="162" height="150"></td> </tr> <tr> <td width="64%"><b>非定常約束</b>——約束方程中顯含時(shí)間t</td> </tr> <tr> <td width="64%">變擺長單擺：</td> </tr> <tr> <td width="64%"><font color="#FF00FF">質(zhì)點(diǎn)：</font>小球</td> </tr> <tr> <td width="64%"><font color="#FF00FF">約束：</font>鉸鏈和繩</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><font color="#FF00FF">約束方程：</font></td> <td><img border="0" src="pic2/3071_175.GIF" width="143" height="30"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">3. <font color="#0000FF">完整約束</font>和<font color="#0000FF">非完整約束</font></td> </tr> <tr> <td width="20"></td> <td width="540"><b>完整約束——</b><br> 約束方程中不包含坐標(biāo)對時(shí)間的導(dǎo)數(shù)，或雖包含，但可積（轉(zhuǎn)換為有限形式）；（如前）</td> </tr> <tr> <td width="20"></td> <td width="540"><b>非完整約束——</b>約束方程中包含坐標(biāo)對時(shí)間的導(dǎo)數(shù)，且不可積。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="33%">二質(zhì)點(diǎn)追蹤問題：</td> <td width="33%" rowspan="3"> <p align="center"><img border="0" src="pic2/3071_176.GIF" width="166" height="132"></td> <td width="34%"><font color="#FF00FF">質(zhì)點(diǎn)系</font>：A、B</td> </tr> <tr> <td width="33%">質(zhì)點(diǎn)A、B在平面內(nèi)運(yùn)動，且A的速度始終指向B。</td> <td width="34%"><font color="#FF00FF">約束</font>：A速度指向B</td> </tr> <tr> <td width="33%"> </td> <td width="34%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><font color="#FF00FF">約束方程</font>：</td> <td><img border="0" src="pic2/3071_177.GIF" width="101" height="47"></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">4. <font color="#0000FF">雙面約束（固執(zhí)約束）</font>和<font color="#0000FF">單面約束（非固執(zhí)約束）</font></td> </tr> <tr> <td width="20"></td> <td width="540"><b>雙面約束（固執(zhí)約束）——</b><br> 不僅能限制質(zhì)點(diǎn)沿某一方向的運(yùn)動，還能限制相反方向的運(yùn)動，約束方程為等式方程；（如前單擺）</td> </tr> <tr> <td width="20"></td> <td width="540"><b>單面約束（非固執(zhí)約束）</b>——只能限制質(zhì)點(diǎn)沿某一方向的運(yùn)動，約束方程為不等式方程。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">單擺：用繩連</td> <td width="50%" rowspan="4"> <p align="center"><img border="0" src="pic2/3071_178.GIF" width="147" height="173"></td> </tr> <tr> <td width="50%"><font color="#FF00FF">約束方程</font>：</td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3071_179.GIF" width="95" height="32"></td> </tr> <tr> <td width="50%"> <table border="1" cellpadding="0" cellspacing="0" bordercolor="#FF0000"> <tr> <td>我們遇到的一般是完整、定常、幾何、雙面約束（或具有雙面約束性質(zhì)的單面約束），其約束方程可用含各質(zhì)點(diǎn)直角坐標(biāo)的代數(shù)方程表示。此處只討論上述情形。</td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"></td> </tr> <tr> <td width="20"></td> <td width="540"></td> </tr> <tr> <td width="560" colspan="2"> <p align="center"> <a href="3070.htm"><font color="#FF6666">[ 上一節(jié) ]</font></a> <a href="3071_2.htm"><font color="#00CC00">[ 下一節(jié) ]</font></a> </td> </tr> </table> </BODY></HTML> ?? 快捷鍵說明
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