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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>4 刚体平面运动微分方程</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td>即动量定理（质心运动定理）和动量矩定理（刚体定轴转动微分方程）的综合应用。</td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> </td> <td width="50%" rowspan="3"> <p align="center"><img border="0" src="pic1/3053_457.GIF" width="202" height="157"></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3053_458.GIF" width="136" height="96"></td> </tr> <tr> <td width="50%">注：一般需补充运动学或静力学方程。<br> </td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例5</b>（例5-20，典型题目，较难，综合动力学、静力学、运动学知识）</td> <td width="50%" rowspan="2"> <p align="center"><img border="0" src="pic1/3053_459.GIF" width="202" height="180"></td> </tr> <tr> <td width="50%">均质鼓轮（轮轴）质量为M = 50kg，对质心的回转半径ρ = 70mm，轴上绕一绳索，其上作用一水平力P = 200N。已知轮与地面间的静、动摩擦系数分别为f = 0.20， f'= 0.15。<br> 求轮心C的加速度aC 和轮的角加速度ε。</td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例6</b>（P217，例5-21，多种解法（可有4种），亦为典型题目，用到许多运动学知识）</td> <td width="50%" rowspan="4"> <p align="center"><img border="0" src="pic1/3053_460.GIF" width="244" height="208"></td> </tr> <tr> <td width="50%">已知：AB = l，质量m，初时θ<font size="1">0</font>，杆静止。求此时杆的角速度、角加速度、A、B处反力，并求A端脱离墙壁时的θ。</td> </tr> <tr> <td width="50%"><b>解1</b>：<font color="#800000">（书上解法）</font></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3053_461.GIF" width="130" height="93"></td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic1/3053_462.GIF" width="196" height="56"></td> <td> 5个方程联立，得ε（积分得ω）、N<font size="1">A</font>、N<font size="1">B</font></td> </tr> </table> </td> </tr> <tr> <td><b>解2</b>：<font color="#800000">（较好）</font></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic1/3053_463.GIF" width="122" height="29"></td> <td> <img border="0" src="pic1/3053_464.GIF" width="33" height="27"> </td> <td> ε（积分得ω）</td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="20%" rowspan="2"><img border="0" src="pic1/3053_465.GIF" width="196" height="56"></td> <td width="20%" rowspan="2"><img border="0" src="pic1/3053_466.GIF" width="106" height="62"></td> <td width="20%" align="center"><img border="0" src="pic1/3053_464.GIF" width="33" height="27"></td> <td width="20%">N<font size="1">A</font></td> <td width="20%" rowspan="2"> <p align="center">无需<br> 解联立方程</td> </tr> <tr> <td width="20%" align="center"><img border="0" src="pic1/3053_464.GIF" width="33" height="27"></td> <td width="20%">N<font size="1">B</font></td> </tr> </table> </td> </tr> <tr> <td><b>解3</b>：<font color="#800000">（较好）</font></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic1/3053_467.GIF" width="95" height="25"></td> <td> <img border="0" src="pic1/3053_464.GIF" width="33" height="27"> </td> <td> ω（求导得ε）</td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="20%" rowspan="2"><img border="0" src="pic1/3053_468.GIF" width="196" height="56"></td> <td width="20%" rowspan="2"><img border="0" src="pic1/3053_469.GIF" width="106" height="62"></td> <td width="20%" align="center"><img border="0" src="pic1/3053_464.GIF" width="33" height="27"></td> <td width="20%">N<font size="1">A</font></td> <td width="20%" rowspan="2"> <p align="center">无需<br> 解联立方程</td> </tr> <tr> <td width="20%" align="center"><img border="0" src="pic1/3053_464.GIF" width="33" height="27"></td> <td width="20%">N<font size="1">B</font></td> </tr> </table> </td> </tr> <tr> <td><b>解4</b>：<font color="#800000">（较好）</font></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic1/3053_470.GIF" width="95" height="25"></td> <td> <img border="0" src="pic1/3053_464.GIF" width="33" height="27"> </td> <td>ω</td> <td> </td> <td><img border="0" src="pic1/3053_471.GIF" width="122" height="29"></td> <td> <img border="0" src="pic1/3053_464.GIF" width="33" height="27"> </td> <td>ε</td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="20%" rowspan="2"><img border="0" src="pic1/3053_472.GIF" width="196" height="56"></td> <td width="20%" rowspan="2"><img border="0" src="pic1/3053_473.GIF" width="106" height="62"></td> <td width="20%" align="center"><img border="0" src="pic1/3053_464.GIF" width="33" height="27"></td> <td width="20%">N<font size="1">A</font></td> <td width="20%" rowspan="2"> <p align="center">无需<br> 解联立方程</td> </tr> <tr> <td width="20%" align="center"><img border="0" src="pic1/3053_464.GIF" width="33" height="27"></td> <td width="20%">N<font size="1">B</font></td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例7</b>（P219，例5-22，亦为典型题目，用到许多运动学知识）</td> <td width="50%" rowspan="3"> <p align="center"><img border="0" src="pic1/3053_474.GIF" width="255" height="146"></td> </tr> <tr> <td width="50%">均质杆AB，质量m，长l。在图示位置释放。求此时杆的角加速度。</td> </tr> <tr> <td width="50%">注：此题位置为一特定位置，故在运动分析时，不宜像例6可直接用求导法，而需用合成法（基点法）</td> </tr> </table> </td> </tr> <tr> <td></td> </tr> <tr> <td> <p align="center"> <a href="3053_2.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a href="3053_5.htm"><font color="#00CC00">[ 下一节 ]</font></a> </td> </tr></table></BODY></HTML> ⌨️ 快捷键说明
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