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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_46</title> <link rel="stylesheet" href="reset.css" type="text/css" media="all"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> </head> <body> <table summary="top nav" border="0" width="100%"> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_45.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_46</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_47.html">next page ></a></td> </tr> <tr> <td id="ebook_page" align="left" colspan="3" style="background: #ffffff; padding: 20px;"> <table border="0" width="100%" cellpadding="0"><tr><td align="center"> <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td> <td align="right"></td> </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 46</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">which can be verified by direct substitution. Therefore,</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="5df16b67ef73f6a5cd2cbea73f5a7d2d.gif" border="0" alt="0046-01.GIF" width="484" height="161" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Therefore</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="b083f3537d63f1e7113270fc0f42cc6e.gif" border="0" alt="0046-02.GIF" width="413" height="40" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">where </font><font face="Symbol" size="3">U</font><font face="Times New Roman, Times, Serif" size="3">(<i>t</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>k</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">) = [</font><font face="Symbol" size="3"><i>u</i></font><font face="Times New Roman, Times, Serif" size="3">(<i>t</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>k</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">)脳] and <img src="761e8cbc07d046eff900fea1218c5c28.gif" border="0" alt="C0046-01.GIF" width="210" height="34" />. Equation (2.63) is properly defined theoretically, even as ||</font><font face="Symbol" size="3"><i>u</i></font><font face="Times New Roman, Times, Serif" size="3">|| </font><font face="Symbol" size="3">庐</font><font face="Times New Roman, Times, Serif" size="3"> 0, but must be implemented numerically with care.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">In approaches such as that described above, in which the direction-cosine matrix is calculated directly, the Euler angles could be determined, for control purposes, by the following equations:</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="ede20d69e4e09f4d54deca0c196abae3.gif" border="0" alt="0046-03.GIF" width="351" height="59" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="f9fa426dbce64352169b4ffefad16ab4.gif" border="0" alt="0046-04.GIF" width="351" height="20" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="e797cfa40275376c76fa67a910c4489f.gif" border="0" alt="0046-05.GIF" width="351" height="19" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">where arctan2(<i>y, x</i>) is a four quadrant inverse tangent function.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">2.5.3.2<br />Euler Angle Derivatives</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Section 2.4 described the use of Euler angles (</font><font face="Symbol" size="3"><i>f</i></font><i><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3">q</font><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3">y</font></i><font face="Symbol" size="3"></font><font face="Times New Roman, Times, Serif" size="3">) to determine the direction-cosine matrix. This approach requires that the navigation system maintain the Euler angles based on the gyro measurements of the angular rate vector. Therefore it is necessary to calculate and integrate the derivatives (<i>d</i></font><i><font face="Symbol" size="3">f</font><font face="Times New Roman, Times, Serif" size="3">/dt, d</font><font face="Symbol" size="3">q</font><font face="Times New Roman, Times, Serif" size="3">/dt</font></i><font face="Times New Roman, Times, Serif" size="3">, and <i>d</i></font><i><font face="Symbol" size="3">y</font><font face="Times New Roman, Times, Serif" size="3">/dt</font></i><font face="Times New Roman, Times, Serif" size="3">). If the angular rate gyros are rigidly mounted on the vehicle, they will directly measure the body-frame inertial angular rate vector (<i>p, q, r</i>) resolved along the vehicle axis, as shown in Fig. 2.3. Hence it is necessary to transform (<i>p, q, r</i>) to (<i>d</i></font><i><font face="Symbol" size="3">f</font><font face="Times New Roman, Times, Serif" size="3">/dt, d</font><font face="Symbol" size="3">q</font><font face="Times New Roman, Times, Serif" size="3">/dt, d</font><font face="Symbol" size="3">y</font><font face="Times New Roman, Times, Serif" size="3">/dt</font></i><font face="Times New Roman, Times, Serif" size="3">).</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">First, note from Fig. 2.11 that <i>p = d</i></font><i><font face="Symbol" size="3">f</font><font face="Times New Roman, Times, Serif" size="3">/dt</font></i><font face="Times New Roman, Times, Serif" size="3">, when <i>d</i></font><i><font face="Symbol" size="3">f</font><font face="Times New Roman, Times, Serif" size="3">/dt</font></i><font face="Times New Roman, Times, Serif" size="3"> is the only rotation. Second, note that <i>d</i></font><i><font face="Symbol" size="3">q</font><font face="Times New Roman, Times, Serif" size="3">/dt</font></i><font face="Times New Roman, Times, Serif" size="3"> would correspond to the angular rate vector (<i>d</i></font><i><font face="Symbol" size="3">q</font><font face="Times New Roman, Times, Serif" size="3">/dt</font></i><font face="Times New Roman, Times, Serif" size="3">)J''</font><font face="Times New Roman, Times, Serif" size="3" color="#FFFF00"></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>聽 </td> </tr> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_45.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_46</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_47.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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