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</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="07275d69f65dbceadfd1b949cb33f575.gif" border="0" alt="0292-01.GIF" width="289" height="18" /></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, if the components of <img src="03bdb735fc34d02eff6142a34e1f0b79.gif" border="0" alt="OMEGAAB.GIF" width="23" height="17" /> are (</font><font face="Symbol" size="3"><i>w</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3"><i>w</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3"><i>w</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>3</sub></font><font face="Times New Roman, Times, Serif" size="3">)</font><font face="Times New Roman, Times, Serif" size="2"><sup><i>T</i></sup></font><font face="Times New Roman, Times, Serif" size="3">, then</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="0aea88f9f7105a3d9519063fdde69d4f.gif" border="0" alt="0292-02.GIF" width="326" height="60" /></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">This skew-symmetric form of <img src="03bdb735fc34d02eff6142a34e1f0b79.gif" border="0" alt="OMEGAAB.GIF" width="23" height="17" /> will be convenient in later analysis. The equivalence expressed in Eq. (A.1) is denoted as <img src="c774fac9bac0bba78caed09df4e1a54d.gif" border="0" alt="C0292-02.GIF" width="90" height="18" />. Also, based on the properties of cross products,</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="7b6d97eaa527172392d890adaedd227f.gif" border="0" alt="0292-03.GIF" width="289" height="17" /></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 various places in the text it is useful to be able to write cross products in one of the following matrix forms:</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="364c6f4ce61ec6c307714b54d8b63329.gif" border="0" alt="0292-04.GIF" width="284" height="16" /></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="0f0eb1f075807113b9a683602354f914.gif" border="0" alt="0292-05.GIF" width="244" height="17" /></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 X and Y are the skew-symmetric matrices corresponding to x and y, which are defined corresponding to Eq. (A.2).</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><table cellpadding="0" cellspacing="0" border="0" width="100%"><tr><td height="12"></td></tr><tr><td><table cellspacing="0" width="288" cellpadding="4"><tr><td colspan="2" valign="top"><font face="Times New Roman, Times, Serif" size="2">TABLE A.2 Reference Frame Symbol Definitions</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>a</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Accelerometer coordinates (nonorthogonal)</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>b</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Body coordinates</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>e</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">ECEF coordinates</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>g</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Gyro coordinates (nonorthogonal)</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>i</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Inertial coordinates</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>p</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Platform coordinates</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>t</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Tangent-plane coordinates</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>n</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Navigation frame</font></td></tr></table></td></tr></table><br /></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_291.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_292</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_293.html">next page ></a></td> </tr> </table> </body> </html>
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