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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_190</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_189.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_190</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_191.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 190</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><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 align="center"><font face="Times New Roman, Times, Serif" size="3"><img src="60e37b2d6889dd7b1b21c2c243b33fc6.gif" border="0" alt="0190-01.GIF" width="305" height="172" /></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" width="100%"><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 align="center"><font face="Times New Roman, Times, Serif" size="2">Figure聽6.1<br />Effective聽gravity聽vector.</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">The local gravity vector indicates the direction that a weight would hang at a location indicated by R. Figure 6.1 shows the relation of these three accelerations. The vector magnitudes are not drawn to scale. In reality ||</font><font face="Symbol" size="3">W</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>ie</i></sub></font><font face="Symbol" size="3">W</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>ie</i></sub></font><font face="Times New Roman, Times, Serif" size="3">R|| </font><font face="Symbol" size="3">禄</font><font face="Times New Roman, Times, Serif" size="3"> 1/300||G||[166, 139]. In this figure, </font><font face="Symbol" size="3">l</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>c</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> denotes geocentric latitude and <i>D</i> represents deviation of the normal.</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="17"></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">6.2<br />General Kinematic 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">The derivation of the INS kinematic equations is broken up into three sections. In these sections the position, velocity, and attitude kinematic equations are discussed in that order.</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 the derivations below the derivative notation of Ref. 41 is used. Specifically, (<i>d/dt</i>)() denotes the intrinsic variation of the quantity in parenthesis expressed in a nonrotating (inertial) frame. The components of the resulting quantity can be resolved in any desired frame of reference after differentiation. The operation <img src="2c7e0a85476fd6d6701de54628f2f2f5.gif" border="0" alt="C0190-01.GIF" width="12" height="18" /> denotes the time derivative of the term in parenthesis on a term-by-term basis with the ordinary product and chain rules. The two operations are equivalent only in inertial frames of reference.</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 each of the following subsections, <i>P</i> denotes a point and R denotes the vector from the origin <i>O</i> to <i>P</i>. Also, the direction-cosine method for maintaining reference-frame rotational transformations is used throughout the discussion. This is only for convenience. Three methods for maintaining the required rotational transformations are presented and discussed in Sec. 2.5.</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">The main references for the following sections are Refs. 41, 43, 111, 125, 129, 138, 142, and 153.</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"><i>6.2.1<br />Position Dynamic Equations</i></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">Assuming that the velocity can be found (see Sec. 6.2.2) in the desired navigation frame, the position vector in that frame is found by direct integration:</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 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="dfb6f27031218fa766d5a4054494fef3.gif" border="0" alt="0190-02.GIF" width="315" height="37" /></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_189.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_190</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_191.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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