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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_31</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_30.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_31</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_32.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 31</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="d7854f7c99b0e699017f94e4a332bacc.gif" border="0" alt="0031-01.GIF" width="272" height="134" /></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2.7<br />Two聽coordinate聽systems.</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">With two distinct coordinate systems </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> and </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, the same point is represented by different coordinates (<i>x</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>y</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>z</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="1"><sub>f</sub></font><sub><font face="Times New Roman, Times, Serif" size="1">1</font></sub><font face="Times New Roman, Times, Serif" size="1"></font><font face="Times New Roman, Times, Serif" size="3"> and (<i>x</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>y</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>z</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="1"><sub>f</sub></font><sub><font face="Times New Roman, Times, Serif" size="1">2</font></sub><font face="Times New Roman, Times, Serif" size="1"></font><font face="Times New Roman, Times, Serif" size="3"> in each coordinate system, as shown in Fig. 2.7. The transformation of point coordinates from one coordinate system to another will require two operations: <i>translation</i> and <i>rotation</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">Consider that in </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, V</font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3"> = (<i>x</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>y</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>z</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="1"><sub>f</sub></font><sub><font face="Times New Roman, Times, Serif" size="1">2</font></sub><font face="Times New Roman, Times, Serif" size="1"></font><font face="Times New Roman, Times, Serif" size="3"> is the vector relative to </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3"> from the origin of </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3"> to the point <i>P</i>. In </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, the coordinates of <i>P</i> will be the vector sum of O</font><font face="Times New Roman, Times, Serif" size="1"><sub>12</sub></font><font face="Times New Roman, Times, Serif" size="3"> and V</font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3"> represented relative to </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">: V</font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> = O</font><font face="Times New Roman, Times, Serif" size="1"><sub>12</sub></font><font face="Times New Roman, Times, Serif" size="3"> + V</font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">. In </font><font face="Symbol" size="3"><i>f</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></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="cb99e98619fb457e3205349e34205584.gif" border="0" alt="0031-02.GIF" width="331" 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">The present question of interest is how to calculate [V</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="1"><sub>f</sub></font><sub><font face="Times New Roman, Times, Serif" size="1">1</font></sub><font face="Times New Roman, Times, Serif" size="1"></font><font face="Times New Roman, Times, Serif" size="3"> if (<i>x</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>y</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>z</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="1"><sub>f</sub></font><sub><font face="Times New Roman, Times, Serif" size="1">2</font></sub><font face="Times New Roman, Times, Serif" size="1"></font><font face="Times New Roman, Times, Serif" size="3">, (<i>x</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>O</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>y</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>O</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>z</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>O</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="1"><sub>f</sub></font><sub><font face="Times New Roman, Times, Serif" size="1">1</font></sub><font face="Times New Roman, Times, Serif" size="1"></font><font face="Times New Roman, Times, Serif" size="3">, and the relative orientation of the two coordinate systems are known. This knowledge would allow translation of </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3"> coordinates to </font><font face="Symbol" size="3"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> coordinates by means of Eq. (2.12).</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>⌨️ 快捷键说明
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