Solving the Equations of Motion

<BODY LANG="EN" > <HR> <center> <table border=1> <tr> <td><A HREF="node3.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="rocket.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node5.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><A HREF="contents-node4.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </tr> </table> </center> <HR> <H1>Solving the Equations of Motion</H1> <P> It should be obvious to you, however, that the equation we have derived is not going to be easy to solve. Why? Mainly because of the drag force term containing the <EM>square</EM> of the velocity, the same (unknown) velocity that appears in the derivative term, <nobr><I>dV</I>/<I>dt</I>.</nobr> Note also that the mass is a function of time. In fact, the only thing constant in our equation is the thrust, <I>T</I>. We're not likely to find a solution to this equation with pencil and paper. <P> But instead of giving up and leaving this to rocket scientists, let's try something relatively simple at first, and then work our way up to more physically realistic cases. <nobr>M<font size=-1><small>APLE</small></font></nobr> and the computer should do most of the dull work, leaving us free to think about the important physical and mathematical ideas contained here. <P> <HR> <center> <table border=1> <tr> <td><A HREF="node3.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="rocket.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node5.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><A HREF="contents-node4.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </tr> </table> </center> <HR> <ADDRESS> Boyd Gatlin </ADDRESS> <P> </BODY>