Re: [Algorithms] Looking for a differential equation closed form
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Re: [Algorithms] Looking for a differential equation closed form
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From: Stuart G. <gda...@gx...> - 2010-03-10 20:08:00
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html; charset=UTF-8" http-equiv="Content-Type"> </head> <body bgcolor="#ffffff" text="#000000"> Rather rusty too (7 years ago now :)) and a computer scientist rather than a mathematician these days, but I think what you're saying is that you want to solve an equation which looks like this:<br> <br> dv/dt = W/m + ((a+bt)/m).v + ((c+dt)/m).v^2<br> <br> In that, W is the weight force, v is the velocity of the object, m is its mass, t is time, and a through d are arbitrary constants. (The equation originally comes from writing m[dv/dt] = W + (a + bt)v + (c + dt)v^2.)<br> <br> In that case (and bearing in mind that I only did up to further maths at A-level, so take this with a pinch of salt), it appears to be what is called a Riccati equation:<br> <br> <a class="moz-txt-link-freetext" href="http://planetmath.org/encyclopedia/RiccatiDifferentialEquation.html">http://planetmath.org/encyclopedia/RiccatiDifferentialEquation.html</a><br> <br> Not sure if that helps for Google purposes? There's a bit on Wikipedia as well, for what it's worth. PlanetMath itself has an index of differential equations, which can be found here:<br> <br> <a class="moz-txt-link-freetext" href="http://planetmath.org/?op=getobj&from=objects&id=7023">http://planetmath.org/?op=getobj&from=objects&id=7023</a><br> <br> Hope that helps a little - wish I could be of more use!<br> <br> Stu<br> <br> On 10/03/2010 16:49, Jon Watte wrote: <blockquote cite="mid:c7b...@ma..." type="cite">I'm looking for a closed form solution for a differential equation. I did pass this stuff 20 years ago, but was more interested in graph theory, discrete math and DSP, so it's all vanished from my brain :-) <div><br> </div> <div>The equation is given a point mass that leaves a start position with a start velocity. On this point mass is acting a fixed gravitational force (in a fixed direction), as well as a linear and quadratic motion-opposed force (air drag) based on a linear and quadratic coefficient of air drag. So far, it's pretty much your standard "cannonball" equation (although I'd really appreciate a convenient reference for this solution, too). However, in this case, I also want to make the drag coefficients a linear function of time -- drag(linear, quadratic) = const(linear, quadratic) + factor(linear, quadratic) * time.</div> <div><br> </div> <div>If someone could plug this into Mathematica (or look it up in a handy formula reference), I'd really appreciate it. If someone could take the time to point at the proper online reference, that'd be wonderful, too!</div> <div><br> </div> <div>Sincerely,</div> <div><br> </div> <div>jw</div> <div><br clear="all"> <br> --<br> Americans might object: there is no way we would sacrifice our living standards for the benefit of people in the rest of the world. Nevertheless, whether we get there willingly or not, we shall soon have lower consumption rates, because our present rates are unsustainable. <br> <br> </div> <pre wrap=""> <fieldset class="mimeAttachmentHeader"></fieldset> ------------------------------------------------------------------------------ Download Intel&#174; Parallel Studio Eval Try the new software tools for yourself. Speed compiling, find bugs proactively, and fine-tune applications for parallel performance. See why Intel Parallel Studio got high marks during beta. <a class="moz-txt-link-freetext" href="http://p.sf.net/sfu/intel-sw-dev">http://p.sf.net/sfu/intel-sw-dev</a></pre> <pre wrap=""> <fieldset class="mimeAttachmentHeader"></fieldset> _______________________________________________ GDAlgorithms-list mailing list <a class="moz-txt-link-abbreviated" href="mailto:GDA...@li...">GDA...@li...</a> <a class="moz-txt-link-freetext" href="https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list">https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list</a> Archives: <a class="moz-txt-link-freetext" href="http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list">http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list</a></pre> </blockquote> </body> </html> |
