Thread: RE: [Algorithms] Differential equations bestiary?
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From: Willem de B. <wd...@mi...> - 2005-11-08 16:50:28
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Are you looking for analytical or numerical solutions? And what does your differential equation look like; eg., first order, n-th order, and constant coefficients, etc? Willem -----Original Message----- From: gda...@li... [mailto:gda...@li...] On Behalf Of Danny Kodicek Sent: 08 November 2005 16:25 To: gda...@li... Subject: [Algorithms] Differential equations bestiary? Anyone know of a site where I could find a list of solutions to various=20 differential equation families? I've spent most of the last couple of days=20 working on something that ought to be pretty simple, but I'm having to=20 reinvent the wheel to do it. Thanks Danny (PS: I don't know how on-topic this is, perhaps it should go to a general=20 computational algorithms or maths list, but I'm on too many lists as it=20 is... Still, I'm sure it's the kind of thing that many people here would find useful) ------------------------------------------------------- SF.Net email is sponsored by: Tame your development challenges with Apache's Geronimo App Server. Download it for free - -and be entered to win a 42" plasma tv or your very own Sony(tm)PSP. Click here to play: http://sourceforge.net/geronimo.php _______________________________________________ GDAlgorithms-list mailing list GDA...@li... https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=3D6188 |
From: Danny K. <dr...@we...> - 2005-11-08 17:13:49
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>Are you looking for analytical or numerical solutions? Analytical, preferably > And what does your differential equation look like; eg., first order, n-th order, and constant coefficients, etc? My particular differential equation in this case is 2nd order, homogeneous, constant coefficients: d^2y/dt^2=A/y^2 Actually, I think I've solved this one, as y=-Q(kt+p)^(2/3), with Q chosen appropriately and k, p according to the initial conditions seems to fit the bill. But frankly my brain is starting to hurt and I think I've done enough scribbling for now. And in any case, I'm not even entirely sure this is the differential equation I want! Danny |
From: Andrew V. <and...@ni...> - 2005-11-08 17:43:03
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This seems fairly useful: http://eqworld.ipmnet.ru/en/solutions/ode/ode-toc3.pdf I reckon the solution to your equation is: y = ( (2/9A)^(-1/3) ) * t^(2/3) HTH, Andrew. > -----Original Message----- > From: gda...@li... > [mailto:gda...@li...] On > Behalf Of Danny Kodicek > Sent: 08 November 2005 17:14 > To: gda...@li... > Subject: Re: [Algorithms] Differential equations bestiary? > > >Are you looking for analytical or numerical solutions? > > Analytical, preferably > > > And > what does your differential equation look like; eg., first > order, n-th order, and constant coefficients, etc? > > My particular differential equation in this case is 2nd > order, homogeneous, constant coefficients: > > d^2y/dt^2=A/y^2 > > Actually, I think I've solved this one, as y=-Q(kt+p)^(2/3), > with Q chosen appropriately and k, p according to the initial > conditions seems to fit the bill. But frankly my brain is > starting to hurt and I think I've done enough scribbling for > now. And in any case, I'm not even entirely sure this is the > differential equation I want! > > Danny > > > > > ------------------------------------------------------- > SF.Net email is sponsored by: > Tame your development challenges with Apache's Geronimo App > Server. Download it for free - -and be entered to win a 42" > plasma tv or your very own Sony(tm)PSP. Click here to play: > http://sourceforge.net/geronimo.php > _______________________________________________ > GDAlgorithms-list mailing list > GDA...@li... > https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > |
From: Danny K. <dr...@we...> - 2005-11-08 18:17:50
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> This seems fairly useful: > http://eqworld.ipmnet.ru/en/solutions/ode/ode-toc3.pdf Ooh, that looks *very* much like the kind of thing I was looking for, thanks. > > I reckon the solution to your equation is: > > y = ( (2/9A)^(-1/3) ) * t^(2/3) That's a particular solution, but for the general solution you need (kt+p) instead of t. But I'm glad your calculations agree with mine :) Right now, though, I'm more inclined to cheat... Best Danny |
From: Stephan R. <ke...@so...> - 2005-11-08 19:26:26
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Hey all, Turns out that after 2 or even 3 years of not doing any 3D work, I am finally back into 3D related project!! So with much enthusiasm, I sit down starting on my new engine, doesn't take long for the grey hairs to appear!! Turns out that my memory after such a long time has gotten a little bit...rusty to say the least =) And unfortunately, the engine I had written a few years ago has long ago died some unknown to me death on some long lost hard disk. Got my basic camera working, first-person type camera just yaw and pitch, works just fine. Using quaternions to do the job. So I figure hey lets be really cool and slerp from my current rotation to the target rotation!!! A little while later, that is working too. Sort of, until I run into the longer / shorter path issue and my camera decides it wants to turn the other way than it really should... Dig a little deeper in my rather rusty memory, and I remember...dot product of current orientation with the target orientation < 0 = bad, and need to do something about it. What I don't remember is, what I need to do about it =) Can anyone refresh my memory a little? Thanks!!! Stephan Rose |
From: Jamie F. <ja...@qu...> - 2005-11-08 19:48:16
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Simply negate the target rotation when the dot product is negative, and you'll take the short way round. Jamie Stephan Rose wrote: > Hey all, > > Turns out that after 2 or even 3 years of not doing any 3D work, I am > finally back into 3D related project!! > > So with much enthusiasm, I sit down starting on my new engine, doesn't take > long for the grey hairs to appear!! Turns out that my memory after such a > long time has gotten a little bit...rusty to say the least =) And > unfortunately, the engine I had written a few years ago has long ago died > some unknown to me death on some long lost hard disk. > > Got my basic camera working, first-person type camera just yaw and pitch, > works just fine. Using quaternions to do the job. So I figure hey lets be > really cool and slerp from my current rotation to the target rotation!!! A > little while later, that is working too. Sort of, until I run into the > longer / shorter path issue and my camera decides it wants to turn the other > way than it really should... > > Dig a little deeper in my rather rusty memory, and I remember...dot product > of current orientation with the target orientation < 0 = bad, and need to do > something about it. What I don't remember is, what I need to do about it =) > > Can anyone refresh my memory a little? > > Thanks!!! > > Stephan Rose > > > > ------------------------------------------------------- > SF.Net email is sponsored by: > Tame your development challenges with Apache's Geronimo App Server. Download > it for free - -and be entered to win a 42" plasma tv or your very own > Sony(tm)PSP. Click here to play: http://sourceforge.net/geronimo.php > _______________________________________________ > GDAlgorithms-list mailing list > GDA...@li... > https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 |
From: Stephan R. <ke...@so...> - 2005-11-09 10:37:56
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Thanks, now its working flawlessly, I tried all sorts of stuff except this very simple thing, figures couldn't find the forest because of all the trees again! Thank you =) -----Original Message----- From: gda...@li... [mailto:gda...@li...] On Behalf Of Jamie Fowlston Sent: Tuesday, November 08, 2005 20:43 To: gda...@li... Subject: Re: [Algorithms] Simple camera related question Simply negate the target rotation when the dot product is negative, and you'll take the short way round. Jamie Stephan Rose wrote: > Hey all, > > Turns out that after 2 or even 3 years of not doing any 3D work, I am > finally back into 3D related project!! > > So with much enthusiasm, I sit down starting on my new engine, doesn't take > long for the grey hairs to appear!! Turns out that my memory after such a > long time has gotten a little bit...rusty to say the least =) And > unfortunately, the engine I had written a few years ago has long ago died > some unknown to me death on some long lost hard disk. > > Got my basic camera working, first-person type camera just yaw and pitch, > works just fine. Using quaternions to do the job. So I figure hey lets be > really cool and slerp from my current rotation to the target rotation!!! A > little while later, that is working too. Sort of, until I run into the > longer / shorter path issue and my camera decides it wants to turn the other > way than it really should... > > Dig a little deeper in my rather rusty memory, and I remember...dot product > of current orientation with the target orientation < 0 = bad, and need to do > something about it. What I don't remember is, what I need to do about it =) > > Can anyone refresh my memory a little? > > Thanks!!! > > Stephan Rose > > > > ------------------------------------------------------- > SF.Net email is sponsored by: > Tame your development challenges with Apache's Geronimo App Server. Download > it for free - -and be entered to win a 42" plasma tv or your very own > Sony(tm)PSP. Click here to play: http://sourceforge.net/geronimo.php > _______________________________________________ > GDAlgorithms-list mailing list > GDA...@li... > https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 ------------------------------------------------------- SF.Net email is sponsored by: Tame your development challenges with Apache's Geronimo App Server. Download it for free - -and be entered to win a 42" plasma tv or your very own Sony(tm)PSP. Click here to play: http://sourceforge.net/geronimo.php _______________________________________________ GDAlgorithms-list mailing list GDA...@li... https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 |