Re: [Algorithms] Looking for a differential equation closed form

[Jon W. <jw...@gm...>]

That solution gets me halfway there. Pretty good! It doesn't do squared air
drag, doesn't do variable air drag over time, and needs to be
re-parameterized into vectors instead of separate scalars -- but the MAPLE
code at the end is probably the best part, because I could probably go from
there to my desired solution. Thanks!

Sincerely,

jw


--
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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.



On Wed, Mar 10, 2010 at 5:47 PM, Beau Albiston <alb...@cy...> wrote:

> Perhaps this might help?
>
> http://www.scar.utoronto.ca/~pat/fun/NEWT3D/PDF/PRJCTILE.PDF
>
> -Beau
>
> On 3/10/10 10:49 AM, Jon Watte wrote:
> > 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 :-)
> >
> > 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.
> >
> > 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!
> >
> > Sincerely,
> >
> > jw
> >
> >
> > --
> > 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.
> >
> >
> >
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