Re: Looking for a differential equation closed form

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:

dv/dt = W/m + ((a+bt)/m).v + ((c+dt)/m).v^2

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.)

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:

http://planetmath.org/encyclopedia/RiccatiDifferentialEquation.html

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:

http://planetmath.org/?op=getobj&from=objects&id=7023

Hope that helps a little - wish I could be of more use!

Stu

On 10/03/2010 16:49, 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

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