Author Topic: A differential equation (Read 5038 times) Tweet Share

QuantumJG · « **Reply #15 on:** November 26, 2009, 11:27:47 pm »

how do you run that excel program?

kamil9876 · « **Reply #16 on:** November 26, 2009, 11:32:17 pm »

The perils of Liebniz notation.

Ahmad · « **Reply #17 on:** November 26, 2009, 11:43:26 pm »

Highlight cells A3 to D3, right click and copy them. Then highlight the first 4 cells of the next 100 rows, right click and paste. Then you'll probably get the idea and paste into the next 60,000 rows or whatever

humph · « **Reply #18 on:** November 27, 2009, 02:03:04 am »

Good old non-linear ODEs. They come up all the time in electromag stuff. In first year I remember deriving an ODE to find the acceleration of a metal pellet out of a Gauss gun:
$\frac{d^2 x}{dt^2} = \frac{\tau n^2 I^2 \mu_0}{ms^2} \left(\frac{s/2 + x}{\sqrt{(s/2 + x)^2 + r^2}} - \frac{s/2 - x}{\sqrt{(s/2 - x)^2 + r^2}}\right) \left(\frac{1}{\left((s/2 + x)^2 + r^2\right)^{3/2}} - \frac{1}{\left((s/2 - x)^2 + r^2\right)^{3/2}}\right)$
where
$x$ is position of the projectile inside the Gauss gun,
$t$ is time,
$m$ is the mass of the projectile,
$\tau$ is its volume,
$s$ is the length of the coil of the Gauss gun,
$I$ is the current running through the coil,
$r$ is the radius of the coil,
$n \phantom{}$ is the number of turns of the coil, and
$\mu_0 = 4\pi \times 10^{-7}$ is a constant.

Needless to say, even trying to solve this ODE numerically was a bit beyond us

/0 · « **Reply #19 on:** November 27, 2009, 02:24:06 am »

Quote from: Ahmad on November 26, 2009, 11:43:26 pm

Highlight cells A3 to D3, right click and copy them. Then highlight the first 4 cells of the next 100 rows, right click and paste. Then you'll probably get the idea and paste into the next 60,000 rows or whatever

lol excel is throwing a tantrum about all that data

humph · « **Reply #20 on:** November 27, 2009, 03:43:39 am »

Quote from: kamil9876 on November 26, 2009, 11:32:17 pm

The perils of Liebniz notation.

It's why you should always just write $f''(x) = -\frac{2G}{f(x)}$ . Though it does make solving separable equations seem less elementary, though all you really have to do is remember change of variables rule when integrating.

QuantumJG · « **Reply #21 on:** November 27, 2009, 12:25:27 pm »

Quote from: humph on November 27, 2009, 02:03:04 am

Good old non-linear ODEs. They come up all the time in electromag stuff. In first year I remember deriving an ODE to find the acceleration of a metal pellet out of a Gauss gun:
$\frac{d^2 x}{dt^2} = \frac{\tau n^2 I^2 \mu_0}{ms^2} \left(\frac{s/2 + x}{\sqrt{(s/2 + x)^2 + r^2}} - \frac{s/2 - x}{\sqrt{(s/2 - x)^2 + r^2}}\right) \left(\frac{1}{\left((s/2 + x)^2 + r^2\right)^{3/2}} - \frac{1}{\left((s/2 - x)^2 + r^2\right)^{3/2}}\right)$
where
$x$ is position of the projectile inside the Gauss gun,
$t$ is time,
$m$ is the mass of the projectile,
$\tau$ is its volume,
$s$ is the length of the coil of the Gauss gun,
$I$ is the current running through the coil,
$r$ is the radius of the coil,
$n \phantom{}$ is the number of turns of the coil, and
$\mu_0 = 4\pi \times 10^{-7}$ is a constant.

Needless to say, even trying to solve this ODE numerically was a bit beyond us

That is an intense second order ODE!

zzdfa · « **Reply #22 on:** November 27, 2009, 11:13:15 pm »

coincidence o.o

http://forums.xkcd.com/viewtopic.php?f=17&t=50471

kamil9876 · « **Reply #23 on:** November 27, 2009, 11:16:25 pm »

great minds think alike

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Author Topic: A differential equation (Read 5038 times) Tweet Share

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