/sci/ - Science & Math

>>7766327
>I've become a scientist against my will
What, did someone hold a gun to your head and say, "YOU WILL DO SCIENCE, OR ELSE!"?

>>7766237
Probably /v/, from the looks of it.

>>7764114
>weak and strong force
He means the asteroid as a whole, not the atoms you diploid.

It's the same force that keeps a chunk of rock together down here on Earth: electrostatic attraction. The thing is basically a giant pebble

>>7763426
Dude, you're posting on a site owner by a jap. This is weeb territory, get over it.

Anyway, the problem is a spambot could simply use Cramer's rule to solve the equation. It'd be tough to implement this in a way that's actually secure.

>>7702142
Still, what are common techniques used to solve such problems?

>>7702142
Any ideas then?

Also, changing the order of substitution removes a sign ambiguity:
[eqn]
v_0 X = X^2 + Y^2\\
v_0 \Upsilon = \chi^2 + \Upsilon^2
[/eqn]

Ok, defining:
[eqn]
X := \left(x_1'(t)\right)_x\\
Y := \left(x_1'(t)\right)_y
[/eqn]
and
[eqn]
\chi := \left(y_1'(t)\right)_x\\
\Upsilon := \left(y_1'(t)\right)_y
[/eqn]
Eliminating the variable [math]t[/math] ultimately leads to these very interesting relations:
[eqn]
\left(v_0 X\right)^2 = \left(X^2 + Y^2\right)^2\\
\left(v_0 \Upsilon\right)^2 = \left(\chi^2 + \Upsilon^2\right)^2
[/eqn]
Any thoughts on what this means?

>>7701928
We are talking about the same thing. It might be a D, I don't know, but I transcribed it as a 0, and I think I prefer it that way because it appears to be an initial velocity vector.

>>7701922
I think it's [math]V_0[/math], but I can kinda see why it might look like a D. Nevertheless, they refer to the same thing.

Also, I renamed [math]a[/math] as [math]p_0[/math] since the author told me it was the initial position.

>>7701901
My thought was perhaps the writer noticed that scalar term kept coming up in the equations, so he then defined [math]v_0[/math] to be that term.

>>7701863
Damn, that can't be it, because that would just result in [math]v_0 = \sqrt{v_0^2}[/math]

Wait, what if it's not [math]\vec{V}_0 = \hat{n}v_0[/math], but rather [math]v_0 = \sqrt{(x')^2+(y')^2}[/math]? Have I been reading this wrong the entire time?

Here's what I've gathered so far:

https://www.scribd.com/doc/292305422/Diff-Eqs

>>7700981
How is that even applicable? It's not an optimization problem.

>>7700540
Honestly, this is why I like using parenthesis very liberally. Some of that comes from my programmer habits, but fundamentally I do it to avoid any sort of ambiguity, Common Core or not.

Of course, the public doesn't generally realize the "implicit multiplication" issue, and so sees this image and thinks, "wut?"

I'm not looking for an analytic solution, and I really doubt that a meaningful one exists at all, but what I'd like to do is seperate out all the symbolic and functional components so I can have something numerically solvable.

Also, here's a table of variable dependencies I scribbled.

For clarification, [math]x[/math],[math]y[/math],[math]x_1[/math], and [math]y_1[/math] all depend on [math]t[/math], but [math]v_0[/math], [math]\vec{V}_0[/math], [math]\theta[/math], [math]\vec{n}[/math], and [math]a[/math] are all constants.

A colleague of mine scrawled out some equations on a whiteboard a few days ago. As far as I can tell, they are a set of cross-coupled, vector-valued, two-dimensional, first-order nonlinear differential-algebraic equations.

I don't know what context exactly they are from, but IIRC they have something to do with the intercept of ballistic trajectories.

I've tried pretty much every trick in the book to sort this out. They're not seperable, they don't match any well-studied nonlinear ODE, and none of the integral transforms are of any help.

Let's see if anyone has any ideas. Equations are spread across three pictures.

>>7689471
First and second laws of thermodynamics, and the Schwarzchild bound.

>>7689465
If it's a solution in water, you could determine the amount of water by dissolving a substance of known solubility in water, but insoluble in alcohol. Measure the amounts you put in and keep adding until the solution is saturated. Then work from there.

>>7683187
In summary:
You'd need a feedwater pump to force the liquid down (easily doable)
Drilling is enormously damn expensive, and piping that can withstand the pressures involved wouldn't be cheap either
Second law of thermodynamics says you have to get rid of waste heat (easily resolved, more or less)
In places where magma is relatively close to the surface, such as Iceland, this is effectively already done in the form of geothermal power

The Earth's heat is not solely residual, but it also is generated by radioactive fission in the mantle. Even if all the world's electricity demand were covered in this way, our sun would turn red giant before we could completely cool off the enormous thermal mass.

Any further questions?

>>7689457
Density?