OT: Looking for a good physics site

[narf poit chez BOOM]

...I'm missing something here. You're saying the positions must be equal, but at the same time they start unequal.

No... both will return zeros of the quadratic function (aka x-intercepts). I wasn't talking about the integer value 0. A negative zero/intercept is thrown out, as per previous post.
...I have no idea what you just said. I can't even decypher the grammer. For one thing, the only zero I've ever known is an integer, except for the fact that zero isn't actually all that numerical.

[Fyron]

...I'm missing something here. You're saying the positions must be equal, but at the same time they start unequal.

Huh? Unknown and unequal are not the same thing.

...I have no idea what you just said.

http://en.wikipedia.org/wiki/Zero_of_a_function

[narf poit chez BOOM]

I'm missing something. Probably something obvious. Are you saying the function backtracks from where the positions are equal to where they are at start?

Ok, so occasionally the formula will return zero.

Perhaps it would help if you looked at my code? It could help us figure out the difference between what I think I should be doing versus what I should actually be doing.

[Suicide Junkie]

The two final positions are variables, and unknown. But they are equal to each other by definition, since equal positions is the definition of interception.
Knowing that they are both equal reduces the number of unknowns by one (Instead of positionA and positionB, you have two copies of positionIntercept). This allows you to solve for Time. If the interception is impossible, Time will end up being an imaginary number.

[narf poit chez BOOM]

Ok, thanks, that makes sense.

One of the problems is that it tends to flicker between thinking it is unsolveable and having an intercept angle. (I have a bit of code that gives it an angle of '0' if it's unsolveable). That's one reason I posted the code.

You guys are great, you know that, right?

[Suicide Junkie]

That would happen when you are just barely able to intercept it.

One thing to note is that if you try to burn at 100% power up to halfway, and then decelerate at 100% power the rest of the way... then you have NO ACCEL left over to correct for rounding errors.

You should probably have the ship try to use 90% of its maximum accel, and try more thrust if that isn't enough...
If both ships are of equal accel, you've got to just head for it and hope the target isn't actively trying to avoid you.

[narf poit chez BOOM]

That's a good suggestion. And it would fit in with how engine sare generally operated - Few are run at 100% power.

[Fyron]

Ok, so occasionally the formula will return zero.

If one of the zeros/x-intercepts of the equation occurs at 0,0, then sure... The formula always returns two zeros/x-intercepts; that is the entire purpose of it.

[narf poit chez BOOM]

Oh, you mean it returns an intercept that is zero relative to the target.

Ok, so it should work. Now I just have to figure out why my implementation doesn't.

[Fyron]

Oh, you mean it returns an intercept that is zero relative to the target.

No, I don't mean that. I mean every quadratic function has 2 zeros/roots/x-intercepts. They are only a function of where the graph of the quadratic equation in question crosses the x axis. There will usually be two such locations, due to quadratic polynomial equations being parabolas and all (a parabola that has its vertex on the x axis will have both root solutions equal to each other).

The concept of zeros/roots/x-intercepts is unrelated to the problem of calculating where two ships should intercept each other in space. There is a lot of overlapping terminology, which is probably the root (hehehe) of the confusion. The zeros/roots/x-intercepts of the particular function we derived happen to be the time values (T) when the two objects will be in the same location at once, which is why they are useful for the solution.