OT: Looking for a good physics site

[narf poit chez BOOM]

I'm trying to code intercept calculations for two spaceships, both capable of velocity, acceleration and different positions.

I don't want hints. I have been working on this code off and on for months. I don't care about figuring it out myself. I just want to know how to code it.

Many explicitives were deleted in the making of this post.

[Suicide Junkie]

Is the target ship going to have a constant acceleration, or will it actively evade?

[narf poit chez BOOM]

I'm just looking for straight-line acceleration right now. More complex stuff can wait.

Thanks for any and all help.

[narf poit chez BOOM]

Also, I just want the enemy ship to hit the target ship - Missile interception. I can probably manage to work out how to match velocities from that.

[Suicide Junkie]

Wasn't that where you were having all the problems before?
Reversing thrust at half way causing all kinds of grief?

[narf poit chez BOOM]

I've gone through a number of calculations. None of them worked completely. The closest I got was an angle calculation that works for velocity only.

I have never gotten any kind of interception that works perfectly for velocity, acceleration and position, either missile interception or matching interception.

And by 'perfectly', I mean, 'Intercepts, in a straight line, a target moving in a straight line'.

[douglas]

I'll see if I can work out the math for a least-time position only intercept, assuming the target has constant acceleration and the only variable is what direction the missile accelerates in.

[narf poit chez BOOM]

Well, they also start at different positions.

Thanks, wether you manage it or not.

[Jack Simth]

That's not physics, that's math (mind you, Physics IS math, but nowhere are you actually needing to deal with things like, oh, gravity - you're just looking at acceleration).

A position under constant acceleration vs. time for a given axis has an equation that can be formatted as:

P(T)=(1/2)A(T^2)+VT+S

P(T): Position at time T (the function)
T: Time (the only variable)
A: Acceleration (a constant for this exercise)
V: Initial Velocity (at T = 0; a constant)
S: Starting position (P(0); a constant)

You're looking to calculate an intercept - well, you've got a lot to worry about, but basically, you're looking for a way to get two different position functions at the same point at the same time:

So basically, you have P1(T) = P2(T), and want T and A (do I need to reword that?).

As each object has a different starting position (otherwise, T=0 always works; this is the definition of interception), Acceleration, and initial velocity are likely to be different; you're looking to solve:

(1/2)A(T^2)+V T+S = (1/2)A(T^2)+V T+S

Do note that your intercepting ship can potentially control it's acceleration. Well, let's start manipulating:

(1/2)A(T^2)+V T+S = (1/2)A(T^2)+V T+S

(1/2)(A - A)(T^2)+(V - V)T+(S- S) = 0

Oh, hey - we now have a quadratic equation; sub (1/2)(A - A) with a, (V - V) with b, and (S- S) with c, and T with x. The Quadratic formula will do the job:

x = (-b +/- sqrt(b^2 - 4ac))/(2a)

Note: a is a variable, as the interceptor will need to choose it. You've got a variable on both sides - but that's okay, as you'll want at least two dimensions, and you've got a separate equation for each dimension; you'll end up with a system of equations (one for each dimension) and some relationship between the a on the various axes (usually the Pythagorean therom).

Edit:
That is, of course, assuming you don't want to stop at the end, other than ramming the target....

[narf poit chez BOOM]

Tankee! Tankee very much!

...But, um, if the enemy acceleration needs to be chosen to use the formula and the formula tells it in which direction to accelerate and thus, how much to accelerate...

...Isn't that a closed loop?

/me goes off to see what happens if /me uses that by inputing '0' for the enemy acceleration.

...Uh, the first one is the pursuer, right?

...'+/-'?