Re: OT: Looking for a good physics site
 

They're simultaneous equations - they give time (which can be later used for the x/y of the encounter), and acceleration on both axes when solved together.

Re: OT: Looking for a good physics site
 

(Position difference) = (speed diff) * T + (Accel Diff) * T * T

After time T, you want the position change due to Speed and Accel to be equal to the current position difference.

I think I missed a negative on the left side:
X1=0; X2=4
V1=0; V2=0
A1=2; A2=0
-(0-4) = 0-0 *T + (2 - 0) * T^2
4 = 2 T^2
T = sqrt(2)

Re: OT: Looking for a good physics site
 

(1/2) * A * T^2 + V * T + P = D

D - V * T + P = (1/2) * A * T^2

A = 5
T = 3
P = 50
V = 15
D = 117.5

117.5 - 15 * 3 + 50 = (1/2) * 5 * 3^2
117.5 + -45 + 50 = 2.5 * 9
72.5 + 50 = 22.5 // Ok, I know this isn't going to work...
122.5 != 22.5

D - V * T - P = (1/2) * A * T^2
72.5 - 50 = 22.5
22.5 = 22.5

Woot!

BBS

Re: OT: Looking for a good physics site
 

Could someone tell me why '1/2 * 5 * 3^2 - 117.5 + 50 = 45?' returned -45? Thanks. I can't see the error.

(1/2) * A * T^2 + V * T + P = D

A = 5
T = 3
P = 50
V = 15
D = 117.5

(1/2) * A * T^2 + V * T - D = P
(1/2) * 5 * 3^2 + 15 * 3 - 117.5 = 50?
2.5 * 9 + 45 - 117.5 = 50?
22.5 + 45 - 117.5 = 50? // Don't think so...
-50 != 50

Um...Where, exactly, did I make a mistake?

Re: OT: Looking for a good physics site
 

Brain fried; can't answer post fully at the moment.

That aspect, though...

It's 0 because it's a manipulation of two separate position functions that I want to be in the same place at the same time (definition of interception). They are both position functions, and I want them equal, so I assigned them that way, and tossed the same t in there: p1(t) = p2(t). I then expanded the functions to their components, and merged them onto one side (leaving the other side as 0).

Re: OT: Looking for a good physics site
 

Ok, thanks. That makes sense.

My sympathies on the fried brain.

Re: OT: Looking for a good physics site
 

It should probably be noted that constant acceleration is a basic premise of these formulae; to get a join-fleet, your acceleration will have to vary over time unless you are already in the same location (in which case, A1 = A2 for all time).

Re: OT: Looking for a good physics site
 

Yeah - they're the dumb-fire (accelerates in a straight line in whatever direction you pointed it - doesn't make decisions in-flight) missile targeting solution (goal: HIT THE TARGET HARD) for a target that isn't evading (e.g., another dumb-fire missile). If the target is evading, or you can track target mid-flight, you want something a little more organic (such as a simple "accelerate in direction of current target's location")

Re: OT: Looking for a good physics site
 

I was thinking I could probably get a matching intercpt by treating the targets' velocity and acceleration as 0, by adding them (Or perhaps subtracting them) from or to the enemies' velocity and acceleration.

Or something like that.

(1/2) * A * T^2 + V * T + P = D

A = 5
T = 3
P = 50
V = 15
D = 117.5

(1/2) * A / D^2 + V / D + P = T
1/2 * 5 / 117.5^2 + 15 / 117.5 + 50 = 3?
1/2 * 0.042 + 0.127 + 50 = 3?
0.021 + 0.127 + 50 = 3? // It was at this point that my suspicions became rather definite...
50.148 != 3

(1/2) * A * T^2 + V * T + P = D

(1/2) * A * D^2 + V * D + P = T
1/2 * 5 * 117.5^2 + 15 * 117.5 + 50 = 3?
2.5 * 13,806.25 + 1,762.5 + 50 = 3? // Yeah, didn't think so.
34,515.625 + 1,812.5 != 3
36,328.125 != 3 // Curiousity.

(1/2) * A * D^0.5 + V / D + P = T?
1/2 * 5 * 117.5^0.5 + 15 / 117.5 + 50 = 3?
2.5 * 10.84 + 0.128 + 50 = 3? // Erm, no...
77.228 != 3.

(1/2) * A * T^2 + V * T + P = D

(1/2) * A / D + V / D + P = T^2 + T
1/2 * 5 / 117.5 + 15 / 117.5 + 50 = 12?
1/2 * 0.043 + 0.128 + 50 = 12?
0.0215 + 0.128 + 50 = 12? // Er, no...
50.1495 != 12

Ok, my brain is frying...

Re: OT: Looking for a good physics site
 

(1/2) * A * T^2 + V * T + P = D

A = 5
T = 3
P = 50
V = 15
D = 117.5

T^2 + T = (1/2) * A + V + P?
3^2 + 3 = 1/2 * 5 + 15 + 50?
9 + 3 = 2.5 + 15 + 50? // Erm, no...
12 = 17.5 + 50?
12 != 67.5

T^2 * T = (1/2) * A + V + P?
3^2 * 3 = 1/2 * 5 + 15 + 50?
9 * 3 = 2.5 + 15 + 50? // Fiddle, fiddle...
27 = 17.5 + 50?
27 != 67.5

T^2 * T = (1/2) * A + V + P + D?
3^2 * 3 = 1/2 * 5 + 15 + 50 + 117.5?
9 * 3 = 2.5 + 15 + 50 + 117.5? // ...Lute?...
27 = 17.5 + 50 + 117.5?
27 != 67.5 + 117.5?

T^2 * T = ((1/2) * A + V) * 2 + P + D?
3^2 * 3 = (1/2 * 5 + 15) * 2 + 50 + 117.5?
9 * 3 = (2.5 + 15) * 2 + 50 + 117.5? // ...Mumble...
27 = 17.5 * 2 + 50 + 117.5?
27 = 35 + 50 + 117.5?
27 != 202.5

T = (((1/2) * A + V) * 2 + P + D) / ((1/2) * A + V + P)?
3 = ((1/2 * 5 + 15) * 2 + 50 + 117.5) / (1/2 * 5 + 15 + 50)?
3 = ((2.5 + 15) * 2 + 50 + 117.5?) / (2.5 + 15 + 50)?// ...Hmm...
3 = (17.5 * 2 + 50 + 117.5) / (17.5 + 50)?
3 = (35 + 50 + 117.5) / (17.5 + 50)?
3 = 202.5 / 67.5
3 = 3!

A = 8
T = 4
P = 35
V = 25
(1/2) * A * T^2 + V * T + P = D

1/2 * 8 * 4^2 + 25 * 4 + 35 = D
4 * 16 + 100 + 35 = D
64 + 135 = D
199 = D

A = 8
T = 4
P = 35
V = 25
D = 199

T = (((1/2) * A + V) * 2 + P + D) / ((1/2) * A + V + P)?
4 = ((1/2 * 8 + 25) * 2 + 35 + 199) / (1/2 * 8 + 25 + 35)?
4 = ((4 + 25) * 2 + 234) / (4 + 60)?
4 = (29 * 2 + 234) / 64?
4 = (58 + 234) / 64?
4 = 292 / 64?
4 != 4.5625 // Nope...Error check...Still nope. So close, yet so far.