Originally Posted by

**spammanon** Since you don't express a force of attraction in your equations, the balls will only collide if your constants have specific values. I wrote this in Matlab and couldn't get the balls to collide except when:

rpx=rpy

rvx=rvy

rax=ray

Substituting this into your equation means you are choosing your coordinate axis so that the x coord is along the distance between the balls. Then your equation is solvable.

After experimenting further I have found other values that lead to solutions, but not just any value of the constants will give solutions. It seems to me something is wrong with your assumptions, because if there is no force acting to attract the balls, they need not always collide.

I used your equation and entered values of t from 0 to 50 , then plot to see about where it crosses the axis. Only for certain combinations of values will the function cross the axis.

For example:

>> r1 = 1; r2 = 2; rPx = 40; rPy = 41; rVx = 3; rVy = 4; rAx = 5; rAy = 5;

>> f=@(t)(rPx+(rVx*t)+(rAx*0.5*t.^2)).^2+(rPy+(rVy*t) +(rAy*0.5*t.^2)).^2-(r1+r2)^2;

>> plot([-50:.001:50],f([-50:.001:50]))