this is my first question on the forum and my algebra is rusty so please be indulgent ^^'
I want to predict collision between two uniform circular motion objects for which i know velocity (angular speed in radian), distance from the origin (radius), cartesian coordinate of the center of the circle.
I can get Cartesian position for each object given for t time (timestamp) using :
Oa.x = ra X cos(wa X t)
Oa.y = ra X sin(wa X t)
Oa.x: Object A x coordinates
ra: radius of a Circle A
wa: velocity of object A (angular speed in radian)
t: time (timestamp)
Same goes for object b (Ob)
I want to find t such that ||Ca - Cb|| = (rOa + rOb)
rOa: radius of object a
Squaring both side and expanding give me this :
||Ca-Cb||^2 = (rOa+rOb)^2
(ra * cos (wa * t) - rb / cos (wb * t))^2 + (ra * sin (wa * t) - rb / sin (wb * t))^2 = (ra+rb)^2
From that i should get a quadratic polynomial that i can solve for t, but how can i find a condition that tell me if such a t exist ? And possibly, how to solve it for t ?