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March 1st, 2008, 05:56 PM  #1 
Newbie Joined: Mar 2008 Posts: 1 Thanks: 0  I have a trig/calculus/geometry problem here...
I am making a pool (billiards) simulation program and am having some problems... I need to reverse engineer a relatively simple formula. Imagine two spheres on a plane, a White sphere and a Black one. The Black sphere always begins stationary. The White one always begins traveling exactly along the X axis to the right. The exact speed of travel is irrelevant to this problem. Eventually the balls collide. A portion of the momentum of the white ball is transferred to the black one. This results in each ball proceeding off at a particular angle after impact. I know how to calculate these angles platonicly (in the ideal sense) However the formula that I am trying to reverse engineer, applies some kind of "fudge". This is to say, that the momentum is transferred imperfectly in some way. Particularly, you would expect the balls to depart each other at a right angle after impact. However, I find that the angle they depart from one another at is less and less the closer and closer they get to a direct collision. The more "oblique" the angle of impact, the closer the departing angle is to 90 degrees. I need to be able predict the resulting angle of each ball. What formula can I use that will mimic the following data as closely as possible? Start = X,Y coordinate of ball. TRAV = A portion of their travel AFTER impact. TRAV IS NOT THE TOTAL DISTANCE TRAVELED AFTER IMPACT. IT IS ONLY USED TO DETERMINE THE ANGLE Angle = The angle of travel after impact (in radians) White Start 129,130 Black Start 174,147 TRAV WHITE 182,126 462,40 Diff=280,86 Angle=0.29799 TRAV BLACK 175,151 203,231 Diff=28,80 Angle= 1.23412 White Start 129,130 Black Start 184,146 TRAV WHITE 192,123 370,40 Diff=178,83 Angle=0.43631 TRAV BLACK 188,154 230,234 Diff=42,80 Angle= 1.0873 White Start 129,130 Black Start 174,144 TRAV WHITE 175,121 287,38 Diff=112,83 Angle=0.63776 TRAV BLACK 182,153 250,235 Diff=68,82 Angle= 0.87846 White Start 129,130 Black Start 184,141 TRAV WHITE 175,124 259,38 Diff=84,86 Angle=0.7971 TRAV BLACK 192,147 302,234 Diff=110,87 Angle= 0.66917 White Start 129,130 Black Start 184,138 TRAV WHITE 171,125 234,37 Diff=63,88 Angle=0.94947 TRAV BLACK 196,144 378,234 Diff=182,90 Angle= 0.45924 White Start 129,130 Black Start 184,135 TRAV WHITE 168,126 212,54 Diff=44,72 Angle=1.03242 TRAV BLACK 199,139 461,217 Diff=262,78 Angle= 0.28935 White Start 129,130 Black Start 184,132 TRAV WHITE 167,128 207,75 Diff=40,53 Angle=0.92428 TRAV BLACK 200,134 378,158 Diff=178,24 Angle= 0.13402 

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