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Write a system that will simulate a single shot of a billiards game.

¤ Simplifying assumptions ¤ All balls have the same mass ¤ In reality the cue is heavier than the rest. ¤ Balls will always remain in contact with the table ¤ Ignore vertical motion of balls ¤ Collisions between balls will be totally elastic ¤ All momentum is conserved

¤Describes position of balls and initial forces ¤ All values will be given in common units. ¤ R G B x y z

  ¤ (R, G, B) is color of the ball
  ¤ (x,y,z) is position of ball

¤ 1st ball is assumed to be the cue ball (the ball to which force is to be applied) ¤ Describes position of balls and initial forces ¤ Initial impact ¤ X Y Z x y z ¤ (X, Y, Z) = linear momentum to apply to cue ¤ (x,y,z) = initial rotational momentum ¤ = vector gives axis of rotation ¤ = magnitude gives angle ¤ Describes position of balls and initial forces ¤ Friction coeffients ¤ us ur e

 us = friction constant (sliding)  ur = friction constant (rolling)  e = Coefficient of restitution (for cushion collisions) 

¤ Only consider translational motion ¤ Only consider translational effects of friction. ¤ Use Euler integration

¤ Add pockets (5 points) ¤Consider rotational motion (15 points) ¤ Account for rotation resultant from friction (5 points) ¤ Rotational momentum transfer due to collisions (10 points) ¤Implement Runge-Kutta Integration ¤ 2nd order / midpoint (5 points) ¤ 4th order (5 points)

High Restitution shot with Pockets implemented:

High Restitution shot without Pockets implemented: