Code examples

2. Code examples • Mechanics: random balls • Biology/evolution: flocking • Game of tag

3. Intro to bodies interactions • The attraction between two bodies is given by F= g*m1*m2/r2 • Where F is force, g is the gravitational “constant” [aka fudge factor], m’s are masses for bodies one and two and r is the distance between them.

4. r the distance between two bodies Point 2 • Using the Pythagorean theorem we can find the distance between two points hypotenuse = r y x Point 1 a2 + b2 = c2 Hence, x2 + y2 = r2

5. Trigonometry review y • cos = x • sin  = y • tan  = y/x • atan y/x =   x

6. mmm vectors…. y Mass 2 ‘out there’ • We need to separate the x and y directions of the force. •  is the angle • So F, the force arrow has an x and y part. • Fx = (cos ) * F • Fy = (sin ) * F F  x Mass 1 at ‘center’

7. Put it all together Lets ignore m2 [its very very very small], then F= g*m1*m2/r2, becomes F = g*m/r2 But, r2 = x2 + y2, so F = g*m/(x2 + y2) But, Fx = (cos )*F, so Fx = (cos )*g*m/(x2 + y2) Similarly, Fy = (sin )*g*m/(x2 + y2)

8. How does the computer know what's what? y • x is x and y is y • But the computer does not know what  is. • atan y/x =   x

9. Using atan y/x =  Remember, Fx = (cos )*g*m/(x2 + y2) And, Fy = (sin )*g*m/(x2 + y2) So, Fx = (cos [atan y/x])*g*m/(x2 + y2) And, Fy = (sin [atan y/x])*g*m/(x2 + y2)

10. What does force do? • If you hit a tether ball then you are the force and the ball then has a velocity as it flies through the air. • Hence we need velocity terms for our bodies: V • Vx = Vx + Fx • Vy = Vy + Fy • The velocity gets added to it self just like with a tether ball: the new velocity adds its old velocity to the new force of hitting it again.

11. Next step translate into code