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

Intro to bodies interactions The attraction between two bodies is given by F= g*m 1 *m 2 /r 2 Where F is force, g is the gravitational constant [aka fudge factor], ms are masses for bodies one and two and r is the distance between them.

r the distance between two bodies Using the Pythagorean theorem we can find the distance between two points x hypotenuse = r y a 2 + b 2 = c 2 Hence, x 2 + y 2 = r 2 Point 1 Point 2

Trigonometry review cos = x sin = y tan = y/x atan y/x = y x

mmm vectors…. 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. F x = (cos ) * F F y = (sin ) * F Mass 1 at center Mass 2 out there y x F

Put it all together Lets ignore m 2 [its very very very small], then F= g*m 1 *m 2 /r 2, becomes F = g*m/r 2 But, r 2 = x 2 + y 2, so F = g*m/(x 2 + y 2 ) But, F x = (cos )*F, so F x = (cos )*g*m/(x 2 + y 2 ) Similarly, F y = (sin )*g*m/(x 2 + y 2 )

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

Using atan y/x = Remember, F x = (cos )*g*m/(x 2 + y 2 ) And,F y = (sin )*g*m/(x 2 + y 2 ) So, F x = (cos [atan y/x])*g*m/(x 2 + y 2 ) And, F y = (sin [atan y/x])*g*m/(x 2 + y 2 )

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 V x = V x + F x V y = V y + F y 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.

Next step translate into code