pool physics

i already solved the momentum and energy things, but the matter is the velocity vector after collision in 2D/3D coordinate.

in pool/billiard, the mass of the balls are the same (m1=m2=m). so to get the velocity after collision is by switching the velocity.

v1a = v2b

v2a = v1b

thanks,

synluba at 2007-7-9 18:53:00 >

My friend and I made this a while ago. Sorry for the lack of comments, it was mostly written very quickly after scribbling on lots of pieces of paper.

It calculates a perfectly elastic collision given a position, velocity vector, and mass.

/*

the all-knowing, all-seeing, do-everything bouncing ball function

give unto me the position of your balls, their masses, and their component vectors

and I shall bestow unto you their resultant vectors in an array of doubles

by abe and john, april 5 2002

*/

double[] calculateBounce( double x1, double y1, double m1, double dx1, double dy1,

double x2, double y2, double m2, double dx2, double dy2 )

{

// calculate a bunch of things

double angle = findAngle( x2 - x1, y1 - y2 ),

b1vector = findAngle( dx1, dy1 ),

b1mag = findDist( dx1, dy1 ),

b1parl = b1mag * Math.cos( b1vector - angle ),

b1perp = b1mag * Math.sin( b1vector - angle ),

b2vector = findAngle( dx2, dy2 ),

b2mag = findDist( dx2, dy2 ),

b2parl = b2mag * Math.cos( b2vector - angle ),

b2perp = b2mag * Math.sin( b2vector - angle ),

newb1parl = collision( b1parl, m1, b2parl, m2 ),

newb1vector = findAngle( newb1parl, b1perp ) + angle,

newb1mag = findDist( newb1parl, b1perp ),

newb2parl = collision( b2parl, m2, b1parl, m1 ),

newb2vector = findAngle( newb2parl, b2perp ) + angle,

newb2mag = findDist( newb2parl, b2perp ) ;

// return an array with the resultant vectors { dx1, dy1, dx2, dy2 }

return new double[] { newb1mag * Math.cos( newb1vector ), newb1mag * Math.sin( newb1vector ),

newb2mag * Math.cos( newb2vector ), newb2mag * Math.sin( newb2vector ) } ;

}

double collision( double v1, double m1, double v2, double m2 )// linear bouncing

{

return ( m1 - m2 ) / ( m1 + m2 ) * v1 + 2 * m2 * v2 / ( m1 + m2 ) ;

}

public double findDist( double x, double y )

{

return Math.sqrt( x * x + y * y ) ;

}

public double findAngle( double x, double y )

{

if( x == 0 && y >= 0 )

return Math.PI / 2 ;

if( x == 0 && y < 0 )

return 3 * Math.PI / 2 ;

double a = Math.atan( (double) y / x ) ;

if( x < 0 )

a += Math.PI ;

return a ;

}

danperkinsa at 2007-7-9 18:53:00 >