>Dale Blackwell wrote:
>
>> Is anyone familiar with the math associated with the rebound trajectory of
>> two balls colliding on a two dimensional surface?
>>
>> I remember that when a ball collides with any line it rebounds (or is
>> reflected) at an angle equal to that which it approached the line.
>>
>> If two balls have collided with each other it is possible to construct a
>> perpendicular thru the line that connects their centers.  Is it this line
>> which determines the angles of incidence and reflection of the two balls?
>
>No--that line is _one_ of the factors that affect the angles, but the angles
>are also affected by the masses and the initial velocity vectors of the two
>balls.  (The angles are also affected by whether there are any energy losses
>during the collision, and whether any energy gets converted between
>translational and rotational modes (i.e., the effects of spin), but you can
>often get a pretty good simulation even ignoring those effects.)
>
>If you assume perfectly elastic collisions (no energy loss), and assume no
>spin effects, then you can work out the final velocity vectors by appealing to
>the laws of conservation of energy and conservation of momentum.  Say m1 and
>m2 are the masses of the balls, s1i and s2i are their initial speeds, and s1f
>and s2f are their final speeds.  Conservation of energy says:
>
>m1*(s1i^2) + m2*(s2i^2) = m1*(s1f^2) + m2*(s2f^2)
>
>Also, say v1i and v2i are the balls' initial velocity _vectors_, and v1f and
>v2f are their final velocity vectors.  (I distinguish between "s" and "v"
>because the math for vectors is different from the math for non-vectors.)
>Conservation of momentum says:
>
>m1*v1i + m2*v2i = m1*v1f + m2*v2f
>
>If you know how to do vector math, you can combine these equations to find the
>speed & direction of each ball after the collision.  I did this once (a long
>time ago) for a billiards simulation, but I don't have my final derived
>equations handy.
>
>- Rick
>
Thank you Rick,

The application I am working toward will not require the sophistication of
your equations.  I am assuming no energy loss or spin effects.  I very much
appreciate your reponse and will certainly tap your expertise if my
requirements escalate to that level.

Again, many thanks.

Dale Blackwell


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