How to handle simultaneous particles collision in simulation?

[nsNas]

Suppose there are 3 balls colliding at the same time. I find that the order in which I resolve collisions makes a difference in the final result, which ofcourse makes no sense.

To explain and keep things simple, consider 3 balls in 1D, all same mass, elastic collision. The numbers at the top are the speeds and the arrows is the direction. Assume they are currently all touching each others, i.e. in collision

 -->2   -->1 <---3
   O     O       O
   A     B       C

This shows ball A hitting ball B from the back and ball B and C are colliding face on.

Now if we resolve collision A with B first, followed by resolving collision B with C, but using the new speed of B, this should give the same result if we instead have resolved collision of B with C, followed by resolving A with B (using the new speed of B).

But it does not.

first case: A with B, followed by B with C

A with B gives

 -->1   -->2
   O     O  
   A     B

and B with C gives (but using new B speed of 2 above, not the original speed of 1)

 <--3   -->2
   O     O  
   B     C

Hence the final result is

-->1   <--3  ---->2
   O     O       O
   A     B       C

second case: B with C, followed by A with B

B with C gives

 <--3   --->1
   O     O  
   B     C

A with B (but using new speed of B of 3 above, not original 1)

<--3    -->2
   O     O  
   A     B

Hence final result is

 <--3  -->2   ---->1
   O     O       O
   A     B       C

You can see the final state is different.

What Am I doing wrong? and more importantly, what is the correct method to handle this?

For simulation with many balls and also collision with walls, this case is very possible. (for example, ball hitting a wall and being hit by another ball at the same time, would give same problem as above, the order gives different results).

Currently I use a loop to iterate over all objects and resolve collisions between each 2 at a time. Hence the order I use is arbitrary (order is just the index of the ball in an array).

 

[Sourabh N]

You're on the right track, but the problem is, you have not worked it through. Let me show this for one of the cases.

first case: A with B, followed by B with C

A with B gives

 -->1   -->2
   O     O  
   A     B

and B with C gives (but using new B speed of 2 above, not the original speed of 1)

 <--3   -->2
   O     O  
   B     C

Hence the final result is

-->1   <--3  ---->2
   O     O       O
   A     B       C

Is that the final configuration? Can A really go to the right with speed 1 when B is going to the left with speed 3?

 

[nsNas]

Is that the final configuration? Can A really go to the right with speed 1 when B is going to the left with speed 3?

Of course not, but this will cause collision between A and B in the next time step.

What else do you suggest doing? In all collision detections I've seen, one goes over each particle at a time, resolves its collisions with all others, and then update the simulation one time step (i.e. move all particles using their new speeds), and repeat.

How else should one handle this otherwise?

 

[Sourabh N]

Of course not, but this will cause collision between A and B in the next time step.

What else do you suggest doing? In all collision detections I've seen, one goes over each particle at a time, resolves its collisions with all others, and then update the simulation one time step (i.e. move all particles using their new speeds), and repeat.

How else should one handle this otherwise?

I think this is the right way to handle it. But do the next time step! Your original question said your "final result" is different in the two cases. The final result is when ALL collisions that could happen, have happened.