# Simulating Coliding Springs - Is it possible without invoking conservation laws?

1. Feb 6, 2006

### cfp

Hi,

I am working on a simulation and I have a problem of similar nature to the following:

Consider a horizontal frictionless pipe containing two damped springs with the same diameter as the pipe. Suppose both of the springs are moving horizontally through the pipe, one faster than the other; so eventually they will collide.

Now imagine we're simulating this situation, and suppose step N is the first step in which the two spring interpenetrate.

Clearly the positions of the ends of the two springs have to be adjusted to remove the interpenetration.

I have a strong (non-justified) hunch that just taking the average of the end points, perhaps weighted by the springs masses would be accurate enough.

Furthermore, if I did this it seems at least like I'd get conservation of momentum and conservation of energy for free.

Can anyone tell me why this would be grossly inaccurate?

Thanks a lot,

Tom

2. Feb 6, 2006

### Meir Achuz

The spring constants and the length of the springs would also be needed.
If the paramenters (L,k,m) of the two springs ar different, you could be way off. It should not be too hard to write down the correct equations.

3. Feb 7, 2006

### cfp

For what I'm simulating getting analytic solutions isn't really feasible. There will be several thousand springs, many connected to each other, and all free to move in 2D space.

My thought was that given interpenetrating springs, there are three ways of correcting it:

1) You do what I originally suggested and just adjust the positions of the interpenetrating ends in a naive way (e.g. take their average).
2) You keep the centre of mass where it ended up, and bring in all end positions as much as is necessary to remove the interpenetration.
3) You keep the far ends fixed and adjust the interpenetrating ends to the positions they would converge to at infinity under these constraints.

Now 2) will result in the far ends of the spring being contracted as well, which is clearly wrong. In fact it is clearly wrong for the centre of mass to stay in the same place, if we were solving continuously the centre of mass would not have come as far as it did before the collision ocurred.

And 3) seems grossly wrong because in reality it would take the spring a long time to settle to the value we would be setting it too. Very different to a 1/60th of a second time step!

Can anyone illuminate this any further?

Thanks,

Tom