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# 2D bowling pin collisions

by Andrew Kickertz — last modified Nov 08, 2011 11:40 AM

I started thinking more about collisions of bowling pins a couple weeks ago, and I've come up with something that I think is pretty cool.  It is a 2D frictionless simulation of 1 ball and 10 pins operating primarily on the following equations:

$$\nu_0 = (V_0 - V_0')\cdot\hat{n}$$

$$V_f = V_0 - m\nu_0 / M (1+e)$$

$$V_f' = V_0' + m\nu_0 / M' (1+e)$$

where $$\nu_0$$ is the normal component of the incident velocity, $$V_0$$ and $$V_0'$$ are the initial velocities of the 2 bodies, $$M$$ and $$M'$$ are the masses, and $$m$$ is the effective mass.  Note that these equations must be performed in a coordinate system spanned by vectors tangent and normal to the both bodies at the contact point.  These formulas come from Stronge's (2000) book, Impact Mechanics.

Check out the videos:

### Props

Posted by Jason Moore at Nov 08, 2011 01:45 PM
Nice work, and cool animations!

How can it be frictionless if the pins slow down. Is it just that the contact between balls and pins is frictionless? Or between the ground?

### Re Props

Posted by Andrew Kickertz at Nov 14, 2011 11:55 AM
Thanks. I don't know what happened to my previous reply, but the short story is that the bodies only slow down during collisions. There is no friction between bodies or between bodies and the lane - not yet.

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