![]() Here's figure 2 of Tichler et al's paper. I think you'll agree it's quite close to the billiard break. In this paper they study the propagation of shocks through interfaces between packings of billiard balls of two different masses. The derivation of the above equation is apparently in Nesterenko's book "Dynamics of Heterogeneous Materials", though I learned it from this very relevant paper coauthored by some friends of mine: Transmission and reflection of strongly nonlinear solitary waves at granular interfaces, byĪ. It might be interesting to compare the solutions of this equation with suitable boundary conditions to simulations along the line of Jim Belk's for a very large pool ball rack (large enough at least so that one can follow the shock wave for an appreciable length of time). I think the paper I cite below may give you some idea of what can happen as we vary the initial angle. Great prices and discounts on the best products with free shipping and free returns on. Also, none of the above discussion really depends on the "perfectly centered" initial condition. Shop a wide selection of Billiards & Pool Ball Racks at. ![]() (If one wants to study shock waves in systems of particles interacting with other force laws, then some of the exponents here change). ![]() The force between two balls is given by the formulaį \ =\ \begin)\right]$.The cue ball has a initial speed of 10 units/sec.The Sardo M-5000 is the Official Rack of the 2005 through 2007 International Pool Tour and will be used in all IPT events. Then, place the 8-ball in the center of the rack. Each ball has a mass of 1 unit and a radius of 1 unit. No pictures are available from the manufacturer yet but here is the description of the new rack: Lou Sardo Products is proud to announce the Sardo M-5000 rack is now available. To rack a pool table, first place the 1-ball at the front of the rack. ![]() All balls are assumed to be perfectly elastic and almost perfectly rigid.This break was computed in Mathematica using a numerical differential equations model. Here is a copy of my answer for it there. This question was cross-posted on Math Stack Exchange. ![]()
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