collision geometry (i.e., collision requirements are satisfied for this case), then the specific case (k) has an impact parameter ( 8k) set to one; else it is set to zero. The probability for collision for this case (k) can then be described as: where 0j refers to the position probability function, yi refers to the momentum probability function (also a function of position), and 8 is the impact parameter. The total probability of collision would then be the sum over all possible states: Though computational intensive, with distributed processing techniques and array processors the problem is conceptually manageable in the light of current technology. This prototype would allow flexible modeling for both the impact geometry (collision requirements definition) and statistical ensemble state probability assignment) for the position/momentum variables. Conclusions While the CRYSTAL procedure is neither elegant nor closed form, it can provide researchers with sufficient flexibility to choose from a variety of impact geometries and probability density models for the position/momentum vectors so as to estimate a probability of collision occurring. Further research (including actual data acquisition) will be a necessity to validate the selection of the position/momentum probability models, the dynamic models used for the propagation of position, and the impact definition models. [1] Uncertainty in position, spreading with time: See “Wave Packets”, pg 31 Quantum Physics, S. Gasiorowicz, John Wiley & Sons Inc, NY © 1974. [2] Probability and Statistics, Schaums Outline, Convolution Theorum for X] + X2. [3] Kaman Sciences Corp report “Fitting a Polynomial to a Circular Orbit,” Dr. J. Wayne Porter, 18 Mar 1993.
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