Therefore, the integral is bounded, (exists) and an appropriate quadrature formula can be used. For a weight function of exp (-x2) with limits < x < <» , the Gauss- Hermite quadrature can be used. which can in form be written as: The weights and abscissas (for numerical solution) are readily available in reference texts. This procedure is to be performed over w/z and v/y spaces, the results from each space then multiplied so as to compute the total “collision” probability. Dynamic Collision Probability In the previous section only uncertainty in the static position was addressed. This section will attempt to address the collision probabilities of simple dynamic systems. As a first look, let's examine the interaction of probability theory and dynamics using the following simple system:
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