Generalized solutions of the pursuit problem in three-dimensional Euclidean space

摘要

A more rigorous formulation of the pursuit in E3 is presented. The classical solution is extended, and we then proceed to formulate a new method of solution defined as the intercept approach. This new technique involves the specification of an arbitrary `escape function' having real zeroes. The method has been used to model the path of a dog in pursuit of a fish in a newly developed computer game – FISHER. A simple numerical problem is solved to illustrate the ease of use of the new approach over the classical method.