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Applications of the Elementary Theory of Catastrophes in Aviation
Abstract
In this chapter, the author considers the connection between the mathematical theory of catastrophes and certain characteristics of the aviation system. The basis for this connection is the similarity of the concept of “catastrophe” in aviation and mathematics. With small perturbations of some systems, their state changes little. At small perturbations of other systems, a sharp transition occurs to another state. This transition is called a jump or a catastrophe. A catastrophe can also be called a loss of stability. Comparison of the notion of “stability” in aviation and mathematics is part of this study. The mathematical representation of the simplest aviation systems and their disasters is shown in elementary examples. It does not use a deep mathematical apparatus as well as special studies of aviation systems. The aim of the work is to direct the aviation specialist's eye to the mathematical theory of catastrophes, and to direct the mathematician's attention to the problems of aviation safety.
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