Methods for deriving differential equations of arbitrary dynamic processes

Using only the notion of extremum and neglecting any laws of nature, we develop a method for the derivation of differential equations describing arbitrary processes for which we only know their dependence on some set of parameters. This provides the possibility of theoretically not only the equations but also the underlying physical laws. In particular, we have found quite a few earlier-unknown differential equations with properties that may have good prospects of being used in various fields of engineering and especially in aircraft flight dynamics. On the basis of the suggested extremal theory of dimensions, we also show that it becomes possible to find the form of an arbitrary unknown differential equation and define arbitrary processes and basic physical constants with the use of singular extremals and their envelopes.