Searching for unknown motion laws based on the extremal theory of dimensions1

A technique is developed to search for differential equations that describe any dynamic processes for which only their dependence on some parameters is known. A set of new differential equations are found; they posses interesting properties and are promising to be used in various branches of engineering, especially in flight dynamics. The extremal theory of dimensions was used and was shown to allow finding the form of differential equations for any complex dynamic processes and determining physical laws for them.