Example of an Unsolvable Problem in Dynamics

Abstract

When looking back at the various chapters of this book we may note that even by a seemingly straightforward extension of a problem (e. g., from periodic to quasi-periodic motion) the solution of the new problem introduces qualitatively new difficulties. Here we want to demonstrate that seemingly simple questions exist in dynamic systems which cannot be answered even in principle. Let us consider a dynamic system whose states are described by state vectors q. Then the system may proceed from any given state to another one q’ via transformations, A, B, C within a time interval τ,

$$ q' = Aq,{\text{or }}q' = Bq, \ldots $$

((12.1))

.