Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular frequency and in the general spin‐case

Abstract

AbstractIf a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper.In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II.Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as—if the equations are viewed as a three‐dimensional dynamical system—the unique stable equilibrium, which depends on the spin. This equilibrium turns out to be globally attractive, which can be proved by the construction of a suitable Ljapunov function. Then, the ball flight system can be transformed into a fourth‐order scalar differential equation.