A bound for solutions of a fourth order dynamical system

Abstract

We consider the homogeneous linearised equation of yawing motion of a spinning projectile

$$\xi '' + {\rm A}(s) \xi ' + B(s) \xi = 0$$

where A and B are complex functions of the real independent variable s. It is shown that

$$\left| {\xi (s)} \right| < \operatorname{Re} ^{ - \tfrac{1}{2}\int_0^s {\left\{ {\mathbb{R}(A(\eta )) + v(\eta )} \right\}d\eta } } $$

where R is a positive constant and ν(s) is a real function of s.