Page 75 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

58 SLENDER STRUCTURES AND AXIAL FLOW

origin in Figure 2.13. In the case of equation (2.167), the corresponding values would be
Iill = 1, Ixzl 2 4. As seen in Figure 2.14, however, whereas both exist about (*15,0),
only the smaller one does about (0, 0}, as already remarked.
The results presented here have all been obtained numerically, and hence one can see
not only the existence of fixed points and limit cycles, but also whether they are stable or
not. If fixed points and limit cycles are determined analytically, however, then one must
assess their stability separately; .this and other analytical aspects of nonlinear dynamics
are deferred to Chapter 5 and particularly to Appendix F.