Stability Analysis of a Yawing Flat Plate Into the Water Current

The present study deals with the stability analysis of an oscillating flat plate into the water current. The flat plate, which is attached to a torsion spring and located vertically in the water current, has only 1 DOF that is yawing motion. The experiments have shown that as the current velocity exceeds a special threshold, the flat plate becomes unstable and begins to oscillate. This oscillation can be utilized to extract energy. A free vibration experimental technique is used in this study. The experimental results are analyzed using the flutter derivative theory, in which the flutter derivatives of the motion are extracted using GLS (General Least-Square) method. The results confirm that the flat plate becomes dynamically unstable. Also, there is a Liapunov stable fixed point on the origin at the phase portrait of the yawing motion.

Liapunov stability and adding machines

Let X be a locally connected locally compact metric space and f: X → X a continuous map. Let A be a compact transitive set under f. If A is asymptotically stable, then it has finitely many connected components, which are cyclically permuted. If it is Liapunov stable, then A may have infinitely many connected components. Our main result states that these form a Cantor set on which f is topologically conjugate to an adding machine. A number of consequences are derived, including a complete classification of compact transitive sets for continuous maps of the interval and the Liapunov instability of the invariant Cantor set of Denjoy maps of the circle.

Transformation groups of strong characteristic 0

It is shown that a transformation group (X, T, Π) is of strong characteristic 0 if and only if it is of P-strong characteristic 0 for some replete semigroup P in the phase group, provided that all orbit closures are compact. It is shown also that, under certain conditions, (X, T, Π) is of P-strong characteristic 0 if and only if (X × X, T, Π × Π) is Liapunov stable.