Dynamic Instability of Certain Conservative and Non-Conservative Systems

This paper is concerned primarily with the analysis and resolution of the problems and contradictions that arise in the classification as conservative or non-conservative of a certain type of dynamical system. The systems concerned have equations of motion of gyroscopic type when the deflections are expressed with reference to particular co-ordinate axes, and they exhibit dynamic instability. Three examples are considered which possess their own special characteristics and subtleties; these are the rotating flexible asymmetric shaft, the helicopter ground resonance system and the clamped clamped flexible tube conveying fluid. For each of these cases, the energy input mechanism is examined and the problems of classification resolved.