Dynamics of a Nonsmooth Supercavitating Vehicle System

As a representative example of a C continuous system, a four-dimensional model of the dive-plane dynamics of the supercavitating body shown in Figure 1 is considered. This model includes a dominant, nonsmooth nonlinearity associated with the planing force [1,2]. The original non-smooth system is approximated by a smooth counterpart, and it is examined as to how well the smooth system captures the dynamics of the original system. It is shown that the dynamics of the smooth system does not capture all of the bifurcations observed in the nonsmooth system. The tail-slap phenomenon, which is associated with the tail of the vehicle moving in and out of the cavity, is also examined and the possibility of occurrence of this phenomenon due to Hopf and grazing bifurcations is also studied. Control possibilities to delay the onset of tail slap or trigger tail slap are also examined, and they will be discussed at the meeting. Figure 1: A supercavitating body with an envelope enclosing it. REFERENCES[1] Dzielski, J. and Kurdila, A., “A Benchmark Control Problem for SupercavitatingVehicles and an Initial Investigation of Solutions,” Journal of Vibration and Control,Vol. 9, pp. 791—804 (2003).[2] Lin, G., Balachandran, B., and Abed, E., “Dynamics and Control of SupercavitatingBodies,” in Proceedings of ASME IMECE2004, Anaheim, CA (2004).