Dynamics properties and control for oilwell drillstrings

It is considered the model with distributed parameters of the torsional vibrations for the drilling system. The basic model is obtained by using the generalized variational principle of Hamilton and it is completed by adding the dynamics of the driving motor in two cases: a d.c. motor and an induction motor. For this setup there is considered the steady state with constant rotating speed, the system in deviations and its stabilization using an energy like control Liapunov functional suggested by the energy identity which is specific to partial differential equations. The paper contains also comments on mathematical issues connected with the basics of the approach and suggestions for future research.