Qualitative properties of a model of coupled drilling oscillations

Abstract

The model of the axial and torsional vibrations for a drillstring with distributed parameters is obtained using the variational approach within the Hamiltonian Mechanics. Further there is considered the model of the axial vibrations which is a linear system with control and perturbation input signals. To the aforementioned equations of the model a system of equations with deviated argument is associated by integration along the characteristics. The system with deviated argument is of neutral type and allows construction of the basic theory but has its difference operator marginally (critically, not strongly) stable. This aspect is discussed finally and suggests the use of the methodology of the singular perturbations.