On Kinetics of a Dynamically Unbalanced Rotator with Sliding Friction in Supports

摘要

The dynamics is analytically and numerically modelled for both free and forced rotations of a rigid body around the central but non-principal vertical axis Oz under action of dry friction forces in plain bearings and heel supports in combination with other dissipative and conservative axial torques. The inertia forces due to D'Alembert principle cause the supports' reactions and hence the decelerating friction torque depending on not only angular speed but acceleration too. This dependence makes the dynamical equations not resolved with regard to the senior derivative and ambiguous, and being thus resolved they have an irrational or singular right hand side. This irrationality/singularity results in their featured solutions or paradoxical absence of those in frames of absolutely rigid body approach. The kinetics obtained is analyzed and compared with the standard ones of rotation under action of conservative elastic and drag torques.