Rotation of a body with two movable internal masses on a rough plane

Abstract

The two-dimensional motion of a system consisting of a hollow rigid body, resting on a rough plane, and two internal mobile point masses, capable of moving parallel to the longitudinal axis of symmetry of the body is considered. Friction in the contact area is modelled by a local Amonton–Coulomb law. A dynamically matched linear model is used to describe the normal stress distribution. The possibility of achieving rotation of the system by a certain relative motion of internal masses is investigated. Two control laws for the movable masses are considered: piecewise-linear and harmonic, for which the equations of motion are integrated numerically for different values of the parameters of the control laws. The features of the motion of the system for the chosen laws are analysed. It is established that, for a two-phase piecewise-linear control law, rotation of the system reaches a steady state. The parameters of the piecewise-linear control law, which deliver a maximum of the mean angular velocity of the body in the steady mode of motion are obtained.