Effects of rotation on the nonlinear friction of a damped dimer sliding on a periodic substrate

Abstract

Rotational effects on the nonlinear sliding friction of a damped dimer moving over a substrate are studied within a largely one-dimensional model. The model consists of two masses connected rigidly, internally damped, and sliding over a sinusoidal substrate potential while being free to rotate in the plane containing the masses and the direction of sliding. Numerical simulations of the dynamics performed by throwing the dimer with an initial center of mass velocity along the substrate direction show a richness of phenomena including the appearance of three separate regimes of motion. The orientation of the dimer performs tiny oscillations around values that are essentially constant in each regime. The constant orientations form an intricate pattern determined by the ratio of the dimer length to the substrate wavelength as well as by the initial orientations chosen. Corresponding evolution of the center of mass velocity consists, respectively, of regular oscillations in the first and the third regimes, but a power law decay in the second regime; the center of mass motion is effectively damped in this regime because of the coupling to the rotation. Depending on the initial orientation of the dimer, there is considerable variation in the overall behavior. For small initial angles to the vertical, an interesting formal connection can be established to earlier results known in the literature for a vibrating, rather than rotating, dimer. But for large angles, on which we focus in the present paper, quite different evolution occurs. Some of the numerical observations are explained successfully on the basis of approximate analytical arguments but others pose puzzling problems.