Movement of a material particle on an inclined plane all the points of which describe circles in oscillatory motion in the same plane

Abstract

Differential equations of material particle movement on an inclined rough plane, which performs oscillatory motion in such a way that its every point describes a circle in the same plane, have been deduced. Peculiarities of relative particle movement on a plane depending on the angle of its inclination to the horizon have been investigated. The equations have been solved using numerical methods. Relative velocities have been found and particle motion trajectories have been constructed. Kinematic characteristics of relative particle movement depending on the angle of plane inclination, angular velocity, the coefficient of particle friction on a plane and the radius of circular motion of plane points have been determined.