Motion of a Particle on an Inclined Plane Rotating Around a Vertical Axis

The relative motion of a particle along an inclined plane in a moving coordinate system is considered. The moving system is an accompanying Frenet trihedron that circles along a plane curve, i.e., revolves around a vertical axis. The Frenet formulas are used to derive a system of differential equations of relative motion of the particle. Unlike the traditional approach, the independent variable is not time, but the arc length of the directing curve along which the trihedron moves. The system of equations is written in terms of projections onto the unit vectors of the moving trihedron. It is solved numerically. The trajectories of a particle sliding along the inclined plane and graphs of other kinematic characteristics are plotted.