Exact analytical solution to inclined plane motion with constant resistance

Abstract

This study describes the entire block-sliding movement process from various aspects to reveal the law governing its movement on a slope. An analytical solution of the block motion on an inclined plane is provided based on the variable substitution for various friction coefficient values in this study. The block movement’s initial angle and equivalent friction coefficient are determined by describing its trajectory, kinetic energy change, movement duration, maximum horizontal displacement, and other indicators. The block movement’s initial angle affects its movement duration, whereas the equivalent friction coefficient indirectly represents the degree of influence of friction on the block movement. The influence of singular points on the sliding trajectory is considered under certain initial conditions. Finally, this study provides a calculation method for assessing the block motion state with given initial conditions, which offers a theoretical reference for the application of the block slope-sliding model in the engineering field.