On modeling and simulation of tethered systems with sharp, rough contacts

We extend the analysis of a reeled, tethered system in a constant gravitational field by (i) proposing a differential–algebraic representation when the tether is inextensible and (ii) examining the interaction between the tether and a sharp, fixed guide when contact is rough. The governing equations are derived using an approach that clearly illustrates how singular supplies of linear momentum, such as friction at the fixed guide, feature in the equations of motion. After semidiscretization via finite differences, we formulate the system of differential equations and algebraic constraints as a differential–algebraic equation and solve for various motions of the reeled tether. In addition, we show that, by comparison to a rounded contact analysis with arbitrarily small radius, the reaction force acting on the tether at the guide does not converge to the value of this force when the guide is modeled as a sharp point of contact.