The transient dynamics of a cable-mass system due to the motion of an attached accelerating mass

The objective of this paper is an analytical and numerical study of the transient vibrations of a taut inclined cable with a riding accelerating mass that is suspended in space. The moving mass is accelerated by a thrust down the inclined cable and is able to be aerodynamically brought to a halt. The thrust is a follow force that is tangential to the deformed con®guration of the cable. The cable is suspended from two points of di€erent elevation. The higher point of the cable is anchored to the ground, and the lower point of the cable is controlled so that its tension at that point is held at a constant level. Hence, the length of the cable is not ®xed and is a parameter to be determined during any run. The restriction in which an inextensible cannot vibrate in the limit of vanishing sag then is removed. The mechanics of the problem is Newtonian. Methods of analysis will consist of the dynamics of small deformations superimposed on the static catenary state. The problem is nonlinear due to the presence of friction and the convective acceleration interaction of the moving mass and the cable. Galerkinʹs procedure for removal of spatial dependence and numerical integration are used to obtain convergent solutions.