The vibrating string and rod free to slide, at both end points, on a vertical guide

Some algebraic properties of the matrices involved in a discrete linear mod el simulating the transversal motion of a linear vibrating string, or rod, with both end points free to slide on vertical guides, are studied. The dis crete linear model, which is conservative, turns out to be, according to th e physics of the problem, generally unstable. Nevertheless, it is proved Ch at the linear models are suitable to simulate the motion of the linear stri ng and rod. An extension of the model to the nonlinear string is also consi dered and some numerical examples are given. Also, in this case, the numeri cal results seem to be in accordance with the physics of the problem. (C) 2 000 Elsevier Science Ltd. All rights reserved.