Static equations for thin inextensible elastic rods, or elastica as they are sometimes called, have been studied since before the time of Euler. In this paper, we examine how to model the dynamic behavior of elastica. We present a fairly high speed, robust numerical scheme that uses (i) a space discretization that uses cubic splines, and (ii) a time discretization that preserves a discrete vers...

In this article we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cy...

We consider a cantilever beam which possesses possibly non-uniform permanent magnetization, and whose shape is controlled by an applied magnetic field. model the as plane elastic curve we suppose that field acts upon means of distributed couple pulls magnetization towards its direction. Given list target shapes, look for design profile controls such shapes assumed when acted are close possible ...