Dynamics of a rope modeled as a discrete system with extensible members

Abstract

A discrete model of a rope with extensible members, involving a simple spring-mass conception, is considered. Lagrange's equations of motion are presented and their complexity is discussed from the computational point of view. Numerical experiments are performed for a system with both scleronomic and rheonomic constraints. Simulated behaviour of the model is analyzed mostly in terms of consequences of the extensible character of the system. Results validity is examined with use of basic energy principles.

Application of the rigid finite element method to modelling ropes

“…Consider motion of the rope which is initially deflected aside, which means that the deflection angle is equal for all the rigid elements: For purposes of the comparative analysis, a combination of the models described in [2,3] has been used. This system can be regarded as a multiple physical pendulum (MPP) with some additional features.…”

Dynamics of a rope modeled as a multi-body system with elastic joints

“…However, a key idea of MEBDF is to include the so called 'superfuture' value x i+1 in the same computation step. We included an outline of the method in [8]; more details are described in papers of Cash [10,11,14]. Now let us turn to numerical experiments.…”

“…This approach has led to an expanded set of differential equations, and, more importantly, the simulated behaviour was found to become disordered, chaoticlooking and therefore quite far from the intuitive view on the rope dynamics. In [8] we modified the simple model to include longitudinal elasticity. Now, we focus on transverse elasticity of the rope.…”

Application of the MEBDFV solver to dynamic simulation of some specific multibody systems: an example of a cervical spine model

“…The typical examples are conventional and inverted multiple pendula which over the last few decades have been the subject of theoretical and experimental studies mainly from the viewpoint of nonlinear dynamics and control theory (see e.g. [3][4][5][6][7][8][9][10]). In general, multibody systems with a chain topology are especially likely to be modelled via the standard Lagrangian formulation.…”