The equation of motion of a chain

Chain paradoxes

“…Below in this section, the reader will be introduced to these problems collectively, also indulging in some historical notes on the supposedly paradoxical aspects that they have shown since the work of Buquoy nearly two centuries ago. 8 Before doing so, however, we need to supplement the theory by showing that the choice for the shock dissipation D in (2.27) is the most appropriate for chains.…”

Un modèle relaxé pour les câbles inextensibles

“…Je remercie Y. Colin de Verdière pour avoir attiré mon attention sur la question de Finextensibilité d'un câble, et M. Schatzman qui m'a indiqué l'existence d'un travail de M. Reeken sur ce sujet [7,8] Nous montrons ici qu'un angle (kink) du câble est une déformation qui ne dissipe pas d'énergie, en considérant que l'inextensibilité est la limite du cas inextensible raide. Ceci contredit une supposition de [8], mais surtout permet de lever l'ambiguïté sur la détermination du mouvement en présence d'angles.…”

“…Ceci contredit une supposition de [8], mais surtout permet de lever l'ambiguïté sur la détermination du mouvement en présence d'angles. C'est ainsi que le problème du fouet (exemples 4.b de [8]) est complètement résolu, de même que celui du cercle.…”

Generalized solutions for inextensible string equations

“…[4]) to be the one for which the stretch is constrained to be equal to 1, whatever system of forces is applied to it. As in [23], some authors refer to it as a chain which is a long but very thin material that is inextensible but completely flexible, and hence mathematically described as a rectifiable curve of fixed length. Dynamics of pipes, flagella, chains, or ribbons of rhythmic gymnastics, mechanism of whips, and galactic motion are only a few phenomena and applications that can be related to inextensible strings (see [6,14,12] for more details).…”

“…Even though the analysis of the dynamics of inextensible strings subject to different kinds of boundary conditions is a notable problem which goes back to Galileo, Leibniz and Bernoulli (cf. [23,4,19]), and it has been investigated by many authors in various contexts (see e.g. [6,15,14,26,31]), there are still very few results about general wellposedness.…”