✦ LIBER ✦

Dynamical shape control and the stabilization of non-linear thin rods

✍ Scribed by J. Sokolowski; J. Sprekels

Publisher: John Wiley and Sons
Year: 1991
Tongue: English
Weight: 579 KB
Volume: 14
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670140104

No coin nor oath required. For personal study only.

✦ Synopsis

Communicated by B. Brosowski

In this paper we consider the problem of stabilizing the motion of the tip of a thin rod by controlling the shape of the rod, that is its length, dynamically. Well-posedness of the associated state equations, valid on a moving domain, is proved, and the necessary conditions of optimality for the control problem are derived.

The theory applies to materials where the stress-strain relation is both non-linear and non-monotone, so that hysteresis effects arising from solid-solid phase transitions in the rod are included.

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