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Nonlinear dynamical theory of the elastica. (English) Zbl 0589.73057
The objective of this paper is a rigorous study of the dynamical behaviour of an inextensible elastic rod described by a simple geometrically nonlinear planar director theory. Two types of boundary conditions have been considered. In both cases the applied concentrated load is potential (conservative). The main results obtained in the paper concern existence, uniqueness and stability in the sense of Lyapunov. However the bifurcation problem is omitted since it has been studied in the paper by the second author [Arch. Ration. Mech. Anal. 85, 311-354 (1984; Zbl 0545.73039)].
The paper reads well and constitutes a valuable contribution to the mathematical theory of dynamical behaviour of elastic rods.
Reviewer: J.J.Telega

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H55 Stability of dynamical problems in solid mechanics
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[2] DOI: 10.1137/1020069 · Zbl 0395.73039
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[4] DOI: 10.1007/BF00249969 · Zbl 0472.73036
[5] DOI: 10.1137/1.9781611970531
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[13] DOI: 10.2307/1971108 · Zbl 0432.35055
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