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**Spatially complex equilibria of buckled rods.**
*(English)*
Zbl 0655.73029

The authors explore in a very innovative way the well known Kirchhoff analogy of the mathematical structure of the equations of a rod loaded at its end and the equations of a heavy rigid body pivoted at a fixed point. In this analogy the arc length along the axis of the rod plays the role of a time like coordinate. By emphasizing the Hamiltonian structure of the rod equations, from the existence of transverse homoclinic and heteroclinic orbits the existence of spatially chaotic equilibrium states of the rod are concluded.

From a physical (experimental) point of view, probably the problem is more complicated because rod problems are boundary value problems and hence chaotic deformations will lead to points of contact of the different parts of the rod.

From a physical (experimental) point of view, probably the problem is more complicated because rod problems are boundary value problems and hence chaotic deformations will lead to points of contact of the different parts of the rod.

Reviewer: H.Troger

### MSC:

74G60 | Bifurcation and buckling |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

### Keywords:

Melnikov function; regular perturbation methods; qualitative description of classes of solutions; limiting cases; geometrical symmetries; vanishing of certain stress components; Kirchhoff analogy; rod loaded at its end; heavy rigid body pivoted at a fixed point; Hamiltonian structure; transverse homoclinic; heteroclinic orbits; existence of spatially chaotic equilibrium states; boundary value problems; chaotic deformations
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\textit{A. Mielke} and \textit{P. Holmes}, Arch. Ration. Mech. Anal. 101, No. 4, 319--348 (1988; Zbl 0655.73029)

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### References:

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