We study a single mode for the Kirchhoff string vibrating in space. In 3D a single mode is generally almost periodic in contrast to the 2D periodic case. In order to show a complete geometrical description of a single mode we prove some monotonicity properties of the almost periods of the solution, with respect to the mechanical energy and the momentum. As a consequence of these properties, we observe that a planar single mode in 3D is always unstable, while it is known that a single mode in 2D is stable (under a suitable denition of stability), if the energy is small.

Free vibrations in space of the single mode for the Kirchhoff string

MARCHIONNA, CLELIA
2013-01-01

Abstract

We study a single mode for the Kirchhoff string vibrating in space. In 3D a single mode is generally almost periodic in contrast to the 2D periodic case. In order to show a complete geometrical description of a single mode we prove some monotonicity properties of the almost periods of the solution, with respect to the mechanical energy and the momentum. As a consequence of these properties, we observe that a planar single mode in 3D is always unstable, while it is known that a single mode in 2D is stable (under a suitable denition of stability), if the energy is small.
2013
Kirchhoff string; single modes; monotonicity of the almost periods; stability.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/747389
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