Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff (Q1375123)
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scientific article; zbMATH DE number 1102998
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff |
scientific article; zbMATH DE number 1102998 |
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Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff (English)
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11 August 1998
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Summary: We consider Lagrangian systems with Lagrangian functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as \(t\to\pm\infty\), to an ``equilibrium at infinity''. This result is applied to the Kirchhoff problem of a heavy rigid body moving through a boundless incompressible ideal fluid, which is at rest at infinity and has zero vorticity.
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Routh method
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calculus of variations
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Lagrangian functions
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quadratic time dependence
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existence of infinitely many solutions
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