Stability study of a periodic system by a period-to-period mapping (Q1923347)
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scientific article; zbMATH DE number 932141
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability study of a periodic system by a period-to-period mapping |
scientific article; zbMATH DE number 932141 |
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Stability study of a periodic system by a period-to-period mapping (English)
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12 November 1996
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The investigated dynamical system is described by a set of \(N\) ordinary differential equations where the right-hand side is periodic in \(t\) with period \(T\). Poincaré's point mapping is applied for the stability study; for this purpose the notion of the P-K solution of the point mapping is introduced. Stability and bifurcation conditions are expressed analytically; an important feature of the method is its general applicability for multiple degrees-of-freedom systems. A method of the second author to obtain the point mapping is summarized. With this method the parametric stability of a homogeneous double pendulum is studied. Some numerical solutions in connection with bifurcations are shown in diagrams.
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stability
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periodic
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multiple degrees-of-freedom systems
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homogeneous double pendulum
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