Open Access
Normal form reduction for multiple-zero eigenvalue using fractional scales
Alexei A. Mailybaev,Angelo Luongo +1 more
- 01 Jan 2008
TL;DR: In this article, a new method for finding normal form equation and invariant manifold in the case of multiple zero eigenvalues with a single Jordan block is presented, which utilizes the concept of fractional scale.
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Abstract: In this paper, we present a new method for finding normal form equation and invariant manifold in the case of multiple zero eigenvalue with a single Jordan block. The method utilizes the concept of fractional scale. This allows using a single scale parameter in the normal form reduction for systems with multiple variables and parameters. The use of fractional scales substantially simplifies the procedure of system reduction. As an example, we perform the normal form reduction near the point of triple zero bifurcation for a double pendulum under a follower force.
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Multiple-Timescale Analysis for Bifurcation from a Multiple-Zero Eigenvalue
TL;DR: In this article, the multiple-zero bifurcation of a general multiparameter dynamic system is analyzed using the multiple scale method and exploiting the close similarities with eigensolution analysis for defective systems.