| Issue |
MATEC Web Conf.
Volume 241, 2018
International Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD 2018)
|
|
|---|---|---|
| Article Number | 01009 | |
| Number of page(s) | 4 | |
| DOI | https://doi.org/10.1051/matecconf/201824101009 | |
| Published online | 03 December 2018 | |
Numerical Approximation of LYAPUNOV-Exponents for Quasiperiodic Motions
University of Kassel, Institute of Mechanics, Engineering Dynamics, 34125 Kassel, Germany
* e-mail: robert.fiedler@uni-kassel.de
** e-mail: hetzler@uni-kassel.de
This paper proposes an approach to approximate the LYAPUNOV -spectrum of quasiperiodic flows on isolated invariant manifolds numerically. Once the invariant manifold has been determined, integrations over the infinite, one dimensional time interval – as calculating the LYAPUNOV -spectrum for instance – can be transformed into an integral over a finite, p-dimensional domain, where p is the dimension of the manifold. The application of the proposed approach is demonstrated by calculating the LYAPUNOV -spectrum of periodic and quasiperiodic motions of a forced VAN-DER-POL equation. The results are compared to results from a classical time integration based method using a continuous GRAM-SCHMIDT orthonormalization.
© The Authors, published by EDP Sciences, 2018
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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