Non-stationary Dynamics in the Bouncing Ball: A Wavelet perspective
Abstract
The non-stationary dynamics of a bouncing ball, comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signature of self-similarity, complex scaling behavior and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to neutral turbulence, viscous dissipation regions and different time varying periodic modulations.
Cite
@article{arxiv.1304.6311,
title = {Non-stationary Dynamics in the Bouncing Ball: A Wavelet perspective},
author = {Abhinna Kumar Behera and Prasanta K. Panigrahi and A. N. Sekar Iyengar},
journal= {arXiv preprint arXiv:1304.6311},
year = {2015}
}
Comments
17 pages, 10 figures, 1 table