Solutions in terms of Elliptic Functions are provided for SAM in the integrable case where the mass ration equals three. My last SAM paper (I promise). To appear in The American Journal of Physics.

chao-dyn↗

arXiv1994

Braid analysis of a bouncing ball

Prunning front is calculated for a bouncing ball system and the results are compared to a braid analysis. To Appear in Physical Review E.

chao-dyn↗

arXiv1994

Topological time series analysis of a string experiment and its synchronized model

Template and prunning front are calculated for an experimental chaotic time series from a mechanical string experiment. An empirical synchronized model is also created for the data set. To appear in Physical Review E.

chao-dyn↗

arXiv1993

Teardrop and heart orbits of a swinging Atwood's Machine

An exact solution is presented for a swinging Atwood's machine. This teardrop-heart orbit is constructed using Hamilton-Jacobi theory. The example nicely illustrates the utility of the Hamilton-Jacobi method for finding solutions to nonlinear mechanical systems when more elementary techniques fail.

chao-dyn↗

arXiv1993

Discrete Dynamical Models Showing Pattern Formation in Subaqueous Bedforms

A new class of ``toy models'' for subaqueous bedform formation are proposed and examined. These models all show a similar mechanism of wavelength selection via bedform unification, and they may have applications to bedform stratigraphy. The models are also useful for exploring general issues of pattern formation and complexity in stochastically driven far from equilibrium systems.

patt-sol↗

arXiv1993

Topological organization of (low-dimensional) chaos

Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with any model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series.

chao-dyn↗