Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim

Gouravaraju, Saipraneeth and Ganguli, Ranjan (2012) Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim. In: APPLIED MATHEMATICS AND COMPUTATION, 218 (21). pp. 10435-10442.

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Abstract

Helicopter trim involves solution of nonlinear force equilibrium equations. As in many nonlinear dynamic systems, helicopter trim problem can show chaotic behavior. This chaotic behavior is found in the basin of attraction of the nonlinear trim equations which have to be solved to determine the main rotor control inputs given by the pilot. This study focuses on the boundary of the basin of attraction obtained for a set of control inputs. We analyze the boundary by considering it at different magnification levels. The magnified views reveal intricate geometries. It is also found that the basin boundary exhibits the characteristic of statistical self-similarity, which is an essential property of fractal geometries. These results led the authors to investigate the fractal dimension of the basin boundary. It is found that this dimension is indeed greater than the topological dimension. From all the observations, it is evident that the boundary of the basin of attraction for helicopter trim problem is fractal in nature. (C) 2012 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	APPLIED MATHEMATICS AND COMPUTATION
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	Copyright for this article belongs to the ELSEVIER SCIENCE INC
Keywords:	Basin of attraction;Chaos;Fractal dimension;Helicopter trim;Nonlinear equations;Statistical self-similarity
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	09 Jul 2012 10:05
Last Modified:	10 Jul 2012 04:32
URI:	http://eprints.iisc.ac.in/id/eprint/44751

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