Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim

Sekhar, Chandra D and Ganguli, R (2010) Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim. In: Computers & Mathematics with Applications, 60 (10). pp. 2834-2858.

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Abstract

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	Computers & Mathematics with Applications
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Helicopter; Aeroelastic analysis; Fractals; Newton-Raphson method; System of nonlinear algebraic equations
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	22 Dec 2010 08:53
Last Modified:	22 Dec 2010 08:53
URI:	http://eprints.iisc.ac.in/id/eprint/34584

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