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The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

Deekshatulu, BL (1963) The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems. In: IEEE Transactions on Applications and Industry, 82 (69). pp. 315-317.

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Abstract

Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations xÿn-2ÿ+ f(x)xÿ2n+g(x)xÿn+h(x)=0 ÿ+f(x)xÿn+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the xÿnÿx planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré's fundamental phase plane xÿÿx is conceived of as the simplest case of the general xÿnÿx plane.

Item Type: Journal Article
Additional Information: Copyright 1963 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Others
Date Deposited: 27 Feb 2012 09:44
Last Modified: 27 Feb 2012 09:44
URI: http://eprints.iisc.ernet.in/id/eprint/43088

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