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The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems

Deekshatulu, BL (1963) The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems. In: IEEE Transactions on Applications and Industry, 82 (69). pp. 305-315.

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Abstract

Use of some new planes such as the R-x, R2-x (where R represents in the n-dimensional phase space, the radius vector from the origin to any point on the trajectory described by the system) is suggested for analysis of nonlinear systems of any kind. The stability conditions in these planes are given. For easy understanding of the method, the transformation from the phase plane to the R-x, R2-x planes is brought out for second-order systems. In general, while these planes serve as useful as the phase plane, they have proved to be simpler in determining quickly the general behavior of certain classes of second-order nonlinear systems. A chart and a simple formula are suggested to evaluate time easily from the R-x and R2-x trajectories, respectively. A means of solving higher-order nonlinear systems is also illustrated. Finally, a comparative study of the trajectories near singular points on the phase plane and on the new planes is made.

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 09:46
Last Modified: 27 Feb 2012 09:46
URI: http://eprints.iisc.ernet.in/id/eprint/43086

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