The newton transform: An operational method for constructing integral of dynamical systems

Scott A. Burns; Julian I. Palmore

doi:10.1016/0167-2789(89)90118-8

The newton transform: An operational method for constructing integral of dynamical systems

Scott A. Burns, Julian I. Palmore

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The goal of this paper is to illustrate the rapid construction of phase plane portraits by a method that has no propagated error. This is done by constructing integrals (constants of motion) for differential equations on the plane-even in non-conservative systems, where energy integrals produced by quadrature do not exist. The correct time parameterization is also obtained. This operational method is called the "Newton transform".

Original language	English (US)
Pages (from-to)	83-90
Number of pages	8
Journal	Physica D: Nonlinear Phenomena
Volume	37
Issue number	1-3
DOIs	https://doi.org/10.1016/0167-2789(89)90118-8
State	Published - Jul 1989

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(89)90118-8

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abstract = "The goal of this paper is to illustrate the rapid construction of phase plane portraits by a method that has no propagated error. This is done by constructing integrals (constants of motion) for differential equations on the plane-even in non-conservative systems, where energy integrals produced by quadrature do not exist. The correct time parameterization is also obtained. This operational method is called the {"}Newton transform{"}.",

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AB - The goal of this paper is to illustrate the rapid construction of phase plane portraits by a method that has no propagated error. This is done by constructing integrals (constants of motion) for differential equations on the plane-even in non-conservative systems, where energy integrals produced by quadrature do not exist. The correct time parameterization is also obtained. This operational method is called the "Newton transform".

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The newton transform: An operational method for constructing integral of dynamical systems

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