ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Delay-Coupled Mathieu Equations in Synchrotron Dynamics Revisited: Delay Terms in the Slow Flow

Journal of Environmental Accounting and Management 7(4) (2018) 349--360 | DOI:10.5890/JAND.2018.12.003

Alexander Bernstein$^{1}$, Richard Rand$^{2}$

$^{1}$ Center for Applied Mathematics, Cornell University, Ithaca NY 14853, USA

$^{2}$ Dept. of Mathematics and Dept. of Mechanical and Aerospace Engineering, Cornell University

Abstract

In a previous work, we applied perturbation methods to a system of two delay-coupled Mathieu equations, resulting in a slow flow which contains delayed variables. This previous treatment involved a convenient approximation which involved replacing delay terms in the slow flow by non-delay terms. The current paper explores the effect of keeping delay terms in the slow flow with the hope of illustrating what is lost in making such an approximation. Analytic results are shown to compare favorably with numerical integration of the slow flow itself.

Acknowledgments

The authors would like to thank their colleagues J. Sethna, D. Rubin, D. Sagan and R. Meller for introducing us to the dynamics of the Synchrotron and for their continued support in this research. This work was partially supported by NSF Grant PHY-1549132.

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