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Capture in resonance: Opening a homoclinic orbit through slowly varying coefficients

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Geometric Dynamics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1007))

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Abstract

Capture in sustained resonance is proved to occur for a system of nonlinear ordinary differential equations with slowly varying coefficients which model a rolling and pitching reentry vehicle. Capture is proved to occur by showing that the homoclinic orbit opens up for the small parameter ɛ>0. The size of the opening is measured using the Melnikov integral. Since this integral has usually been applied to time periodic perturbations, it is derived for systems with slowly varying coefficients.

This research was partially supported by NSF Grant MSC 81-02177. A.M.S. Classification 34C35, 70K30.

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Authors and Affiliations

  1. Northwestern University, Evanston, Illinois

    Clark Robinson

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  1. Clark Robinson
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J. Palis Jr.

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© 1983 Springer-Verlag

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Robinson, C. (1983). Capture in resonance: Opening a homoclinic orbit through slowly varying coefficients. In: Palis, J. (eds) Geometric Dynamics. Lecture Notes in Mathematics, vol 1007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061439

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  • DOI: https://doi.org/10.1007/BFb0061439

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12336-1

  • Online ISBN: 978-3-540-40969-4

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