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Trigonometric simplification of a class of conservative nonlinear oscillators

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Abstract

This paper deals with a class of conservative nonlinear oscillators of the form \(\ddot x(t)+f(x(t))=0\), where f(x) is analytic. A transformation of time from t to a new time coordinate τ is defined such that periodic solutions can be expressed in the form x(τ) = A 0+A 1 cos 2τ. We refer to this process of trigonometric simplification as trigonometrification. Application is given to the stability of nonlinear normal modes (NNMs) in two-degree-of-freedom systems.

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY, 14853, USA

    Geoffrey Recktenwald & Richard Rand

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  1. Geoffrey Recktenwald
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  2. Richard Rand
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Correspondence to Richard Rand.

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Recktenwald, G., Rand, R. Trigonometric simplification of a class of conservative nonlinear oscillators. Nonlinear Dyn 49, 193–201 (2007). https://doi.org/10.1007/s11071-006-9121-1

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  • DOI: https://doi.org/10.1007/s11071-006-9121-1

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