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A peculiar periodic solution of a modified Duffing’s equation

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Summary

Odd harmonic periodic solutions of a modified Duffing’s equation are easily and usually obtained on an analogue computer. However, contrary to intuition, for special values of the parameters periodic solutions containing an even harmonic component have been observed. A mathematical proof of the existence of such exceptional solutions is given in this paper.

References

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    Dana Young andP. N. Hess,On the stability of harmonic solutions of a modified form of Duffing’s equation, Proc. of 2-nd U. S. Nat. Congress of Applied Mechanics, 1954, pp. 79–84.

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    N. W. McLachlan,Theory and application of Mathieu functions, Oxford, Clarendon Press, 1947.

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    S. Lefschetz,Lectures on Differential Equations, Princeton University Press, 1948, p. 35.

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    U. S. National Bureau of Standards,Tables relating to Mathieu Functions, Columbia Univ. Press., 1951.

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    S. Lefschetz,Complete families of periodic solutions of differential equations, Comm. Math. Helvetici, vol. 28 (1954), 341–345.

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Additional information

This work was carried out on a joint project of the Univ. of Minn. and Minneapolis-Honeywell Reg. Co. under USAF contract No. AF 33(038)22893 administered under the direction of the Flight Research Lab. USAF of Wright Field.

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Turrittin, H.L., Culmer, W.J.A. A peculiar periodic solution of a modified Duffing’s equation. Annali di Matematica 44, 23–33 (1957). https://doi.org/10.1007/BF02415188

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Keywords

  • Periodic Solution
  • Analogue Computer
  • Implicit Function Theorem
  • Harmonic Component
  • Steady State Response