Abstract
We discuss here the subharmonics of any order in the case of linear damping, sinusoidal external force, and cubic type restoring force, with coefficients not necessarily small. By using ideas of Van der Pol1, Mandelstam — Papalexi1, Andronow — Witt2, we get a proper transformation of the equation, and for its “steady state” and “transient” solutions use of the Poincare’s method for periodic solutions is made.
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References
Van der Pol Phil. Mag., 3, 1927, 65.
L. Mandelstam — N. Papalexi, Techn. Phys., U.S.S.R., 1935, 415.
A. Andronow — A. Witt, Arch, für Electrotechn., 1930.
P. Fatou, Bulletin Société Math, de France, 1928 — 30, pp. 112–115.
H. Poincaré, Sur les courbes définies par une équation différentielle. Œuvres, Gauthier-Villars, Paris, Vol. 1892.
I. Bendixson, Acta Math., 24, 1901.
J. Hadamard, Rice Institute Pamphlet, 20, I, 1933, 9–28.
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© 1985 D. Reidel Publishing Company, Dordrecht, Holland
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Magiros, D.G. (1985). Subharmonics of any order in case of non linear restoring force. Part I. In: Tzafestas, S.G. (eds) Selected Papers of Demetrios G. Magiros. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5368-0_12
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DOI: https://doi.org/10.1007/978-94-009-5368-0_12
Publisher Name: Springer, Dordrecht
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