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Perturbation Methods in Non-Linear Systems pp 274–354Cite as

Resonance

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Part of the book series: Applied Mathematical Sciences ((AMS,volume 8))

Abstract

The earliest verion of the problem along the lines to be described here is found in Bohlin’ s works (Poincaré, 1898, Vol. II), in von Zeipel’s (1911) monograph on the theory of motion of asteroids and in Whittaker’s problem of series solutions and adelphic integrals (1927), all of them directly or indirectly dealing with problems of celestial mechanics. In the theory of nonlinear and linear oscillations, the problem has been dealt with initially and studied by Lyapunov (1966), Bogoliubov (1945), Mitropolsky (1962) and Krylov (1934). Modern literature, that is, after the middle of the century is plentiful of works on resonance, generalizations and many different definitions and approaches.

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Authors and Affiliations

  1. University of Sao Paulo, Brazil

    Georgio Eugenio Oscare Giacaglia

  2. University of Texas at Austin, USA

    Georgio Eugenio Oscare Giacaglia

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  1. Georgio Eugenio Oscare Giacaglia
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Giacaglia, G.E.O. (1972). Resonance. In: Perturbation Methods in Non-Linear Systems. Applied Mathematical Sciences, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6400-2_6

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  • DOI: https://doi.org/10.1007/978-1-4612-6400-2_6

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  • Print ISBN: 978-0-387-90054-4

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