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Multiple-Variable Expansion Procedures

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Book cover Perturbation Methods in Applied Mathematics

Part of the book series: Applied Mathematical Sciences ((AMS,volume 34))

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Abstract

Various physical problems are characterized by the presence of a small disturbance which, because of being active over a long time, has a non-negligible cumulative effect. For example, the effect of a small damping force over many periods of oscillation is to produce a decay in the amplitude of a linear oscillator. A fancier example having the same physical and mathematical features is the motion of a satellite around the earth, where the dominant force is a spherically symmetric gravitational field. If this were the only force acting on the satellite the motion would (for sufficiently low energies) be periodic. The presence of a thin atmosphere, a slightly non-spherical earth, a small moon, a distant sun, etc. all produce small but cumulative effects which after a sufficient number of orbits drastically alter the nature of the motion.

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Authors and Affiliations

  1. Applied Mathematics Program, University of Washington, 98195, Seattle, WA, USA

    J. Kevorkian

  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 12181, Troy, NY, USA

    J. D. Cole

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  1. J. Kevorkian
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  2. J. D. Cole
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© 1981 Springer-Verlag Berlin Heidelberg

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Kevorkian, J., Cole, J.D. (1981). Multiple-Variable Expansion Procedures. In: Perturbation Methods in Applied Mathematics. Applied Mathematical Sciences, vol 34. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4213-8_3

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  • DOI: https://doi.org/10.1007/978-1-4757-4213-8_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2812-2

  • Online ISBN: 978-1-4757-4213-8

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