Abstract
Various physical problems are characterized by the presence of a small disturbance which, because it is 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 an oscillator. A more interesting example having the same physical and mathematical features is that of the motion of a satellite around Earth. Here the dominant force is a spherically symmetric gravitational field. If this were the only force acting on the satellite, the motion would be periodic (for sufficiently low energies). The presence of a thin atmosphere, a slightly nonspherical Earth, a small moon, a distant sun, and so on, all produce small but cumulative effects which, after a sufficient number of orbits, drastically alter the nature of the motion.
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Kevorkian, J., Cole, J.D. (1996). The Method of Multiple Scales for Ordinary Differential Equations. In: Multiple Scale and Singular Perturbation Methods. Applied Mathematical Sciences, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3968-0_4
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