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Multiple-Variable Expansion Procedures

  • J. Kevorkian
  • J. D. Cole
Part of the Applied Mathematical Sciences book series (AMS, volume 34)

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.

Keywords

Periodic Solution Angle Variable Slow Variable Canonical Transformation Linear Oscillator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • J. Kevorkian
    • 1
  • J. D. Cole
    • 2
  1. 1.Applied Mathematics ProgramUniversity of WashingtonSeattleUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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