An approximation theorem in classical mechanics

Cristina Stoica

doi:10.3934/jgm.2016011

Article Contents

2016, Volume 8, Issue 3: 359-374. Doi: 10.3934/jgm.2016011

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An approximation theorem in classical mechanics

Cristina Stoica^1,

1.
Department of Mathematics, Wilfrid Laurier University, 75 University Ave West, Waterloo, ON, N2L 3C5

Received: June 30, 2015

Revised: March 31, 2016

Published: August 2016

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Abstract

A theorem by K. Meyer and D. Schmidt says that The reduced three-body problem in two or three dimensions with one small mass is approximately the product of the restricted problem and a harmonic oscillator [7]. This theorem was used to prove dynamical continuation results from the classical restricted circular three-body problem to the three-body problem with one small mass.
We state and prove a similar theorem applicable to a larger class of mechanical systems. We present applications to spatial $(N+1)$-body systems with one small mass and gravitationally coupled systems formed by a rigid body and a small point mass.

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Mathematics Subject Classification: Primary: 37J20, 70H33; Secondary: 53D20.

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References

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