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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