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JGM

A theorem by K. Meyer and D. Schmidt says that

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.

*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.

JGM

This paper concerns Lagrangian systems with symmetries, near points with
configuration space isotropy.
Using twisted parametrisations
corresponding to phase space slices based at zero points of
tangent fibres, we deduce reduced equations of motion, which are a hybrid of
the Euler-Poincaré and Euler-Lagrange equations.
Further, we state a corresponding variational principle.

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