JGM
An approximation theorem in classical mechanics
Cristina Stoica
Journal of Geometric Mechanics 2016, 8(3): 359-374 doi: 10.3934/jgm.2016011
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.
keywords: Restricted problems in mechanics Lie symmetries continuation of dynamics reduction.
JGM
Euler-Poincaré reduction for systems with configuration space isotropy
Jeffrey K. Lawson Tanya Schmah Cristina Stoica
Journal of Geometric Mechanics 2011, 3(2): 261-275 doi: 10.3934/jgm.2011.3.261
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.
keywords: Euler-Poincaré-Lagrange bundle equations. Euler-Poincaré reduction Symmetric Lagrangian slice theorem

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