Other
Scientific paper
Feb 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cosre..47...53k&link_type=abstract
Cosmic Research, Volume 47, Issue 1, pp.53-67
Other
95.10.Ce
Scientific paper
Planar orbits of three-dimensional restricted circular three-body problem are considered as a special case of three-dimensional orbits, and the second-order monodromy matrices M (in coordinate z and velocity v z ) are calculated for them. Semi-trace s of matrix M determines vertical stability of an orbit. If | s| ≤ 1, then transformation of the subspace ( z, v z ) in the neighborhood of solution for the period is reduced to deformation and a rotation through angle φ, cosφ = s. If the angle ϕ can be rationally expressed through 2π,φ = 2π· p/q, where p and q are integer, then a planar orbit generates the families of three-dimensional periodic solutions that have a period larger by a factor of q (second kind Poincareé periodic solutions). Directions of continuation in the subspace ( z, v z ) are determined by matrix M. If | s| < 1, we have two new families, while only one exists at resonances 1: 1 ( s = 1) and 2: 1 ( s = -1). In the course of motion along the family of three-dimensional periodic solutions, a transition is possible from one family of planar solutions to another one, sometimes previously unknown family of planar solutions.
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