Qualitative investigation of the motions and frequencies in the Lagrange problem

Details Qualitative investigation of the motions and frequencies in the Lagrange problem Qualitative investigation of the motions and frequencies in the Lagrange problem

Dec 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992kosis..30..746s&link_type=abstract

Kosmicheskie Issledovaniya (ISSN 0023-4206), vol. 30, no. 6, p. 746-758.

Mathematics

Branching (Mathematics), Circular Orbits, Equations Of Motion, Lagrangian Function, Orbit Perturbation, Elliptic Functions, Integral Equations

Scientific paper

Bifurcation diagrams of motion integrals are constructed in the Lagrange problem (superposition of central and uniform force fields) by use of the separation of variables. The dependence of quasi-periodical motion frequencies on constants of first integrals is investigated in corresponding regions of the diagrams. All possible types of motion are investigated, including circular orbits, and the regions of their stability and instability. Nondegeneracy of reduced and original problems is proved.

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