The generating family i of periodic solutions of the restricted problem
For μ=0, we study (generating) family i
of symmetric periodic solutions of the
plane circular restricted three-body problem.
This family begins with the direct circular orbits
of infinitely small radius around the primary P1 of greater mass. We demonstrate how the generating family i is formed from the parts of families
Id, EN±, B1, and Сk,k+1. On the initial part of the generating family i, we computed (and plotted) all critical orbits, the period and both traces (the plane and the vertical ones), and characteristics of the family in various coordinate systems. It turned out that characteristics of the family have a rather complicated structure.
We found cyclic regularities in this structure as well as in the structure of the whole family.
Mathematical problems and theory of numerical methods