Web of families of periodic orbits of Generalized Hill's Problem
Periodic solutions of Hill's problem play an important role in understanding the dynamics of motion of a satellite in the vicinity of the smaller of the two active mass. However, the classification and understanding of the structure of their families is impossible without consideration of periodic solutions of a more general problem — Generalized Hill’s problem. Numerical analysis of this problem showed that all up-to-date known families of periodic orbits of Generalized Hill's problem form a common network in the sense that any pair of families directly or indirectly related to each other either through limiting generating solutions, either through common orbits with integer local multiplicity.
periodic solutions, Hamiltonian system, symmetric solution, Hill's problem
Mathematical modelling in actual problems of science and technics