The classical three-body problem is of great importance for its applications to astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which a large number have been computed numerically. Here the author explains and organizes this material through a systematic study of generating families, which are the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. The most critical part is the study of bifurcations. Many cases are distinguished and studied separately and detailed recipies are given. Their use is illustrated by determining generating families, and comparing them with numerical computations for the Earth+Moon and Sun-Jupiter systems.
Introduction.- Definition and Properties.- Generating Orbits of the First Species.- Generating Orbits of the Second Species.-Generating Orbits of the Third Species.- Bifurcation Orbits.-Junctions: Symmetry.- Junctions: Broucke's Principle.- Fragments.- Generating Families.- Correspondence Between Old and New Notations.- The Domain D2.- Number of Branches.- Index of Definitions.- Index of Notations.- References.
Overview
The classical three-body problem is of great importance for its applications to astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which a large number have been computed numerically. Here the author explains and organizes this material through a systematic study of generating families, which are the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. ...