TY  - BOOK
AU  - Hénon,Michel
ED  - SpringerLink (Online service)
TI  - Generating Families in the Restricted Three-Body Problem
T2  - Lecture Notes in Physics Monographs,
SN  - 9783540696506
AV  - QB4 
U1  - 520 23
PY  - 1997///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Physics
KW  - Computer science
KW  - Mathematics
KW  - Astronomy
KW  - Astrophysics
KW  - Engineering
KW  - Complexity
KW  - Computational Mathematics and Numerical Analysis
KW  - Extraterrestrial Physics, Space Sciences
N1  - Definitions 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
N2  - The classical restricted problem of three bodies is of fundamental 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. In this book an attempt is made to explain and organize 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, where several families come together and it is necessary to determine how individual branches are joined. Many different cases must be distinguished and studied separately. Detailed recipes are given. Their use is illustrated by determining a number of generating families, associated with natural families of the restricted problem, and comparing them with numerical computations in the Earth-Moon and Sun-Jupiter case
UR  - http://dx.doi.org/10.1007/3-540-69650-4
ER  -