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- catalog abstract "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.".
- catalog contributor b10822244.
- catalog created "c1997.".
- catalog date "1997".
- catalog date "c1997.".
- catalog dateCopyrighted "c1997.".
- catalog description "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.".
- catalog description "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.".
- catalog extent "xi, 278 p. :".
- catalog identifier "3540638024 (hardcover : alk. paper)".
- catalog isPartOf "Lecture notes in physics. New series m, Monographs, 0940-7677 ; m52".
- catalog issued "1997".
- catalog issued "c1997.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog subject "521 21".
- catalog subject "Artificial satellites Orbits.".
- catalog subject "Astronomy.".
- catalog subject "Astrophysics.".
- catalog subject "Celestial mechanics.".
- catalog subject "Computer science Mathematics.".
- catalog subject "Engineering.".
- catalog subject "Physics.".
- catalog subject "QB362.T5 H46 1997".
- catalog subject "Three-body problem.".
- catalog tableOfContents "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.".
- catalog title "Generating families in the restricted three-body problem / Michel Hénon.".
- catalog type "text".