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Book Cover
Author Llibre, J

Title Dynamics and Mission Design Near Libration Points - Vol Ii : Fundamentals
Published Singapore : World Scientific Publishing Company, 2001


Description 1 online resource (159 pages)
Series World Scientific Monograph Series in Mathematics
World Scientific monograph series in mathematics.
Contents Preface ; Chapter 1 Bibliographical Survey ; 1.1 Equations. The Triangular Equilibrium Points and their Stability ; 1.2 Numerical Results for the Motion Around L4 and L5 ; 1.3 Analytical Results for the Motion Around L4 and L5 ; 1.3.1 The Models Used
1.4 Miscellaneous Results 1.4.1 Station Keeping at the Triangular Equilibrium Points ; 1.4.2 Some Other Results ; Chapter 2 Periodic Orbits of the Bicircular Problem and Their Stability ; 2.1 Introduction ; 2.2 The Equations of the Bicircular Problem
2.3 Periodic Orbits with the Period of the Sun 2.4 The Tools: Numerical Continuation of Periodic Orbits and Analysis of Bifurcations ; 2.4.1 Numerical Continuation of Periodic Orbits for Nonautonomous and Autonomous Equations
2.4.2 Bifurcations of Periodic Orbits: From the Autonomous to the Nonautonomous Periodic System 2.4.3 Bifurcation for Eigenvalues Equal to One ; 2.5 The Periodic Orbits Obtained by Triplication
Chapter 3 Numerical Simulations of the Motion in an Extended Neighborhood of the Triangular Libration Points in the Earth-Moon System 3.1 Introduction ; 3.2 Simulations of Motion Starting at the Instantaneous Triangular Points at a Given Epoch
Summary It is well known that the restricted three-body problem has triangular equilibrium points. These points are linearly stable for values of the mass parameter, æ, below Routh's critical value, æ 1 . It is also known that in the spatial case they are nonlinearly stable, not for all the initial conditions in a neighborhood of the equilibrium points L 4, L 5 but for a set of relatively large measures. This follows from the celebrated Kolmogorov-Arnold-Moser theorem. In fact there are neighborhoods of computable size for which one obtains "practical stability" in the sense that the massless partic
Notes Print version record
Subject Three-body problem.
Lagrangian points.
Lagrangian points.
Three-body problem.
Form Electronic book
ISBN 9789812810649