Dynamics and mission design near libration points. Volume 2, Fundamentals : the case of triangular libration points / G. Gomez ... [et al.].

Format:

Book

Contributor:

Gómez, G. (Gerard)

Series:

World Scientific monograph series in mathematics ; 3.

World scientific monograph series in mathematics ; 3

Language:

English

Subjects (All):

Three-body problem.

Lagrangian points.

Physical Description:

1 online resource (159 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2001.

Language Note:

English

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, <i>μ</i>, below Routh's critical value, <i>μ</i>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 <i>L</i>4, <i>L</i>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 t

Contents:

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

3.3 Simulations of Motion Starting Near the Planar Periodic Orbit of Kolenkiewicz and Carpenter

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611956301

9781281956309

1281956309

9789812810649

9812810641

OCLC:

879023996