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

• Record Nr.: UNINA9910782276703321
• Pubbl/distr/stampa: Singapore ; ; River Edge, NJ, : World Scientific, c2001
• ISBN: 1-281-95630-9; 9786611956301; 981-281-064-1
• Descrizione fisica: 1 online resource (159 p.)
• Collana: World scientific monograph series in mathematics ; ; 3
• Altri autori (Persone): GómezG (Gerard)
• Disciplina: 521.3
• Soggetti: Three-body problem; Lagrangian points
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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
• Sommario/riassunto: 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