Dynamics and Mission Design Near Libration Points - Vol Ii : Fundamentals.
Title:
Dynamics and Mission Design Near Libration Points - Vol Ii : Fundamentals.
Author:
Gómez, G.
ISBN:
9789812810649
Personal Author:
Physical Description:
1 online resource (159 pages)
Series:
World Scientific Monograph Series in Mathematics ; v.3
World Scientific Monograph Series in Mathematics
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 -- Chapter 4 The Equations of Motion -- 4.1 Reference Systems -- 4.2 The Lagrangian -- 4.3 The Hamiltonian and the Related Expansions -- 4.4 Some Useful Expansions -- 4.5 Fourier Analysis: The Relevant Frequencies and the Related Coefficients -- 4.6 Concrete Expansions of the Hamiltonian and the Functions -- 4.7 Simplified Normalized Equations. Tests -- 4.7.1 Tests of the Simplified Normalized Equations -- Chapter 5 Periodic Orbits of Some Intermediate Equations.
5.1 Equations of Motion for the Computation of Intermediate Periodic Orbits -- 5.2 Obtaining the Periodic Orbits Around the Triangular Libration Points for the Intermediate Equations -- 5.3 Results and Comments -- Chapter 6 Quasi-periodic Solution of the Global Equations: Semianalytic Approach -- 6.1 The Objective -- 6.2 The Algorithm -- 6.3 The Adequate Set of Relevant Frequencies -- 6.4 Avoiding Secular Terms -- 6.5 The Coefficients Related to the Different Frequencies -- 6.6 Determination of the Coefficients of Quasi-periodic Functions Using FFT -- 6.7 Results and Conclusions -- Chapter 7 Numerical Determination of Suitable Orbits of the Simplified System -- 7.1 The Objective -- 7.2 Description of Two Families of Algorithms. Reduction of the Linearized Equations -- 7.3 Description of the Methods. Comments -- 7.4 Results and Discussion -- Chapter 8 Relative Motion of Two Nearby Spacecrafts -- 8.1 The Selection of Orbits for the Two Spacecrafts -- 8.2 Variations of the Relative Distance and Orientation. Results -- 8.3 Comments on the Applicability of the Results -- Chapter 9 Summary -- 9.1 Objectives of the Work -- 9.2 Contribution to the Solution of the Problem -- 9.3 Conclusions -- 9.4 Outlook -- Bibliography.
Abstract:
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, μ , below Routh's critical value, μ 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 particle remains close to the equilibrium point for a big time interval (some millions of years, for example). According to the literature, what has been done in the problem follows two approaches: (a) numerical simulations of more or less accurate models of the real solar system; (b) study of periodic or quasi-periodic orbits of some much simpler problem. The concrete questions that are studied in this volume are: (a) Is there some orbit of the real solar system which looks like the periodic orbits of the second approach? (That is, are there orbits performing revolutions around L 4 covering eventually a thick strip? Furthermore, it would be good if those orbits turn out to be quasi-periodic. However, there is no guarantee that such orbits exist or will be quasi-periodic). (b) If the orbit of (a) exists and two particles (spacecraft) are put close to it, how do the mutual distance and orientation change with time?. As a final conclusion of the work, there is evidence that orbits moving in a somewhat big annulus around L 4 and L 5 exist, that these orbits have small components out of the plane of the Earth-Moon system, and that they are at most mildly unstable. Contents: Bibliographical Survey; Periodic Orbits of the Bicircular Problem and Their Stability;
Numerical Simulations of the Motion in an Extended Neighborhood of the Triangular Libration Points in the Earth-Moon System; The Equations of Motion; Periodic Orbits of Some Intermediate Equations; Quasi-Periodic Solution of the Global Equations: Semi-Analytical Approach; Numerical Determination of Suitable Orbits of the Simplified System; Relative Motion of Two Nearby Spacecrafts. Readership: Applied mathematicians, computational physicists and aerospace engineers.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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