World Scientific Monograph Series in Mathematics
4 primary works • 7 total works
Book 2
In this book the problem of station keeping is studied for orbits near libration points in the solar system. The main focus is on orbits near halo ones in the (Earth+Moon)-Sun system. Taking as starting point the restricted three-body problem, the motion in the full solar system is considered as a perturbation of this simplified model. All the study is done with enough generality to allow easy application to other primary-secondary systems as a simple extension of the analytical and numerical computations.
Book 3
Dynamics And Mission Design Near Libration Points - Vol Ii: Fundamentals: The Case Of Triangular Libration Points
by Gerard Gomez, Jaume Llibre, R. Martinez, and Carles Simo
Published 12 February 2001
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, , below Routh's critical value, 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 L4, L5 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 L4 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 L4 and L5 exist, that these orbits have small components out of the plane of the Earth-Moon system, and that they are at most mildly unstable.
Book 4
Dynamics And Mission Design Near Libration Points, Vol Iii: Advanced Methods For Collinear Points
by Gerard Gomez, Angel Jorba, Josep J Masdemont, and Carles Simo
Published 12 February 2001
This book studies several problems related to the analysis of planned or possible spacecraft missions. It is divided into four chapters. The first chapter is devoted to the computation of quasiperiodic solutions for the motion of a spacecraft near the equilateral points of the Earth-Moon system. The second chapter gives a complete description of the orbits near the collinear point, L1, between the Earth and the Sun in the restricted three-body problem (RTBP) model. In the third chapter, methods are developed to compute the nominal orbit and to design and test the control strategy for the quasiperiodic halo orbits. In the last chapter, the transfer from the Earth to a halo orbit is studied.
Book 5
Dynamics And Mission Design Near Libration Points, Vol Iv: Advanced Methods For Triangular Points
by Gerard Gomez, Angel Jorba, Josep J Masdemont, and Carles Simo
Published 12 February 2001
The aim of this book is to explain, analyze and compute the kinds of motions that appear in an extended vicinity of the geometrically defined equilateral points of the Earth-Moon system, as a source of possible nominal orbits for future space missions. The methodology developed here is not specific to astrodynamics problems. The techniques are developed in such a way that they can be used to study problems that can be modeled by dynamical systems.
Dynamics and Mission Design Near Libration Points
by Gerard Gomez, A Jorba, C Simo, and J Masdemont
Published 30 November 2000
In this book the problem of station keeping is studied for orbits near libration points in the solar system. The main focus is on orbits near halo ones in the (Earth+Moon)-Sun system. Taking as starting point the restricted three-body problem, the motion in the full solar system is considered as a perturbation of this simplified model. All the study is done with enough generality to allow easy application to other primary-secondary systems as a simple extension of the analytical and numerical computations.