Fundamentals : the case of triangular libration points
著者
書誌事項
Fundamentals : the case of triangular libration points
（World scientific monograph series in mathematics, v. 2-3 . Dynamics and mission design near libration points ; vol. 1-2）
World Scientific, 2000-2001
- vol. 1
- vol. 2
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注記
Includes bibliographical references
内容説明・目次
- 巻冊次
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vol. 2 ISBN 9789810242749
内容説明
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, μ1. 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.
目次
- 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.
- 巻冊次
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vol. 1 ISBN 9789810242855
内容説明
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.
目次
- Part 1 Halo orbits: analytical and numerical study
- the neighbourhood of the halo orbits - numerical study and applications. Part 2 Analytical solution of the variational equations: analytical computations of the control parameters
- the equations of motion for halo orbits under the effect of perturbations and near triangular points. Part 3 Expansions required for the equations of motion: collinear points case
- the quasi-periodic orbits - equations, method of solution and results
- numerical refinement of the quasi-periodic orbit - the final numerical determination of the orbit and of the projection factors
- the on/off control strategy - simulations and discussion
- other cases and further simulations
- summary and outlook.
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