| Description |
1 online resource (1 volume) : illustrations |
| Series |
World scientific monograph series in mathematics ; vol. 2 |
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World Scientific monograph series in mathematics ; v. 2.
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| Contents |
Introduction: libration points and station keeping. 0.1. The neighborhood of libration points as a useful place for spacecrafts. 0.2. Station keeping of libration point orbits -- ch. 1. Bibliographical survey. 1.1. Numerical results for three-dimensional periodic orbits around L1, L2 and L3. 1.2. Analytic results for halo orbits associated to L1, L2 and L3. 1.3. Motion near L4 and L5. 1.4. Station keeping -- ch. 2. Halo orbits. Analytic and numerical study. 2.1. The restricted three-body problem. 2.2. Analytic determination of the families of halo orbits for the restricted three-body problem. 2.3. Numerical determination of the families of halo orbits for the RTBP. Analysis of bifurcations and terminations. 2.4. References -- ch. 3. The neighborhood of the halo orbits: numerical study and applications. 3.1. Numerical study of the local invariant manifolds. 3.2. The proposed method for the on/off control. 3.3. On the use of solar radiation pressure for station keeping. 3.4. Globalization of the invariant manifolds. 3.5. References -- ch. 4. Analytic solution of the variational equations. Analytic computations for control parameters. 4.1. Analytic solution of the variational equations. 4.2. Analytic computations for control parameters. 4.3. References -- ch. 5. The equations of motion for halo orbits under the effect of perturbations and near triangular points. 5.1. Analysis of the perturbations. 5.2. Equations of motion for perturbed halo orbits. 5.3. Equations of motion near the triangular points. 5.4. Numerical tests of the equations of motion. 5.5. References |
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Ch. 6. Expansions required for the equations of motion. Collinear points case. 6.1. Analytic expansion of the coefficients due to the noncircular motion of the Earth-Moon barycenter. 6.2. Preliminary exploration of the functions to be kept. 6.3. Computation of the approximate frequencies and magnitudes of the perturbations using FFT. 6.4. The final computation of the perturbing terms. 6.5. References -- ch. 7. The quasi-periodic orbits: equations, method of solution and results. 7.1. The final equations of motion for the collinear case. 7.2. The method of solution of the equations for the quasi-periodic orbit. 7.3. The results. Problems related to small divisors. 7.4. References -- ch. 8. Numerical refinement of the quasi-periodic orbit: the final numerical determination of the orbit and of the projection factors. 8.1. A parallel shooting method for the numerical refinement of the quasiperiodic orbit. 8.2. The final nominal orbit and projection factors. 8.3. References -- ch. 9. The on/off control strategy: simulations and discussion. 9.1. A simulation program for the motion of the controlled spacecraft. 9.2. Numerical results of the simulations. 9.3. The feasibility of the control using solar radiation pressure -- ch. 10. Other cases and further simulations. 10.1. The L3 case for the Sun-barycenter problem. 10.2. The L3 case for the Earth-Moon problem. 10.3. The triangular cases for the Sun-barycenter problem. 10.4. Simulations for the triangular cases in the Earth-Moon problem. 10.5. References -- ch. 11. Summary and outlook. 11.1. Summary of the achieved results. 11.2. Possible extensions of the work. 11.3. Theoretical problems |
| Summary |
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 |
| Bibliography |
Includes bibliographical references |
| Notes |
Print version record |
| Subject |
Three-body problem.
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Lagrangian points.
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SCIENCE -- Astronomy.
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Lagrangian points
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Three-body problem
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Sistemas dinâmicos.
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Problemas de n-corpos.
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Estabilidade.
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Sistemas hamiltonianos.
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Métodos de perturbação (sistemas dinâmicos)
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| Form |
Electronic book
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| Author |
Gómez, G. (Gerard)
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| ISBN |
9789812810632 |
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9812810633 |
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