Modern Astrodynamics

by Gurfil

• ISBN13: 9780123735621
• ISBN10: 0123735629
• Format: Hardcover
• Copyright: 2006-10-19
• Publisher: Elsevier Science

Summary

In recent years, an unprecedented interest in novel and revolutionary space missions has risen out of the advanced NASA and ESA programs. Astrophysicists, astronomers, space systems engineers, mathematicians and scientists have been cooperating to implement novel and ground-breaking space missions. Recent progress in mathematical dynamics has enabled development of specialised spacecraft orbits and propulsion systems. Recently, the concept of flying spacecraft in formation has gained a lot of interest within the community. These progresses constitute the background to a significant renaissance of research dealing with astrodynamics and its applications. Modern Astrodynamics is designed as a stepping stone for the exposition of modern astrodynamics to students, researchers, engineers and scientists. This volume will present the main constituents of the astrodynamical science in an elaborate, comprehensive and rigorous manner. Although the volume will contain a few distinct chapters, it will render a coherent portrayal of astrodynamics. * encompasses the main constituents of the astrodynamical sciences in an elaborate, comprehensive and rigorous manner * presents recent astrodynamical advances and describes the challenges ahead * the first volume of a series designed to give scientists and engineers worldwide an opportunity to publish their works in this multi-disciplinary field

Table of Contents

Foreword	ix
Introduction	xi
Perturbed Motion	1	(22)
David A. Vallado
Basic definitions	1	(2)
Forces	3	(1)
Gravity	4	(3)
Drag	7	(5)
3-Body	12	(1)
Solar radiation pressure	12	(1)
Tides	13	(1)
Albedo	14	(1)
Other	14	(1)
Propagating the orbit	15	(1)
Analytical	15	(1)
Numerical	15	(1)
Semianalytical	16	(1)
Variation of parameters	16	(1)
Lagrangian VOP---conservative forces	17	(1)
Gaussian VOP---nonconservative forces	18	(1)
Effect on orbits	19	(1)
J2 Only	19	(1)
Comparative force model effects	20	(1)
Conclusions	21	(2)
References	21	(2)
Gauge Freedom in Astrodynamics	23	(30)
Michael Efroimsky
Introduction	23	(11)
Gauge freedom in the theory of orbits	34	(5)
A practical example on gauges: a satellite orbiting a precessing oblate planet	39	(9)
Conclusions: how we benefit from the gauge freedom	48	(5)
Appendix 1. Mathematical formalities: Orbital dynamics in the normal form of Cauchy	49	(1)
Appendix 2. Precession of the equator of date relative to the equator of epoch	50	(1)
References	51	(2)
Solving Two-Point Boundary Value Problems Using Generating Functions: Theory and Applications to Astrodynamics	53	(54)
Vincent M. Guibout
Daniel J. Scheeres
Introduction	53	(3)
Solving two-point boundary value problems	56	(18)
Hamilton's principal function	74	(3)
Local solutions of the Hamilton-Jacobi equation	77	(13)
Applications	90	(8)
Conclusions	98	(9)
Appendix A. The Hamilton-Jacobi equation at higher orders	99	(3)
Appendix B. The Hill three-body problem	102	(2)
References	104	(3)
Low-Energy Transfers and Applications	107	(20)
Edward Belbruno
Introduction	107	(1)
Capture problem, models, and transfer types	108	(4)
Ballistic capture regions and transfers	112	(8)
Chaos and weak capture	120	(3)
Origin of the Moon	123	(4)
References	125	(2)
Set Oriented Numerical Methods in Space Mission Design	127	(28)
Michael Dellnitz
Oliver Junge
Introduction	127	(1)
Dynamical systems and mission design	127	(3)
Set oriented numerics	130	(5)
Computing invariant manifolds	135	(4)
Detecting connecting orbits	139	(6)
Extension to controlled systems	145	(6)
Conclusion	151	(4)
References	151	(4)
Space Trajectory Optimization and L1-Optimal Control Problems	155	(34)
J. Michael Ross
Introduction	155	(3)
Geometry and the mass flow equations	158	(2)
Cost functions and Lebesgue norms	160	(4)
Double integrator example	164	(6)
Issues in solving nonlinear L1 -optimal control problems	170	(5)
Solving nonlinear L1-optimal control problems	175	(4)
L1-Formulation of the minimum-fuel orbit transfer problem	179	(2)
A simple extension to distributed space systems	181	(4)
Conclusions	185	(4)
References	186	(3)
Orbital Mechanics of Propellantless Propulsion Systems	189	(48)
Colin R. McInnes
Matthew P. Cartmell
Introduction	189	(1)
Solar sailing	190	(5)
Solar sail orbital mechanics	195	(3)
Artificial three-body equilibria for solar sails	198	(5)
Mission applications	203	(5)
Tethers in space	208	(9)
Tethers in orbit	217	(15)
Conclusions	232	(5)
References	233	(4)
Cooperative Spacecraft Formation Flying: Model Predictive Control with Open- and Closed-Loop Robustness	237	(42)
Louis Breger
Gokhan Inalhan
Michael Tillerson
Jonathan P. How
Introduction	237	(2)
Dynamics of formation flight	239	(4)
Formation flight control and the model predictive control formulation	243	(6)
Distributed coordination through virtual center	249	(11)
Open loop robust control and replan frequency	260	(5)
Using closed-loop robust MPC	265	(8)
Conclusions	273	(1)
Nomenclature	274	(5)
References	274	(5)
Index	279