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E-raamat: Applied Nonsingular Astrodynamics: Optimal Low-Thrust Orbit Transfer

  • Formaat: EPUB+DRM
  • Sari: Cambridge Aerospace Series
  • Ilmumisaeg: 16-Aug-2018
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108576758
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Applied Nonsingular Astrodynamics: Optimal Low-Thrust Orbit TransferSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Cambridge Aerospace Series
  • Ilmumisaeg: 16-Aug-2018
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108576758
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This essential book describes the mathematical formulations and subsequent computer simulations required to accurately project the trajectory of spacecraft and rockets in space, using the formalism of optimal control for minimum-time transfer in general elliptic orbit. The material will aid research students in aerospace engineering, as well as practitioners in the field of spaceflight dynamics, in developing simulation software to carry out trade studies useful in vehicle and mission design. It will teach readers to develop flight software for operational applications in autonomous mode, so to actually transfer space vehicles from one orbit to another. The practical, real-life applications discussed will give readers a clear understanding of the mathematics of orbit transfer, allow them to develop their own operational software to fly missions, and to use the contents as a research tool to carry out even more complex analyses.

This unique book provides readers with a clear understanding of the mathematics of orbit transfer while allowing them to develop their own operational software to fly actual missions, and to use the contents as a research tool to carry out even more complex analyses. It also covers a number of practical, real-life applications.

Arvustused

'This book represents a lifetime of valuable contributions to optimal low-thrust orbit transfer.' John E. Prussing, University of Illinois 'This is a book for specialists in orbital dynamics, authored by one of the leading current practitioners in the field. Its subtitle, 'Optimal Low-thrust Orbit Transfer' reflects one of the principal technical drivers behind the book, namely that an increasing number of satellites in Earth orbit are now using more fuel-efficient ion thrusters which have far lower thrust-levels than their chemically-propelled predecessors. As a consequence, there is an increasing need to optimise the longer trajectories - both in terms of time and distance travelled - that result from the use of this technology.' Stuart Eves, The Aeronautical Journal

Muu info

This essential book is the first comprehensive exposition in the area of optimal low-thrust orbit transfer using non-singular variables.
Preface xiii
Nomenclature xvi
1 The Fundamental Classic Analysis of Edelbaum, Sackett and Malchow, with Additional Detailed Derivations and Extensions 1(49)
1.1 Introduction
1(2)
1.2 The Technique of Averaging
3(1)
1.3 Summary of the Mechanics of the Equinoctial Orbit Elements
4(4)
1.4 The Equations of Motion
8(2)
1.5 The Averaged State and Costate Differential Equations for the Thrust-Constrained Case u is independent of r
10(3)
1.6 A Discussion of the Zero Roll and Zero Pitch Case and the Maximization of the Solar Panels' Power Output
13(3)
1.7 The Analysis of the Zero Roll Constraint with Otherwise Free Pitch and Free Yaw
16(9)
1.8 The Perturbations Due to the Oblateness of the Earth
25(2)
1.9 The Flux Model of SECKSPOT and the Augmented State and Adjoint Equations
27(4)
1.10 The Calculations of the Thrust Angle, the Panel Orientation Angle, the Sun Incidence Angle on the Panel, and the Three Sides of the Spacecraft Body, in SECKSPOT
31(4)
1.11 Examples of Minimum-Time Transfers from LEO to GEO
35(4)
1.12 A Discussion of the SECKSPOT Software Capabilities and Limitations
39(10)
References
49(1)
2 The Analysis of the Six-Element Formulation 50(52)
2.1 Introduction
50(1)
2.2 The Edelbaum Low-Thrust Orbit Transfer Problem
50(16)
2.3 The Full Six-State Formulation Using Nonsingular Equinoctial Orbit Elements
66(17)
2.4 Orbit Transfer with Continuous Constant Acceleration
83(18)
References
101(1)
3 Optimal Low-Thrust Rendezvous Using Equinoctial Orbit Elements 102(33)
3.1 Introduction to the Minimum-Time Rendezvous Problem
102(1)
3.2 The Differential Equations in Terms of the Equinoctial Elements
103(3)
3.3 The Euler-Lagrange Differential Equations
106(3)
3.4 Numerical Results
109(3)
3.5 Summary of the Minimum-Time Rendezvous Problem
112(1)
3.6 Minimum-Fuel Time-Fixed Rendezvous Using Constant Low-Thrust
113(1)
3.7 Introduction to the Minimum-Fuel Rendezvous Problem
114(3)
3.8 The Dynamic Equations for the Seven State Variables
117(2)
3.9 The Euler-Lagrange Differential Equations
119(3)
3.10 Examples
122(3)
3.11 Conclusion
125(1)
Appendix 3.1 The Partials of the M Matrix
126(7)
References
133(2)
4 Optimal Low-Thrust Transfer Using Variable Bounded Thrust 135(19)
4.1 Introduction
135(1)
4.2 The Optimization of the Thrust Magnitude
136(9)
4.3 A Simple Example of Rendezvous in Near-Circular Orbit
145(5)
4.4 Conclusion
150(3)
References
153(1)
5 Minimum-Time Low-Thrust Rendezvous and Transfer Using Epoch Mean Longitude Formulation 154(26)
5.1 Introduction
154(1)
5.2 The Equations of Motion for the Epoch Mean Longitude Formulation
155(5)
5.3 The Variational Hamiltonian
160(2)
5.4 Canonical Transformations
162(6)
5.5 Boundary Conditions for Minimum-Time Rendezvous and Example of a Free-Free Minimum-Time Transfer
168(2)
5.6 Conclusion
170(4)
Appendix 5.1 The Nonzero Partials of Matrix M
174(4)
References
178(2)
6 Trajectory Optimization Using Eccentric Longitude Formulation 180(22)
6.1 Introduction
180(1)
6.2 Equations of Motion in Terms of the Eccentric Longitude
181(7)
6.3 Numerical Example
188(3)
6.4 Conclusion
191(1)
Appendix 6.1 The partial dirivative M/partial dirivative z Partial Derivatives
192(5)
Appendix 6.2 The partial dirivative MF/partial dirivative z Partial Derivatives
197(3)
References
200(2)
7 Low-Thrust Trajectory Optimization Based on Epoch Eccentric Longitude Formulation 202(25)
7.1 Introduction
202(2)
7.2 System and Adjoint Differential Equations for the Epoch Eccentric Longitude Formulation
204(9)
7.3 Transversality Condition for Minimum-Time Rendezvous and Examples of Free-Free Minimum-Time Transfer
213(7)
7.4 Conclusion
220(1)
Appendix 7.1 Partial Derivatives of MF0 Matrix with Respect to Orbit Elements
220(5)
References
225(2)
8 Mechanics of Trajectory Optimization Using Nonsingular Variational Equations in Polar Coordinates 227(16)
8.1 Introduction
227(1)
8.2 Dynamic and Adjoint Differential Equations in Polar Coordinates
228(8)
8.3 Numerical Example
236(1)
8.4 Conclusion
237(1)
Appendix 8.1 The B Matrix and its Partial Derivatives
237(5)
References
242(1)
9 Trajectory Optimization Using Nonsingular Orbital Elements and True Longitude 243(17)
9.1 Introduction
243(1)
9.2 Equations of Motion with the True Longitude as the Sixth State Variable
244(6)
9.3 Numerical Results
250(4)
9.4 Conclusion
254(1)
Appendix 9.1 The BL Matrix and its Partial Derivatives
255(4)
References
259(1)
10 The Treatment of the Earth Oblateness Effect in Trajectory Optimization in Equinoctial Coordinates 260(21)
10.1 Introduction
260(1)
10.2 Resolution of the J2 Acceleration in Terms of the Equinoctial Elements
261(4)
10.3 Minimum-Time Transfer Around the Oblate Earth
265(4)
10.4 The Thrust and J2-Perturbed Averaged Dynamic and Adjoint System of Equations
269(5)
10.5 Numerical Example
274(4)
10.6 Conclusion
278(2)
References
280(1)
11 Minimum-Time Constant Acceleration Orbit Transfer with First-Order Oblateness Effect 281(23)
11.1 Introduction
281(1)
11.2 The Analysis of the Second Zonal Perturbation Effect in Minimum-Time Low-Thrust Transfers
282(13)
11.3 The Averaged Rates of the Elements Due to J2 and Their Partial Derivatives
295(7)
11.4 Conclusion
302(1)
References
303(1)
12 The Streamlined and Complete Set of the Nonsingular J2-Perturbed Dynamic and Adjoint Equations for Trajectory Optimization in Terms of Eccentric Longitude 304(24)
12.1 Introduction
304(2)
12.2 System and Adjoint Differential Equations in Terms of the Eccentric Longitude
306(13)
12.3 Accounting of the J2 Perturbation
319(6)
12.4 Conclusion
325(1)
References
326(2)
13 The Inclusion of the Higher-Order Harmonics in the Modeling of Optimal Low-Thrust Orbit Transfer 328(33)
13.1 Introduction
328(2)
13.2 Zonal Harmonics Perturbation Acceleration Components in the Euler-Hill Frame
330(2)
13.3 The Treatment of the J3, J4 Perturbations within the Eccentric Longitude Formulation
332(13)
13.4 The Treatment of the J3, J4 Perturbations within the True Longitude Formulation
345(8)
13.5 Numerical Results
353(4)
13.6 Conclusion
357(1)
Appendix 13.1 Transformation of the J3, J4 Inertial Accelerations to the Rotating Frame
358(1)
References
359(2)
14 Analytic Expansions of Luni-Solar Gravity Perturbations Along Rotating Axes for Trajectory Optimization: The Dynamic System 361(30)
14.1 Introduction
361(1)
14.2 Solar Gravity Perturbation Acceleration Components in the Euler-Hill Frame
362(8)
14.3 Lunar Gravity Perturbation Acceleration Components in the Euler-Hill Frame
370(4)
14.4 The Use of de Pontecoulant's Lunar Theory
374(3)
14.5 Numerical Results
377(6)
14.6 Conclusion
383(6)
References
389(2)
15 Analytic Expansions of Luni-Solar Gravity Perturbations Along Rotating Axes for Trajectory Optimization: The Multipliers System and Simulations 391(33)
15.1 Introduction
391(1)
15.2 The Hamiltonian and Euler-Lagrange Equations
392(7)
15.3 The partial derivative f sun/partial derivative z Partial Derivatives for the Solar Gravity
399(2)
15.4 The partial derivative f moon/partial derivative z Partial Derivatives for the Lunar Gravity
401(3)
15.5 Transfer Simulations
404(6)
15.6 Conclusion
410(1)
Appendix 15.1 The Partial Derivatives fsr, fs0 and fsh
410(13)
References
423(1)
16 Fourth-Order Expansions of the Luni-Solar Gravity Perturbations along Rotating Axes for Trajectory Optimization 424(34)
16.1 Introduction
424(1)
16.2 The Extension to Fourth Order of the Luni-Solar Gravity Perturbation Accelerations
425(6)
16.3 Transfer Examples
431(15)
16.4 Conclusion
446(1)
Appendix 16.1 The Partial Derivatives of (fsr)4, (fs0)4 and (fsh)4
446(11)
References
457(1)
Index 458
Jean Albert Kéchichian is a retired Engineering Specialist from The Aerospace Corporation. His career has included senior level engineering positions at NASA's Jet Propulsion Laboratory and at Ford Aerospace. His main areas of contribution are in spaceflight guidance and navigation. He is a Fellow of The American Astronautical Society, and his work has regularly appeared in Acta Astronautica, the Journal of Guidance Control and Dynamics, the Journal of the Astronautical Sciences, and the Journal of Spacecraft and Rockets. He holds Degrees in Aeronautical and Mechanical Engineering from l'Université de Liège, University of California, Berkeley, and a Ph.D. in Aeronautics and Astronautics from Stanford University.
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