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El. knyga: Analytical Solutions for Extremal Space Trajectories

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(Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, HI)
  • Formatas: EPUB+DRM
  • Išleidimo metai: 23-Aug-2017
  • Leidėjas: Butterworth-Heinemann Inc
  • Kalba: eng
  • ISBN-13: 9780128140598
Kitos knygos pagal šią temą:
Analytical Solutions for Extremal Space TrajectoriesDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 23-Aug-2017
  • Leidėjas: Butterworth-Heinemann Inc
  • Kalba: eng
  • ISBN-13: 9780128140598
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Analytical Solutions for Extremal Space Trajectories presents an overall treatment of the general optimal control problem, and in particular, the Mayer’s variational problem, with necessary and sufficient conditions of optimality. It also provides a detailed derivation of the analytical solutions of these problems for thrust arcs for the Newtonian, linear central and uniform gravitational fields. These solutions are then used to analytically synthesize the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers. Many numerical examples utilizing the proposed analytical synthesis of the space trajectories along with comparison analysis with numerically integrated solutions are provided.

This book can be helpful for engineers and researchers of industrial and government organizations, and university faculty and graduate and undergraduate students working, specializing or majoring in the fields of aerospace engineering, applied celestial mechanics, and guidance, navigation and control technologies, applied mathematics and analytical dynamics as well as avionics software design and development.

  • Features an analyses of Pontryagin extremals and/or Pontryagin minimum in the context of space trajectory design
  • Presents the general methodology of an analytical synthesis of the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers
  • Assists in developing the optimal control theory for applications in aerospace technology and space mission design

Daugiau informacijos

A guide to analytical and numerical solutions in space trajectory analysis
Preface xi
1 Introduction
1(20)
1.1 Optimal Trajectories and Space Guidance
1(3)
1.2 Brief Survey of Studies of Optimal Control Problem: Thrust Arcs
4(12)
1.3 General Strategy and Main Challenges
16(1)
1.4 Brief Description of
Chapters
17(4)
2 Optimal and Extremal Trajectories
21(56)
2.1 Optimal Control Problem
21(2)
2.2 Solution Methods
23(2)
2.3 Neighboring Extremals
25(1)
2.4 First Differential of Extended Functional
26(5)
2.5 Maximality or Minimality of Hamiltonian
31(3)
2.6 Weierstrass Necessary Condition
34(1)
2.7 Weak Extremals and Pontryagin Extremals
35(1)
2.8 Advantages of Pontryagin Extremals Over Typical Extremals
36(2)
2.9 Legendre-Clebsch Necessary Condition
38(1)
2.10 Second Differential of Extended Functional
39(2)
2.11 Auxiliary Optimization Problem and Riccatti Equation
41(2)
2.12 Sufficient Conditions
43(4)
2.13 Jacobi Necessary Condition: Conjugate Points and Their Existence
47(2)
2.14 Necessary Condition for the Case When Huu = 0
49(4)
2.15 Extremals With Corner Points
53(7)
2.16 Lawden's Statement of the Mayer's Variational Problem for a Newtonian Gravity Field
60(2)
2.17 An Alternative Statement of the Mayer's Variational Problem
62(12)
2.18 Methodology of Analytical Determination of Optimal and Extremal Trajectories
74(3)
3 Motion With Constant Power and Variable Specific Impulse
77(24)
3.1 Canonical Equations and First Integrals
77(1)
3.2 Circular Trajectories
78(10)
3.3 Spiral Trajectories
88(8)
3.4 Mitigation of Radiation Dose When Passing Through the Earth Radiation Belt
96(5)
4 Motion With Variable Power and Constant Specific Impulse
101(54)
4.1 First Integrals and Invariant Relationships
101(1)
4.2 Spherical Trajectories
102(7)
4.3 Circular Trajectories
109(1)
4.4 Extremals for Maneuvers With Free Final Time
110(23)
4.5 Extremals for Maneuvers With Fixed Final Time
133(4)
4.6 Robbins Necessary Condition
137(3)
4.7 Conjugate Points
140(1)
4.8 Optimality and Applicability of Lawden Spirals
141(4)
4.9 Hamilton-Jacobi Equation for Intermediate Thrust Arcs
145(7)
4.10 Classification of Intermediate Thrust Arcs
152(3)
5 Motion With Constant Power and Constant Specific Impulse
155(16)
5.1 Canonical Equations and First Integrals
155(1)
5.2 Circular Trajectories
156(7)
5.3 System of Equations for Arbitrary Thrust Arcs
163(2)
5.4 Analytical Solutions for Constant Thrust Arcs
165(6)
6 Extremal Trajectories in a Linear Central Field
171(22)
6.1 Approximation of the Newtonian Field by Linear Central Field
171(6)
6.2 Canonical Equations and First Integrals
177(4)
6.3 Analytic Solutions for Maximum Thrust Arcs
181(5)
6.4 First Integrals for Intermediate Thrust Arcs
186(2)
6.5 Analytical Solutions for Intermediate Thrust Arcs
188(5)
7 Extremal Trajectories in a Uniform Gravity Field
193(12)
7.1 Optimal Control Problem for Powered Descent
193(3)
7.2 Lagrange Multipliers and Optimal Control Regimes
196(3)
7.3 Optimal Trajectory Arcs
199(6)
8 Number of Thrust Arcs for Extremal Orbital Transfers
205(18)
8.1 Method of Application of Analytical Solutions for Thrust Arcs
205(10)
8.2 Number of Thrust Arcs on Extremal Trajectory
215(5)
Determination of the Number of Unknowns, N
216(4)
8.3 Main Result and General Conclusion of This Study
220(3)
9 Some Problems of Trajectory Synthesis in the Newtonian Field
223(74)
9.1 Transfer Between Elliptical Orbits via an Intermediate Thrust Arc With Constant Specific Impulse
223(8)
9.2 Transfer From Given Position Into Elliptical Orbit via an Intermediate Thrust Arc With Variable Specific Impulse
231(5)
9.3 Transfer Between Elliptical Orbits via an Intermediate Thrust Arc With Variable Specific Impulse
236(8)
9.4 Turning Elliptical Orbit's Plane via an Intermediate Thrust Arc With Constant Specific Impulse
244(11)
9.5 Transfer Between Circular Orbits via Two Maximum Thrust Arcs With Constant Specific Impulse
255(17)
9.6 Transfer Between Circular and Hyperbolic Orbits via a Maximum Thrust Arc With Constant Specific Impulse
272(12)
9.7 Planetary Descent and Landing Trajectories With Constant Thrust Acceleration
284(4)
9.8 Comparison of Analytical and Numerical Solutions
288(9)
10 Conclusions
297(2)
Appendix
299(2)
Determination of the Radial Component of Primer Vector
299(2)
Nomenclature 301(2)
References 303(10)
Index 313
Dilmurat Azimov has nearly 25 years of experience in the areas of space trajectory optimization, guidance, navigation and control of flight vehicles, and orbit determination using observations. His expertise includes derivation of the analytical solutions for optimal control problems, and their application in mission design and development and implementation of guidance, control and targeting schemes.
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