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E-raamat: Optimal Spacecraft Trajectories

John E. Prussing (Professor Emeritus of Aerospace Engineering, University of Illinois)

Formaat: 144 pages
Ilmumisaeg: 14-Dec-2017
Kirjastus: Oxford University Press
Keel: eng
ISBN-13: 9780192539199

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Formaat: 144 pages
Ilmumisaeg: 14-Dec-2017
Kirjastus: Oxford University Press
Keel: eng
ISBN-13: 9780192539199

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This graduate textbook on optimal spacecraft trajectories demonstrates the theory and applications of using the minimum amount of propellant possible to reach a target destination. The author aims to produce the only comprehensive treatment of various aspects of this topic. It includes problems at the ends of the chapters and some of the appendices. But it is also suitable as a scholarly reference book as it includes recent research from the author and his colleagues.

Introduction

(3)

1 Parameter Optimization

(9)

1.1 Unconstrained parameter optimization

(2)

1.2 Parameter optimization with equality constraints

(3)

1.2.1 Lagrange multipliers

(3)

1.3 Parameter optimization with an inequality constraint

(4)

Problems

(1)

Reference

(1)

2 Rocket Trajectories

(6)

2.1 Equations of motion

(1)

2.2 High-thrust and low-thrust engines

(1)

2.3 Constant-specific-impulse (CSI) and variable-specific-impulse (VSI) engines

(5)

Problems

(1)

Reference

(1)

3 Optimal Control Theory

(13)

3.1 Equation of motion and cost functional

(2)

3.2 General problem

(6)

3.3 Terminal constraints and unspecified final time

(2)

3.4 Pontryagin minimum principle

(3)

Problems

(1)

References

(1)

4 Optimal Trajectories

(10)

4.1 Optimal constant-specific-impulse trajectory

(4)

4.2 Optimal impulsive trajectory

(1)

4.3 Optimal variable-specific-impulse trajectory

(2)

4.4 Solution to the primer vector equation

(1)

4.5 A vector constant

(2)

Problems

(1)

References

(1)

5 Improving a Nonoptimal Impulsive Trajectory

(24)

5.1 Fixed-time-impulsive rendezvous

(18)

5.1.1 Criterion for a terminal coast

(8)

5.1.2 Criterion for addition of a midcourse impulse

(4)

5.1.3 Iteration on the midcourse impulse position and time

(4)

5.2 Fixed-time impulsive orbit transfer

(6)

5.2.1 Circular terminal orbits

(2)

Problems

(1)

References

(1)

6 Continuous-Thrust Trajectories

(7)

6.1 Quasi-circular orbit transfer

(3)

6.2 The effects of non-constant mass

(1)

6.3 Optimal quasi-circular orbit transfer

(4)

Problems

(1)

References

(1)

7 Cooperative Rendezvous

(11)

7.1 Continuous thrust cooperative rendezvous

(5)

7.1.1 The CSI case

(3)

7.1.2 The VSI case

(1)

7.2 Impulsive cooperative terminal maneuvers

(6)

Problems

(1)

References

(1)

8 Second-Order Conditions

(17)

8.1 Second-order NC and SC for a parameter optimization

(1)

8.2 The second variation in an optimal control problem

(3)

8.3 Review of the linear-quadratic problem

(3)

8.4 Second-order NC and SC for an optimal control problem

(1)

8.5 Conjugate point test procedure

(3)

8.5.1 Single terminal constraint (q = 0)

(1)

8.5.2 Multiple terminal constraints (q > 0)

(1)

8.6 Computational procedure

(7)

Problems

(1)

References

(3)

A Lagrange Multiplier Interpretation

101

(2)

B Hohmann Transfer

103

(8)

B.1 Constrained parameter optimization

103

(3)

B.2 Simple proof of global optimality

106

(5)

Problems

109

(1)

References

110

(1)

C Optimal Impulsive Linear Systems

111

(7)

C.1 Sufficient conditions for an optimal solution

111

(2)

C.2 Maximum number of impulses

113

(5)

References

117

(1)

D Linear System Theory

118

(6)

D.1 Homogeneous case

118

(4)

D.2 Inhomogeneous case

122

(2)

Problems

123

(1)

Reference

123

(1)

E Maximum Range Using Continuous Thrust in a Uniform Gravitational Field

124

(5)

Reference

128

(1)

F Quadratic Forms

129

(2)

F.1 Matrix symmetry

129

(1)

F.2 The derivative of a quadratic form

130

(1)

G Simple Conjugate Point Example

131

(6)

Reference

135

(2)

Index

137

John Prussing is Professor Emeritus of Aerospace Engineering at the University of Illnois at Urbana-Champaign. He holds a SB, SM and a ScD in 1967 in aerospace engineering all from MIT, and served as professor of aerospace engineering between 1969 and 2007, and continues to teach part time, including short courses at NASA. He has published over 80 articles and has authored/co-authored three books.

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