guidance, flight mechanics and trajectory optimization

110
2.1
2.1.1
2.1.2
2.1.3
2.1.3.1
2.1.3.2
2.1.4
2.1.4.1
2.1.4.2
2.1.4.2.1
2.1.4.2.2
2.1.5
2.1.6
2.2
2.2.1
2.2.1.1
2.2.1.2
2.2.2
2.2.3
2.2.4
2.2.4.1
2.2.4.2
2.2.4.3
2.2.4.4
2.2.4.5
2.2.4.6
2.3
2.4
2.4.1
2.4.2
2.4.3
2.4.3.1
2.4.3.2
3.0
TABLE OF CONTENTS
Page
STATEMENT OF THE PROBLEM. ...............
Equations of Motion. ...............
Coordinate Systems ................ 4
Field Free Case. ................. 6
Approximate Equations. ..............
Angular Forms of the Equations .......... ::
Distance Forms of the Equations. ......... 10
Solutions to the Equations of Motion ....... 13
The Out-of-Plane ................. 13
The In-Plane Motion. ............... 16
in-Plane Motion for Circular Target Orbit. .... i6
In-Plane Motion for Elliptical Target Orbits ... 21
Approximate Second Order Solutions ........ 22
The Effects of Perturbations on Rendezvous ....
Guidance Equations ................ ;:
Fixed Inertial Line of Sight (LOS) - Free Space. .
Manual Rendezvous Guidance ............ ;:
Separation of Guidance-Navigation Tasks. .....
Coriolis Balance ................. ;i
Improved Model - The Inclusion of a Gravity
Gradient .................... 37
Impulsive Rendezvous Techniques. ......... 39
Approximating Velocity Impulses. ......... 39
Two Impulse Rendezvous .............. 41
Extension to Non-Circular Orbits ......... 43
Multiple Impulse Rendezvous. ...........
Second Order Improvement ............. z
Direct Calculation using Two-Body Orbits ..... 48
Proportional Guidance. .............. 53
Optimization of the Rendezvous Maneuver. ..... 56
Optimal Stepwise Thrusting ............ 58
Optimum Power Limited Rendezvous ......... 71
Optimum Continuous Thrust Guidance for the
FinalManeuvers ................. ‘75
Free Space Model ................. 75
Linear Gravity Model ............... 80
RECOMMENDED PROCEDURES. . . . . . . . . . . . . . . . . 84
4.0 REFERENCES....................... 87
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