guidance, flight mechanics and trajectory optimization

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1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.1 2.2 2.3 2.4 2.5 4.0 REFERENCES Townsend, G. E., et. al. _ State Determination. and/or Estimation. NAA S&ID, SID 65-1200-5 (28 Feb. 1966). Anthony, M. L. and Sosaki, F. T., Rendezvous Problem for Searlx Circular Orbits. AIAA Journal 3, (1965) p 1666-1673. Leach, R., Matrix Derivation of a Short Term Linear Rendezvous ----- Equation. AIAA Journal 1, (1963) p 1420-1421 Tschauner, J. and Hempel, P. , Optimal Beschleunigungsprogramme fur das Rendezvous-Manover. Astronautica Acta 10 (1964) p 246-307 Tschauner, J. and Hempel, P., Rendezvous zu einem in elliptischer Bahn Umlaufenden Ziel., -- Astronautica Acta 11 (196.5) p 104-109 Tschauner, J., Neue Darstellung des Rendezvous bei Elliptischer Zielbahn. Astronautica Acta 11 (1965) p 312-321 London, H. S., Seconds Approximation to the Solution of Rendezvous Equations. hm AIAA Journal (1963) p 1691 devries; J. P., Elliptic Elements in Terms of Small Increments of Position and Velocity Components. AIXA Journal (1963) p 2626 Kochi, K. C., An Introduction to Midcourse Navigation-Guidance -.--_ Autonetics Document. EM262-265 Section 8 (October 1962) Clohessy, ',i. II., and !:iltshire, R. S., Terminal Guidance System for Satellite Hendezvous. Journal of Aerospace Science, Vol 27 (1960) pages 6.53-658 Chamberlin, J. A., and Rose, J. T., Gemini Rendezvous Program. Journal of Spacecraft and Rockets, Vol 1, No 1 (January 1964) Burton, J. R., and Hayes, 5. E., Gemini Rendezvous, Paper 64-641 AIAA/ION Astrodynamics, Guidance and Control Conference, Los Angeles, California (August 1964) Steffan, K. F., A Satellite Rendezvous Terminal System, Paper 1494-60, ARS 15th Annual Meeting, blashington D. C., (December 1960) Nason, M. L., A Terminal Guidance Law which Achieves Collision Based on Coriolis Balance Technique, Preprint 6140, AAS Seventh Annual Meeting, Dallas, Texas (January 1961) 87 -
2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.11+ 2.15 2.16 2.17 4.1 4.2 4.3 4.4 Kliger, I. E., A Dual Phase Plane Approach tc the Two-Finite-Burns ---___- -_--. -- ___ Kinimum Fuel Rendezvous Problem. Paper 65, AAS Southeastern Symposium on Kissiles and Aerospace Vehicle Sciences, Huntsville, Alabama (December 1966) Gunckel, T. L., Near Earth Rendezvous Guidance Tech@-, NAA Autonetics X6-2411/501 (September 1?66) Gunckel, T. L., Preliminary Guidance and NaviPation Study-for Apollo -A ..-- Lunar Orbit Rendezvous. NAA Autonetics EM 262-210A (Kay 1963) Kuller, E. S., and Sears, ?I. E., Preliminary ~G&I\I Rendezvous ._..-_ -_-___- Guidance Eauations, KIT Instrumentation_LaGatorx, SGA 2-64 (January l96/,) Sears, N. E. and Felleman, P. G., Terminal Guidance for a Satellite -2-L-- ---.- Rendezvous, ARS Controllable Satellite Conference. Paper 778-59 (Pi.1.T. (1959) EhiipirO, 1.1. , iin Attenuated Intercept - -_- Satellite -. __--.__ Rendezvous ~-- System, IAS-ARS Joint Keeting Paper 61-155-1849 (June 1.961) Bonomo, P. J. and Schlegel, L. B., ----- Determination of Orbital Rendezvous Requirements-ii Second ___ Order Improvement, ;‘IAS Space Fii.g~lt re I'_echanics Specialist Conference Paper 66-135 (July 1966) Tomsend, Cr. C. and Tamburro, I Lawden, D., Optional Tra,jectories for Sp ace Xavi,yation Buttcrworths .-- (1963) Breakwell, J., Minimum Impulse Transfer, AIM Preprint 63-~16 AIAA Astrodynamic Conference, Yale University (1.963) Contensor, P., Etude Theoretioue des Tra,jcctories Or&imalcs dans an - Champ de Gravitation, Application au Gas d'un Centre d'Al.tfraction Unique Astion, ;icta 8 (1962) p 134 I':cClue, G. 11., Optimum Two-Impulse Orbital Transfer --PI-- and Rendezvous Between Inclined ---.- Elliptical --- Orbits --- AIAA J 1 (1?63) p 1965-1872 88
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NASA CONTRA REPORT CTOR GUIDANCE, F
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- ..a --.
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_- .-- --- I
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110 2.1 2.1.1 2.1.2 2.1.3 2.1.3.1 2
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. 0 i time difference between a ref
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only line-of-sight thrusting is use
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2.0 STATE-OF-THE-ART The significan
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Thus in cylindrical coordinates, th
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In this form the equations are vali
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For all the equations given to this
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of inertial directions which are ta
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which form the columns of F must be
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Thus, the solution is written The t
Page 29 and 30:
This matrix is simply written as G(
Page 31 and 32:
The fundamental matrix for A can be
Page 33 and 34:
2.1.5 Approximate Second Order Solu
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where the superscript p can be eith
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w” 2 E IOOJ- -100 - 200 AV = 400
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cause a significant effect for rend
Page 43 and 44:
Figure 2.1 Polar Coordinate System
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. will attain, z , can be calculate
Page 47 and 48: This equation may now be solved for
Page 49 and 50: If the matrix 121 model discussed'&
Page 51 and 52: One method which can be employed (a
Page 53 and 54: If a collision is to occur at time
Page 55 and 56: The solution to these equations are
Page 57 and 58: Fixed Range: Range-Rate Schedule Ra
Page 59 and 60: The velocity correction, SVtO) repr
Page 61 and 62: (2.17) The solutions of all of thes
Page 63 and 64: I(7) I COMPUTE c (7) =- MISS g-r -1
Page 65 and 66: 0 MOO0 60000 il 20& 40&o hod00 Y (f
Page 67 and 68: Manipulation of the equations invol
Page 69 and 70: 2.4.1 Optimal Stepwise Thrusting As
Page 71 and 72: Note that if it, can occur, this sc
Page 73 and 74: where F (Q) is the matrix given by
Page 75 and 76: where Since 0 and Eq. 4.23 shows th
Page 77 and 78: In contrast, the fuel optimal probl
Page 79 and 80: significantly reducing the out-of-p
Page 81 and 82: Figure 4.3 Velocity Increments to R
Page 83 and 84: If it is assumed that 4~ is constan
Page 85 and 86: Examples of the effectiveness of th
Page 87 and 88: performed using the Pontryagin Maxi
Page 89 and 90: This equation gives the optimum ste
Page 91 and 92: where 2((t) is given by the first e
Page 93 and 94: Cd&t- d&J dt I where Xc9 #II 2 % 9
Page 95 and 96: 3.0 RECOMMENDED PROCEDURES In the p
Page 97: For the guidance technique which nu
Page 101: 4.20 Bakalyar, G., Continuous Thrus
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