guidance, flight mechanics and trajectory optimization

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where (= constant rocket motor thrust M =' instantaneous mass = MO - Mt t= direction of rocket thrust referenced to the F./&’ Coordinate Definition Figure 4.8 The solution to this set of equations is 81 1 RJNDEZVOUS VEHICLE
Cd&t- d&J dt I where Xc9 #II 2 % 9 $i are the solutions to the homogeneous equations which are found by applying the transition matrix for circular orbits to the initial conditions x (0) p (0) 2(O) pro, with G(tlOJ given by Equation 1.58, When the approximation for a^ (Equation 4.41) is substituted into the previous solutions, the resulting equations can be written in the form where a, b, c, and tJ are constants and the R.. 1s are nonlinear functions of % and tf. This set of equations must be so-ved v for a, b, c and tf; this objective is accomplished by first estimating tf and 8, from the first two 82
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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
Page 21 and 22:
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
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This matrix is simply written as G(
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The fundamental matrix for A can be
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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
Page 41 and 42: cause a significant effect for rend
Page 43 and 44: Figure 2.1 Polar Coordinate System
Page 45 and 46: . 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: where 2((t) is given by the first e
Page 95 and 96: 3.0 RECOMMENDED PROCEDURES In the p
Page 97 and 98: For the guidance technique which nu
Page 99 and 100: 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13
Page 101: 4.20 Bakalyar, G., Continuous Thrus
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