guidance, flight mechanics and trajectory optimization

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The set of differential equations is now written as W’ = Awtf where the transformation from the position <strong>and</strong> velocity differences
The fundamental matrix for A can be written at once as 10 0 0 .O 0 8 1 0 0 0 0 0 0 cos 8 Sin 8 0 0 F(0) = 1 0 0 -Sin 8 cos 0 0 0 for which the inverse is 0 0 0 0 cos 8 Sin 8 0 0 0 0 -Sin 8 cos 0 F-‘(e) = F(4) The solutions to the equations can now be written in the form In this case, the matrix G(0 - Go) = F(B) FD1(Qo) is easily seen to be - 1.60 1.61 GM-8,) = F&J-q) 1.62 Note that F(Oj = F-l(e) = I. In fact, since no loss of generality occurs by choosing 0, = 0, this value will be assumed for the remainder of this section. The six integrals in the solution for w (0) (called "Z"> will be: 2, = s 0 8 u2 d-r e I- = J (73 f32y)d7- 0 1.63
Page 1 and 2: NASA CONTRA REPORT CTOR GUIDANCE, F
Page 3 and 4: - ..a --.
Page 5 and 6: _- .-- --- I
Page 8: 110 2.1 2.1.1 2.1.2 2.1.3 2.1.3.1 2
Page 11 and 12: . 0 i time difference between a ref
Page 13 and 14: only line-of-sight thrusting is use
Page 15 and 16: 2.0 STATE-OF-THE-ART The significan
Page 17 and 18: Thus in cylindrical coordinates, th
Page 19 and 20: In this form the equations are vali
Page 21 and 22: For all the equations given to this
Page 23 and 24: of inertial directions which are ta
Page 25 and 26: which form the columns of F must be
Page 27 and 28: Thus, the solution is written The t
Page 29: This matrix is simply written as G(
Page 33 and 34: 2.1.5 Approximate Second Order Solu
Page 35: where the superscript p can be eith
Page 39 and 40: 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 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 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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