guidance, flight mechanics and trajectory optimization

More documents

Recommendations

Info

Finally, the solutions are expressed as To repeat,the boundary conditions at 8 = 0 are w = w. and are seen t: be satisfied. The final boundary or rendezvous conditions at 0 = Bf are (? = WT = (0, 0, 0, 0, 0, 0). 2.1.4.2.2 In-Plane Motion for Elliptical Target Orbits A technique for obtaining the solutions to the in-plane motion has been mentioned (Section 2.1.3) and references made to two papers by J. Tschauner (References 1.5 and 1.6). It is suggested that these papers be reviewed as required; the ability to obtain these solutions should allow a completely satisfactory representation of the problem of rendezvous with targets in elliptic orbits. 21
2.1.5 Approximate Second Order Solutions A solution to the equations of relative motion which includes both linear and quadratic terms in the gravity expansion and which is applicable to target orbits of small eccentricity is developed by Anthony and Sasaki in Refarencz 1.2. This work is essentially a combination'of the work of London (Reference 1.7) who examined the effect of including the quadratic term for circular target orbits, and that of deVries (Reference 1.8) who considered target orbits of small eccentricity, but included only linear terms in the gravity model. The equations of motion are given in terms of a rotating coordinate system centered at the target as in Figure 1.2. The equations before any approximations are made, were developed previously of motion, in time of non-dimensional variables as Equation (1.22). For convenience reproduced below-along with the definition of the non-dimension~ this set is variables. where and where the open dot superscript (e.g., 2 ) refers -to differentiation with respect to M. Expanding the nonlinear terms of the differential equations in powers of the coordinates and retaining linear and quadratic terms results in the set. (1.66) NOW, for orbits of small eccentricity, the variation of 8 and p with time (and ultimately with PI) can be written as a series expansion in the eccentricity, e,.g. 8 = /fZcz wdt-t*) 22 (1.67)
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 and 30: This matrix is simply written as G(
Page 31: The fundamental matrix for A can be
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
show all

guidance, flight mechanics and trajectory optimization

Create successful ePaper yourself

Delete template?

Save as template?