7.45 The dynamic equations of motion for a station-keeping satellite (such as a weather satellite) are *- 20ý – 3ux = 0, + 2wk = 4, where x = radial perturbation, y = longitudinal position perturbation, u = engine thrust in the y-direction, as depicted in Fig. 7.95. If the orbit is synchronous with the earth's rotation, then o = 27 /(3600 x 24) rad/sec. Problems 625 Figure 7.95 Diagram of a station-keeping satellite in orbit for Reference longitude Desired location Problem 7.45 on orbit

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7.45 The dynamic equations of motion for a station-keeping satellite (such as
a weather satellite) are
* - 2wj – 3wx = 0, y+ 2wx = u,
where
x = radial perturbation,
y = longitudinal position perturbation,
u= engine thrust in the y-direction,
as depicted in Fig. 7.95. If the orbit is synchronous with the earth's
rotation, then o = 27/(3600 x 24) rad/sec.
Problems 625
Figure 7.95
Diagram of a
station-keeping
satellite in orbit for
Reference
longitude
Desired
location
Problem 7.45
on orbit
(a) Is the state x = [ x *yyFobservable?
(b) Choose x = [ x x y ylas the state vector and y as the
Transcribed Image Text:7.45 The dynamic equations of motion for a station-keeping satellite (such as a weather satellite) are * - 2wj – 3wx = 0, y+ 2wx = u, where x = radial perturbation, y = longitudinal position perturbation, u= engine thrust in the y-direction, as depicted in Fig. 7.95. If the orbit is synchronous with the earth's rotation, then o = 27/(3600 x 24) rad/sec. Problems 625 Figure 7.95 Diagram of a station-keeping satellite in orbit for Reference longitude Desired location Problem 7.45 on orbit (a) Is the state x = [ x *yyFobservable? (b) Choose x = [ x x y ylas the state vector and y as the
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