# GM

Document Sample

```					EEC 641 / 741 Homework #1
An orbiting satellite can be modeled with the equations

  r 2   K / r 2
r

r  2r
where r is the distance between the satellite and the planet’s center of mass, and  is the
angular position of the satellite in its orbit. K=GM, where G=6.671011 m3/kg s2 is the
universal gravitational constant, and M=5.981024 kg is the mass of the Earth. Use
6370 km for the radius of the Earth.
1. Simulate the orbiting satellite for one circular orbit at an altitude of 200 miles. Plot r,
 , and their first derivatives.
2. Linearize the system around the circular orbit described above. What is the nominal
state trajectory?
3. Simulate the nonlinear equations and the linearized equations around the nominal
trajectory for one orbit, except that a sudden impulse of 10 microrad/sec is applied to
the angular rate of the satellite at the initial time. Plot r,  , and their first derivatives,
for both the nonlinear and the linearized simulations. Your plots should look
something like the following:

6
x 10                     nonlinear
7                                                200
linearized
6.9                                                     100
rdot

6.8                                                       0
r

6.7                                                     -100

6.6                                                     -200
0       2000     4000      6000                     0        2000     4000    6000

-3
x 10
8                                                 1.2

6
1.15
theta

4
1.1
2

0                                                1.05
0       2000      4000     6000                     0        2000      4000   6000
time (seconds)                                       time (seconds)

4. Repeat step 3 except for an initial impulse of 100 microrad/sec.
5. Hand in your plots, and your simulation source code (the source code should be one
file).

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 5 posted: 9/18/2012 language: English pages: 1
How are you planning on using Docstoc?