The location of a vehicle is described by its longitude A from Greenwich, its la
ID: 1884406 • Letter: T
Question
The location of a vehicle is described by its longitude A from Greenwich, its latitude 8, and its altitude H above the surface of the earth as shown in Figure 3. Of course, the earth itself rotates at angular velocity Oe about its polar axis. A coordinate frame s has its origin at the center of the earth, with the si vector in the plane of the equator, the s2 vector pointing at the vehicle and s3 completing the right handed set. Obtain an expression for the inertial velocity of the vehicle. s3 S2Explanation / Answer
given lambda = longitude
del = latitude
altitude = H
angular speed of earth = we
hence in the fram eof reference given
the locatino of the vehicle is given by
in the frame of reference where earth is at rest ( ibnertial frame)
location
r = (Re + H)cos(del)cos(lambda)i + (Re + H)cos(del)sin(lambda)j + (Re + H)sin(del)k
then
v = r' = [[H']cos(del)cos(lambda) - [Re + H]sin(del)cos(lambda)*del' - [Re + H]cos(del)sin(lambda)lambda' ]i + [[H']cos(del)sin(lambda) - [Re + H]sin(del)sin(lambda)del' + [Re + H]sin(del)sin(lambda)lambda']j + [[H']sin(del) + [Re + H]*cos(del)del']k
here H' is rate of chance of altitude of satellite in s2 direction
del' = rate of change of latitude of satellite
lambda' = rate of change of longitude
if non inertial angular speed of craft in this direction is w2, then lambda' = w2 - we
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