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3

It depends a bit on what technology you’re referring to. The original inertial navigation systems used rotating gyroscopes. Those were and are expensive. Modern MEMS inertial navigation systems (example) don’t use rotating gyroscopes. Instead, they get both linear and angular acceleration (and angular rate) information from their MEMS accelerometer ...


5

If multiple accelerometers are spread around the vehicle, their readings can be combined to determine angular speed (from centripetal acceleration) and angular acceleration somewhat easily. There would probably need to be at least 4 or 5 to cover all the degrees of freedom, with one at the CG to cancel out linear acceleration. To calculate orientation from ...


1

The direction cosine matrix relating the orbit frame and an inertial frame is as followed. Essentially it is a 3-1-3 body-two rotation sequence. I talk about the DCM a little more in detail here (Calculate Argument of periapsis of orbit given focus and two points on ellipse). You will need to know all your orbital parameters in order to calculate this DCM ...


6

tl;dr During ISS assembly the station maneuvered more than it does these days. You are correct that the docked Shuttle / ISS stack maneuvered during the STS-115 mission. The planned attitudes for the last several Shuttle missions are available in the Attitude Timeline sections of their flightplans, published at the JSC FDF page. The STS-115 flight plan is ...


3

The explanation by Mefitico is along the right lines. The trick here is not to assume $u=0$. The thruster configuration can be chosen such that the kernal has all positive components. Then $u$ is selected to guarentee a positive solution, see SanchezPena,R.S.and Alonso,R.andAnigstein,P.A.: Robust Optimal Solution to the Attitude/Force Control Problem, IEEE ...


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