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hw01_FA05 - NS that represents a sequence of two rotations...

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R.G. Melton AERSP 309 HW #1 Fall 2005 (Due Friday Sept. 9 at beginning of class) 1. The onboard computer for a satellite must keep track of how the satellite is oriented relative to the stars (i.e., how the satellite’s body-fixed coordinate system B is oriented wrt the inertial or Newtonian system N ). The satellite needs to transmit this information frequently to Earth; to reduce the amount of data transmitted, the satellite can transmit just part of the DCM C NB and the ground station then reconstructs the entire matrix by using the special properties of DCM’s. To see how this works, find the values of the missing elements in C NB : = 9412 . 0 2569 . 0 7321 . 0 2195 . 0 5916 . 0 7758 . 0 NB C 2. Develop an expression for the DCM C
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Unformatted text preview: NS that represents a sequence of two rotations: a. a copy of the n set is rotated about by an angle α to produce set 2 ˆ n c . b. then a copy of the c set is rotated about by an angle ε to produce set 3 ˆ c s . 3. Using the data in problem 1, find the angle between the satellite’s 2-axis and the 2 ˆ b Newtonian 3-axis at the time that these data were transmitted. 3 ˆ n 4. Show that for a sequence of infinitesimal rotations d θ about the 1-axis and d φ about the 3-axis, the final DCM is independent of the rotational order. Hint: use small-angle approximations for sin and cos. Remember that the product of two infinitesimal quantities → 0....
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