Question: 5 Given $ 100 deg/s = Q = 45 deg y = 360 deg * = 10 deg/s + = 10 deg/s 0 =
5 Given $ 100 deg/s = Q = 45 deg y = 360 deg * = 10 deg/s + = 10 deg/s 0 = 5 deg Find the body axis roll, pitch, and yaw rates using the kinematic equations.
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The angular velocities in body axis frames are related to the angular velocities in Earth axis frames via the following set of kinematic equations rollrate p tanlatitude q cosheading r sinheading pitchrate q coslatitude r sinlatitude yawrate q sinheading coslatitude r cosheading coslatitude In this problem latitude is equal to 45 degrees heading is 10 degrees and bank angle is 5 degrees Lets first find the equivalent quaternion derivatives corresponding to the given angular rates p 100 degsec q 10 degsec r 0 degsec Quaternion conversion 100 deg qw cos2 cos1002 06428 10 deg qx sin2 sin102 01736 45 deg qy sin2 sin452 05 10 deg qz sin2 sin102 00872 dqwdt 05 qx p qy q qz r 05 01736 100 05 10 945 dqxdt 05 qw p qy r qz q 05 06428 100 05 0 3211 dqydt 05 qw q qx r qz p 05 06428 10 01736 0 00872 100 0 dqzdt 05 qw r qx q qy p 05 06428 0 01736 10 05 100 4731 Now we will express dqwdt dqxdt dqydt and dqzdt in terms of degsec and plug in the values to find the roll pitch and yaw rates in the body axis frame ... View full answer
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