MAE142_L7_AngularRate.pdf - Angular Rates Euler Angular...

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Angular Rates Euler Angular Rate Complimentary Filtering MAE 142 NASA Image
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2 MAE 142 Rotational Rates in Body-Fixed Frame roll rate (p) pitch rate (q) yaw rate (r) z B y B x B
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3 MAE 142 Euler Angle Rates Recall that the Euler angles are defined by a sequential rotation order. The rate of change in Euler angles is NOT the same as the body-axis rotational rates! [ p q r ] = [ 1 0 0 0 cos sin 0 sin cos ] [ ˙ 0 0 ]  ⋯ [ 1 0 0 0 cos sin 0 sin cos ][ cos 0 sin 0 1 0 sin 0 cos ] [ 0 ˙ 0 ]  ⋯ [ 1 0 0 0 cos sin 0 sin cos ][ cos 0 sin 0 1 0 sin 0 cos ][ cos sin 0 sin cos 0 0 0 1 ] [ 0 0 ˙ ]
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4 MAE 142 Euler Differential Equations The Euler angle differential equations can be expressed in matrix/vector format. However, this matrix form does NOT represent an orthogonal transformation! [ p q r ] = [ 1 0 sin 0 cos sin cos 0 sin cos cos ][ ˙ ˙ ˙ ] [ ˙ ˙ ˙ ] = [ 1 sin tan cos tan 0 cos sin 0 sin / cos cos / cos ] [ p q r ]
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