Euler Angles. Three Angles  A rotation matrix can be described with three free parameters. Select three separate rotations about body axesSelect three.

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Presentation transcript:

Euler Angles

Three Angles  A rotation matrix can be described with three free parameters. Select three separate rotations about body axesSelect three separate rotations about body axes 1) Rotation of  about e 3 axis. 2) Rotation of  about e 1 axis. 3) Rotation of  about e 3 axis.  These are the Euler angles. e1e1 e2e2 e3e3   

Euler Matrices  Any vector z can be rotated though the Euler angles.  Equivalent matrix operation is the product of three separate operations.

Full Rotation  Any rotation is then expressed with the three angles.

Matching Terms  The terms in the  matrix correspond to the components of the angular velocity vector.  The relationship between angular velocity and Euler angles comes from the S matrix.

Body Frame  The angular velocity in the body frame can be expressed in terms of Euler angles. x1x1 x2x2 x3x3