About: Conversion between quaternions and Euler angles   Sponge Permalink

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Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article explains how to convert between the two representations. Actually this simple use of "quaternions" was first presented by Euler some seventy years earlier than Hamilton to solve the problem of "magic squares." For this reason the dynamics community commonly refers to quaternions in this application as "Euler parameters". A unit quaternion can be described as: where is a simple rotation angle and , , are the "direction cosines" locating the axis of rotation (Euler's Theorem).

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  • Conversion between quaternions and Euler angles
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  • Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article explains how to convert between the two representations. Actually this simple use of "quaternions" was first presented by Euler some seventy years earlier than Hamilton to solve the problem of "magic squares." For this reason the dynamics community commonly refers to quaternions in this application as "Euler parameters". A unit quaternion can be described as: where is a simple rotation angle and , , are the "direction cosines" locating the axis of rotation (Euler's Theorem).
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abstract
  • Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article explains how to convert between the two representations. Actually this simple use of "quaternions" was first presented by Euler some seventy years earlier than Hamilton to solve the problem of "magic squares." For this reason the dynamics community commonly refers to quaternions in this application as "Euler parameters". A unit quaternion can be described as: where is a simple rotation angle and , , are the "direction cosines" locating the axis of rotation (Euler's Theorem). Similarly for Euler angles, we use (in terms of flight dynamics): * Roll - : rotation about the X-axis * Pitch - : rotation about the Y-axis * Yaw - : rotation about the Z-axis where the X-axis points forward, Y-axis to the right and Z-axis downward and in the example to follow the rotation occurs in the order yaw, pitch, roll (about body-fixed axes).
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