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Conversion between quaternions and Euler angles
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<p><a href="/facts/Rotation_formalisms_in_three_dimensions/rpbqPMRw">Spatial rotations in three dimensions</a> can be <a href="/facts/Coordinate_system/Mtd0q4SP">parametrized</a> using both <a href="/facts/Euler_angles/pp30aAX5">Euler angles</a> and <a href="/facts/Quaternions_and_spatial_rotation/8rEnf5sG">unit quaternions</a>. This article explains how to convert between the two representations. Actually this simple use of "quaternions" was first presented by <a href="/facts/Leonhard_Euler/z2fsbjgj">Euler</a> some seventy years earlier than <a href="/facts/William_Rowan_Hamilton/U86CqUlt">Hamilton</a> to solve the problem of <a href="/facts/Magic_square/QGQkSKF2">magic squares</a>. For this reason the dynamics community commonly refers to quaternions in this application as "Euler parameters". </p>